Thursday, May 23, 2013

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.

Tuesday, May 21, 2013

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.)

Tuesday, May 14, 2013

Prime Time with Magicicada!

That’s right folks. We have a very special guest with us this summer: the 17-year periodical cicadas!

All rights to Wikipedia something something.
Tell us a little about yourselves.

Zeeeeee Tick Zeeeeee Tick (Warning: offensive)

Fascinating. So, some interesting factoids about cicadas of which I was previously unaware: When the 13- and 17-year cycle cicadas are underground, they’re still alive, feeding off the root systems of trees. Also, they remain in an immature, but mostly anatomically complete state the entire time—just like humans.

There are plenty of other cicadas out there, but only eastern North America has the famed 13- and 17-year broods. The genus of which these several cicada species are a part is known as Magicicada, which near as I can tell means magic tree cricket.

Anywho, as far as I’m concerned the most interesting fact about cicadas is that their cycles correspond to prime numbers. I’m not the only person who finds this interesting, and there have been a number of studies investigating this rather curious phenomenon.

So what’s the verdict? The best current hypothesis is that it’s a confluence of three separate factors: predator satiation, the last ice age, and hybridization.

The first factor is a common adaptation not unique to the periodical cicadas. As the name implies, the trait involves satisfying the hunger of those that wish to eat you. The gist is that if every single cicada emerges and breeds at the same time, then there are only so many predators that can eat said cicadas, and the vast majority won’t be eaten. If they came out piecemeal throughout the year or over the years, then their predators would have time to get hungry again, and their survival rate would go down.

Okay, so that accounts for why they all come out at once, but it doesn’t account for why they have such long cycles. This is where the ice age factor comes in. Cicadas are used to the nice warm temperatures underground and they’re only able to fly around and mate when the surface temperature is similarly suitable. So they wait until the soil temperature has reached a comfortable 63 °F and then erupt from the ground en masse.

But during glacial periods there is no guarantee that the temperature will stay that high for the 3 or 4 weeks cicadas need to successfully reproduce. What this means is that when the cicadas decide to come out, they’re taking a gamble. If the temperature drops too low during their emergence, then the brood dies off without reproducing. So the best bet is to hold off and only emerge every decade or two, reducing the odds that they hit a cold spell.

(This might seem specious, because you’d think that (ideally) one summer’s temperatures are not correlated with another’s, so no matter when you pop your head above the soil, there’s an equal chance it ends up not being warm enough to breed. More on this later.)

Now we need the final piece of the puzzle: prime numbers. What could possibly account for the appearance of prime numbers in insect reproductive cycles? It turns out the answer is hybridization. Say you’ve got your cicadas emerging en masse every decade or so. There are separate broods of cicadas emerging at different intervals, which means that every once in a while broods will come out at the same time. When that happens, they will interbreed, and the resultant brood will be hybridized.

If this different mix of genes changes the length of the cicada life cycle, the effect is to smear out the arrival times of the cicadas. This smearing out, however, reduces the population density of cicadas on any given summer, which reduces the effectiveness of the predator satiation strategy, which ultimately reduces the number of cicadas that get to breed. So hybridization is a bad strategy. The best strategy is to make sure there is as little overlap as possible in the cycles of various cicada broods.

For example, if you have one brood on a 4-year cycle and another brood on a 16-year cycle, there’s going to be a lot of overlap because 4 is a factor of 16. So we want cycles with few or preferably no factors. We want prime numbers.

I think it’s important to point out here that a lot of talk about evolutionary strategies can be quite misleading. It sounds as if a species is getting together and deciding the best way to reproduce and then carrying out that plan. But that’s not what is happening. In fact, if that were happening, very different reproductive strategies would emerge.

If cicadas wanted to get together and come up with the best strategy, they might decide to evolve faster flight and the ability to survive warmer temperatures. But they’re not given that choice. Species don’t decide what mutations they get. They are stuck with what nature selects for them.

To see how this works out, imagine there are dozens of different cicada broods with a variety of different cycle lengths and patterns of reproduction. If some broods emerge piecemeal and others as one, we know that due to predator satiation, the broods emerging together are more likely to breed. Thus, over a long enough period of time, we’re not going to see the piecemeal broods anymore because they will have been selected against.

So now we have broods that emerge in unison but do so at varying intervals. The question we have to ask ourselves again is, after a very long time, which broods are we most likely to see? We could see the broods that emerge every year or those that emerge every 20 years. Both broods might have their luck run out after 50 cycles, but that corresponds to 50 years for the first batch and 1000 years for the second batch. So after a long enough period of time, we’re only going to see the 20-year broods. This isn’t a strategy; it’s a consequence.

