Roundabout Math, Day 2

Note: For organization's sake, I decided that I would go with the original plan of finishing up this post today, even though I am deeply boggled by something else altogether. (You can skip to the end if you don't care for the math talk.)

-------------------

If you're just tuning in, perhaps you would want to start with yesterday's entry, but basically we are trying to break down the math about roundabouts ("traffic circles"). We left off after having intuited that the maximum velocity of a car should depend on the curvature of the road (ie. radius of the roundabout), and I brought in an external piece of information for calculating that max velocity. Now, onwards!

7. Besides the curvature of the road, what else limits the speed of your car as it actually drives through a roundabout? (Crowdedness, obviously.)

At this point, you could start a guided discussion with the kids about how we might mathematically represent the "crowdedness" of an intersection. My personal feeling about this is that, for high-schoolers, we should use a simple metric, such as what percent of the road is covered with cars? The kids can then go out to the parking lot and measure an average car's length and width, and use it to estimate how many cars can maximally fit into a given roundabout. If there are roundabouts in your neighborhood, now would be a good time to introduce the artifact (aerial photo?) and its dimensions.


8. So, the kids can create a graph that looks like one (or both) of the following, depending on what metric they use for modeling the crowdedness. (If you click on the graphs, they'll open up in another window and make it easier to read.)


In either case, the kids will have to do some geometric calculation in order to figure out the translation between the number of cars and the percent of road crowdedness. I am thinking of something in the neighborhood of:


(Notice that the "drivable area of a roundabout" is no more than finding the area of the ring, with radii r1 and r2 as given in the previous photo.)

9. If we assume -- kind of a big assumption here, but, what the hay -- that the crowdedness linearly impacts the actual speed at which a car can travel, then in theory, by knowing how many cars are in the intersection at any given time, we can construct the average speed of a car and calculate how long it would take for a car to get through the intersection. So, at this point, you can introduce some data that looks like this:

Note that this is a rough sketch of the type of data you would want to provide. You probably want to modify the table to show that at some point during the day, the traffic circle reaches its max capacity.

10. And then, you should be able to ask your kids some relevant questions!

• Assuming that you come to this roundabout three times a day: at 7am, 12pm, and again at 6pm. There is always a 3-second delay as you approach the roundabout and come to a stop, hoping to merge into the traffic. Assuming that you're extremely lucky and are the first person in line waiting at the intersection to enter the roundabout, how long would it be until you go through the roundabout to the other side?



• Assuming now that you come to this same roundabout at 5pm the next day, but find yourself to be the 10th person in line waiting to enter the roundabout. How long would it be until you go through to the other side?



• Assuming that you are considering building a "regular" intersection that is as big as your roundabout, and each full traffic light rotation is 2 minutes. The posted speed limit is 50 kilometers/hour. Estimate the max, average, and least amount of time it would take for your car to go through the intersection, if you are the first in line waiting at the light.



• Explain whether this wait time changes dramatically if you are the 10th car in line at the light.



• Why do people sometimes build roundabouts that also USE traffic lights? What advantage(s) might there be to this hybrid approach?

...In the end, I am still not at all happy with my organization of this as a potential topic for teaching. Even though I think the problem is inherently interesting, there are way too many variables even when it is broken down like this. So, I am going to leave it at that. If you can think of a way to pare down some of the variables further while still keeping the juicier, intuitive parts intact, please - feel free to give me your thoughts! Otherwise, I hope this had been a worthwhile read for you, to follow my venture to nowhere.

-------------------

In the mean time, I will go back to grieving/seething over this bit of local news. I have read parts of the original Spanish article, and it is even more heart-breaking than what Tim has already summarized. The family has 7 children, and because the dad only earns $4 a week driving sand trucks, he cannot afford to feed all 7 of the kids. He actually insisted on making tortillas out of the seed corn, even though his wife had reminded him that there was poison (insecticide) on them. He had told her to just wash the corn well, to get rid of the insecticide. In the end, only two of his seven children were not intoxicated, possibly because even with the tortillas made from the seed corn, there was still not enough food to go around at home. The Spanish article also has a picture of his two kids that died, a 10-year-old and a 12-year-old. Truly, truly devastating.