Now we’re left with only long-period cicadas. Again, the cicadas don’t choose to make their cycles prime numbers. What we see isn’t a choice; it’s statistics. Because prime-numbered cycles correspond to higher reproductive fitness, after a long enough period of time non-prime-numbered cycles die off, and the end result is that we only see those cycles that survived for thousands of years. We see those cicadas that breed all at once on large prime number cycles.

Sorry, no physics in this post, just stamp collecting. I really am going to follow up on the lawnmower post at some point. Really.

Monday, May 13, 2013


I’m still going to do a post about transferring energy from gasoline to lawnmower blades, but a thought occurred to me while I was obsessively rereading my last post that I think might make for a good post in and of itself.

I’ve got a copy of The Way Things Work on my bookcase, and sitting right beside it is a copy of The New Way Things Work. I gobbled up the former book as a kid; it was my first introduction to the idea that electrons release photons whenever they jump down shells, to the concept of computer logic gates, how fission and fusion work, and a whole host of other scientific ideas. I know the book is primarily about machines, but for some reason it was the microscopic stuff that stuck with me more than the mechanical bits.

Anywho, there’s a page about transformers in the book, and I still remember thinking when I read it that transformers were somehow cheating.

You're the man, David Macaulay. Seriously.
You wrap wire around a magnet, wrap more wire around the other end of the magnet, and voila, you’ve increased the electricity pumping through the wire. So why is energy in such short supply? Are there not enough magnets?

I didn’t have a clear understanding of what the conservation of energy meant as a kid (and it can certainly be argued that I don’t now, either, given that I have no idea how Noether’s theorem about symmetry leads to conservation laws), but it still struck me as somehow wrong. And it struck me as wrong for a very long time, right up until about this semester, when I learned what a transformer is really doing.

I think this speaks to the fact that we (the general public) have a very fuzzy idea of what energy is. We know that climbing an electric fence that says “DANGER: 10,000 VOLTS”...

Please don't sue me, Steven Spielberg. somehow more dangerous than licking a 9-volt battery. We also know that “it’s not the voltage that kills you; it’s the amperage.” So both of these are somehow electrical quantities that correspond to bigger and more powerful, but are they related to energy? Related, yes, but they aren’t synonymous with energy.

It turns out that a volt is a measure of energy per charge. You can think of it as the amount of pressure an electron is under. An amp, on the other hand, is the amount of charge moving past some point per second. If you multiply these two quantities together, the charge cancels out and you get energy per second. This quantity is known as the watt, which most people recognize as being what the power company delivers.

But more importantly, this gives us a way to measure energy over time. Because energy is conserved, we know that the amount of energy pumped into a transformer must be equal to the amount of energy pumped out (assuming some ideal transformer with no real world problems). What a transformer does, however, is increase the voltage of the current flowing through it. That is to say, it increases the amount of energy packed into each charge. In order to ensure that the same amount of energy passes through a transformer, less charge must flow out.

(It’s also true, however, that charge is a conserved quantity, so you might think just as much charge has to come out as goes in. But that’s not what conservation really means. It just means that the amount of charge does not change with time; it says nothing of where that charge must go. What’s really happening is that electrons go into the transformer, dump their energy into the transformer’s magnetic field, and then circle back to wherever they came from. The energy they dumped into the magnetic field, however, is then transferred to new electrons at the other end of the transformer. The number of electrons never changes, and the amount of energy never changes, but there are fewer electrons coming out one end than going in the other.)

Say we have a current carrying 1 watt of power at 1 volt and 1 ampere through a transformer. After 1 second, 1 watt pumps 1 joule of energy into the transformer. Then we turn the current off. We expect that 1 joule is going to come out of the transformer a second later. If the transformer increases the voltage of the current to 10 volts, then we have 10 joules per coulomb coming out of the transformer. But since we only have 1 joule to begin with, this means we can only send out 1/10 of a coulomb of charge. Our transformer, then, has turned our 1 volt, 1 ampere current into a 10 volt, 0.1 ampere current. The power is still 1 watt, however, which means that the amount of energy delivered over time is constant.

As the title of the post says, there ain’t no such thing as a free lunch. Transformers don’t cheat; they just do some clever bookkeeping. (I’ve tried to imagine a mechanical analog to a transformer but haven’t been able to come up with anything that doesn’t seem tortured and contrived. Perhaps this is one of the places where the world of electricity and magnetism doesn’t mirror the real world, or perhaps I’m simply having a failure of imagination.)

Until next time, folks.

Monday, May 6, 2013

On the Physical Principles of Graminoid Elimination

On Facebook this past Saturday I commented that I had “mastered E&M and multivariable calculus, but can’t seem to figure out how to start a lawnmower.” Leaving aside the image of a pasty nerd being carried off by an out of control garden tool, I think it’s interesting that the relatively basic physics introduction I’ve been given over the past two semesters is sufficient to explain almost completely how a lawnmower works. So I’m going to share that neatness with my dear and devoted reader(s).

It starts with the starter cord (no surprises there). Pulling the cord almost literally spins the engine’s crankshaft into motion. The crankshaft pulls the piston, which lets fuel and air into the cylinder. The crank continues to turn, the piston compresses the mixture and then, well, then Faraday’s law happens.

There are some chemicals that ignite on contact with air. There are other chemicals that ignite when they are compressed to any degree. Gasoline is not one of those chemicals. Gas is volatile, but not too volatile, which makes it a good method of storing energy. In order to get energy out of gas, you have to mix it with air, compress it, and then raise its temperature all at once.

I don’t want to get too much into the process of combustion, partly because that’s more chemistry than physics, and partly because I don’t understand it very well. But the very basic principle is something Dr. Dave Goldberg explained to me a few years ago when I asked why matter and anti-matter annihilate. His answer: because they can. Essentially, because matter and anti-matter are oppositely charged, it’s very easy for them to disappear and be replaced by electrically neutral photons with the same amount of energy.

The same principle applies to combustion. Oxygen doesn’t have enough electrons, and gasoline has electrons to give. So when you mix the two together, gasoline gives up electrons, breaks down into simpler compounds, and releases energy, because it can. That energy heats and expands the mixture, pushing the piston out and turning the crankshaft, which subsequently turns the lawnmower’s blade.

Why this releases energy is complicated. The simple explanation is that more energy is stored in the system than it takes to release that energy. The usual analogy is to a ball sitting at the top of a hill. When you kick a ball, you transfer kinetic energy from your foot to the ball, and the ball moves away from you until that kinetic energy has been lost to friction and air resistance.

But if you kick a ball so that it rolls down a hill, the energy you provide is enough to “release” the gravitational potential energy stored in the ball, so that by the time it gets to the bottom of the hill it has way more kinetic energy than you provided from your foot alone. So gasoline, because of its structure (yes, that’s a copout), has a lot of potential energy just waiting to be released if you give it a big enough push.

The key is that gasoline is less likely to give up the electrons that form its chemical structure than it is to give up the electrons that bond one molecule of gas to another, so you need more energy to get at those deeper electrons. This energy is provided in the form of a spark that raises the temperature of the mixture.

Where does the spark come from? The spark plug, of course. A spark plug is essentially just a capacitor that is designed to fail. As I explained a couple posts back, charging a capacitor creates an electric field. If the electric field gets too strong, the insulating material between the capacitor plates ionizes. That is, its electrons are stripped away, which turns it into a conductor, causing all those stored electrons in the capacitor to flood across the gap at high speed, producing lightning. This lightning is a spark. But where does a tiny gas-powered lawnmower get the necessary voltage to produce lightning?

This guy:

Courtesy Wikipedia

Lawnmowers use a device known as a magneto. As the engine spins, it rotates a permanent magnet inside a coil of wire. This changing magnetic field induces a current in the coil. But with every turn of the engine, that current is interrupted by a contact breaker, so the current drops down to zero.

Or it would, if it weren’t running through a coil of wire. This coil acts like an inductor, and inductors create electromagnetic fields whose strength is determined by how quickly the local electromagnetic field is changing. So even if there is only a very small current through an inductor, if that current is immediately cut off then the change in current is very large, which in turn produces a very strong electromagnetic field.

But we're not done there. After the magneto comes this:

What would I do without you, Wikipedia?

There’s a second stage, a transformer, which increases the voltage even more, enough to induce a spark in the spark plug. The other pole of the permanent magnet has its own set of wires coiled about it, but it has far more windings than the first set. When the magnetic field produced by the inductor changes due to the broken contact, this induces an electric field in the secondary coil.

But the interesting thing about Faraday’s law is that it talks about changing magnetic flux rather than just a changing magnetic field. Flux is the flow of magnetic field lines through an area. The larger the area, the greater the flux. And the area we’re dealing with here is the circle formed by a loop of wire. But if you have a hundred loops of wire, you have a hundred times the area as far as Faraday’s law is concerned, which means the voltage induced is a hundred times larger.