Needless to say, it horrifies me to read about this. The Salvadorean government does little to help the extreme poverty that they know to exist right on their doorsteps. ugh.

Not-so-good Recent Happenings in El Salvador

Yesterday saw the declaration of another Alerta Naranja -- an Orange Alert for possible landslides as a result of the recent rain. It is worrisome, because we are only two months into the rainy season, which is supposed to last through October. The heavy rains do not affect Geoff and me, fortunately, because we live in well-insulated concrete areas of the capital city. But, everywhere else, things are awful when it rains. Most Salvadoreans live in huts built with mud walls, at the foot of deforested hills. :( In this most recent bout of rain, the restaurant that Ali's boyfriend helps to run down by the beach had collapsed. Its original base of rocks, sand, and silt had been entirely washed away by the river, and before his family can rebuild the restaurant, they will need to first fill the base with rocks and concrete...

In other news, while I was still in China, I read a news article about a bus that was set aflame by gangsters in El Salvador. 16 people were trapped inside that bus and burned to death. It's deeply horrifying and sad. --Will justice be served? I hope so, but I wouldn't hold my breath. Some suspects have been arrested*, but the prison/judicial system here is so lousy that there is really no guarantee what fate they will receive.

*By the way, Geoff heard that the reason why cops wear masks when they make arrests in El Salvador is so that they cannot become the target of a counterattack of vengeance. I don't know if this explanation is true, but you can see in the pictures from XinHua that they are indeed wearing the famed masks.

...Maybe some day, the conditions in El Salvador will improve. Sadly, if that day does ever arrive, it will take a really, really long time. In the meanwhile, the disparity between the have's and the have-not's is heart-rending, and the plight of the poor continues unabated.

Oktoberfest, El Centro

Geoff and I have had a few very uneventful weekends, because I've had to catch up on work before the quarter ends. By this weekend, both of us were going stir-crazy and wanting to go away somewhere for the weekend. But, we had promised our friend Andrea that we would go to her Oktoberfest party, so we decided to stick around the city...

We decided, instead, to make the best out of Andrea's party. We went and bought a ton of beers (a mix of cheap and nice beers), bought two giant beer mugs, got some plastic cups for beer pong, and made jello shots! Andrea's party turned out to be totally fun, even though the Americans mostly turned in somewhat early. We ended up partying with her Salvadorean friends, plus Jon, after everyone else had left. We taught the Salvadorean girls how to play flip cup and beer pong, and they taught us how to play Vikingo and Marcas. And we silly-danced. It was pretty awesome times. :)

------------------------

One thing we did try to do this weekend was to go down to El Centro to visit the Palacio Nacional, the Catedral Metropolitana, and the Teatro Nacional, which are all on the same block in El Centro. We got inside the cathedral, and it was pretty neat, but both the National Palace and the National Theatre were closed to visitors. What a shame! We were also warned by our taxi driver to not walk around past the 2 block-by-3 block area, since El Centro is not at all a safe barrio. Anyway, the cab driver said we'd be OK if we stayed around the very bustling parts of town, so we didn't press our luck. We left pretty soon after visiting the cathedral, since I wasn't feeling very safe. Afterwards, Geoff said that he felt like people were giving him pretty unfriendly vibes. I am not sure whether I had felt the same, but it was definitely a very impoverished part of the city. As soon as we had gotten out of the cab, a waft of something in the air had told me that there were homeless people nearby; and sure enough, you could see them every few feet, huddled next to a building or holding out their hands to beg for money. According to things I've read on the internet, El Centro suffers from a lot of street violence, and isn't really safe to visit at any hour.

Generally speaking, I'm feeling a little frustrated by the security situation here. Some days, it seems like we cannot really go anywhere. Even on our way down to a popular bar one night (La Luna Arte y Casa), a kid jumped out in front of our taxi cab in an attempt to stop us -- probably for no good. The cab driver eventually drove around the kid, and the cop car behind us picked up the kid and took him down to the station, but it's hard to say that we're going to keep being so lucky.

-------------------------

Anyway, the first quarter is already over! Can you believe it?

I need a break. We've only had one long weekend since the school started. The next 3-day weekend will be the weekend of Halloween. I cannot wait!

A History of Poverty

To help understand why things are the way they are down here, I think we need to talk briefly about the recent history of El Salvador. Some of this information I gathered from various readings on the internet; others came from word-of-mouth (ie. from talking to my principal, who has lived here for 3+ years).

In El Salvador, for many generations the country had no middle class. There were the land-owning elite, namely "the 14 families", who literally divided the entire country into 14 gigantic jigsaw pieces (after driving out the native Indians), and those who were landless and impoverished. To give an idea of how far-reaching the wealth is of those elite families, my principal pointed to the giant volcano that backdrops the city of San Salvador, and said that two-thirds of that mountain is still owned by a single board member of our school today! All of that land teems with coffee plantations, and one can only imagine how much money is associated with that volume of production.

As with any sort of wealth disparity comes social unrest. The country divided itself over time into two parties -- the same two parties that still exist today -- the Republican party, or ARENA, and the Socialist party, or FMLN. Locals simply refer to the latter as Frente, which literally means "Front" and refers to the idea that the FMLN came about as a coalition of smaller populist parties. Over time, both parties began to use violence -- torture, rape, and killings -- to further their cause, and by the late 1970s, the situation had boiled over to a full-blown Civil War.

Because the landless Salvadoreans were sympathizers of Fidel Castro and because this period in Salvadorean history corresponded in timeline to the U.S. fear of the spread of Communism, the U.S. administrations from Carter to Bush Sr. gave a total of 7 billion dollars in aid to El Salvador in support of the ruling elite. Sadly, since this choosing of sides was political in nature, whether it was justified remains questionable. An excerpt from Amnesty International's 1985 annual report states, "Many of the 40,000 people killed in the preceding five years had been murdered, by government forces, who openly dumped mutilated corpses, in an apparent effort, to terrorize the population." --This is not to gloss over the violence brought on by the opposing guerrillas, but simply to state that both sides were definitely violent to an extreme in this internal conflict.

In any case, in 1992 a peace accord was signed, partly because the guerrillas were running out of steam. For a period of 5 years that followed, parts of the land were re-distributed slowly to eligible soldiers on both sides under the supervision of the United Nations, and the guerrillas re-established themselves as a legitimate political party.

In June, the first ever Frente president took over in a legitimate election. It had been expected to be a landslide victory, ever since he had emerged as a popular, moderate, and charismatic candidate. But, the 6 months before the election saw a lot of rumors spreading fear that he was a Communist and was going to drive away all the business owners in the country. In the end, he won by a margin less than 3%. The jury is still out, since he is so new, but we can only hope for the best.

-----------------------

Some worrisome news from a Salvadorean blog I read:

The online periodical Contra Punto reports the latest homicide statistics for the first 7 months of 2009 and they are troubling. Murders are up 37% in El Salvador for the first seven months of 2009 compared with the same period in 2008. So far in 2009, there have been 2428 violent deaths, compared to 1767 in 2008. These statistics come from the Attorney General's office who asserts that the majority of these murders are gang-related.

Speaking of gangs, supposedly the rampant gang activity down here is, again, closely tied to the history of poverty in this country -- and maybe surprisingly, also related to the Salvadorean immigration to/deportation from the States.

In any case, Geoff's and my neighborhood is relatively safe. Like most of our neighbors, we have 24-hour security guards who hold machine guns behind closed gates -- not that they actually would use the guns in a time of need, but as far as appearances go, I think they give off some sort of a protective vibe, anyway. And for now, Geoff and I have given up on walking home at night, just to be on the safe side. Cab rides are only a few dollars to get to anywhere in the city, so it's really not worth it to walk even 15 minutes in the dark...