So by exploiting Faraday’s law to create a rapidly changing magnetic field through a very large area, pulling on a starter cord can induce a large enough voltage to create lightning, which ignites the fuel in the lawnmower’s engine. Pretty cool.

I also wanted to look at converting the chemical energy of gasoline into the rotational energy of the lawnmower blade, but I think this post is long enough already. So tune in next time and there might be a discussion of energy density, thermodynamics, and angular momentum.

Friday, May 3, 2013

Out of Phase

With the semester winding down, I think it’s a good time to discuss a slightly annoying idiosyncrasy I’ve observed this spring. E&M has, as a co-requisite, vector calculus. My school expects these two classes to be taken together, and E&M involves a fair amount of vector calc. But despite this connection, or perhaps because of it, my math and physics have been, you might say, out of phase.

What do I mean by out of phase? I think a thousand words can sum it up best…

As you can see here, Lt. Cmdr. Geordi La Forge’s hand is out of phase with the engineering console. They’re in the same place at the same time, and yet somehow they’re not actually interacting. The solution, of course, is a concentrated burst of anyons. Yep.

Or maybe I mean something a little more like this:

We just got through a unit on AC circuits, which are significantly more complex (heh) than DC circuits. The main reason is that the three basic elements of a circuit all respond differently to alternating current. Resistors don’t much care. They reduce the voltage across them, but (ideally) their response isn’t dependent on the incoming voltage. Thus, the voltage across a resistor looks like whatever current is coming from the AC source.

A capacitor, on the other hand, has its maximum voltage when it’s fully charged. And when it’s fully charged, the current across it is zero. Thus, the voltage across a capacitor is at its peak when the blue line crosses zero.

And inductors resist changes in current, which means an inductor will always have a voltage that is positive when the source is decreasing, and negative when the source is increasing.

Why did I go through all of that? Well, for two reasons. First, the differences between those circuits give rise to the different voltage graphs above, and those differences are known as phase shifts. Resistors are “in phase” with their voltage source, whereas inductors and capacitors are “out of phase.” That is, they don’t line up.

When two waves that are in phase with each other combine, they produce one wave that is bigger than either of the two waves. Conversely, out of phase waves that hit cancel each other out. This is known as interference, and maximizing the acoustics of a room is all about making sure sound waves are in phase when they get to the audience.

Secondly, a complete description of the wave-like behavior of AC circuits involves complex numbers—the square roots of negative numbers—a topic which has only been given the briefest of overviews in any math class I’ve ever taken. Consequently, the entirety of the complex aspect of AC circuits was covered in a single line from my professor: “And if we increase this factor over here, you see that we get imaginary numbers.” So, you see, my math and physics classes are out of phase.

But it doesn’t stop there. Near the beginning of the semester, we learned that the electric field can be thought of as the change in voltage across space. The text and our professor briefly mentioned that this is referred to as a gradient and involves partial derivatives. But at that moment in math, we were learning how to plot three-dimensional vectors.

Later on, we learned about Gauss’ law for electricity, which lets you figure out the amount of charge enclosed by a surface if you know what the electric fields coming out of that surface look like (and vice versa). When you first learn how to use Gauss’ law, you’re only asked to apply it to surfaces that are highly symmetric, which makes the math a lot easier. But it turns out that Gauss’ law is a very general principle in vector calculus involving surface integrals. And what, pray tell, were we learning about in math at that moment? Partial derivatives, of course.

Now, as the semester draws to a close, our professor has shown us Maxwell’s equations in all their glory. All their integral glory, anyhow. We’ve seen them in one form or another already, and we’ve used three of them. The one we haven’t used is Gauss’ law for magnetism, which is like the electricity law except it says there’s no such thing as magnetic charge and there’s never any net flow of magnetic field lines through a surface. Why is there a law saying the answer to your question is no? Because, our professor explained, the law is more useful in its differential form, where it uses a vector calculus principle known as divergence. We’ll be getting to divergence next week in math. Right now we’re studying surface integrals.

Maybe I'm misinterpreting all this. Maybe learning about the idea in physics first primes us for the material in math later. But I'm not sure I buy that argument. I feel as if we'd be better served by having to take vector calculus first, or by having E&M and calculus classes that were more, well, in phase with each other.

Anywho, so when are we going to learn the math behind complex numbers and phases? Apparently it involves phasor arithmetic and phasor diagrams. I don't know about you, but I encountered phasor diagrams waaaay before I started taking math classes...