Imagine you wanted to measure the coastline of Great Britain. You might remember from calculus that straight lines can make a pretty good approximation of curves, so you decide that you’re going to estimate the length of the coast using straight lines of the length of 100km (not a very good estimate, but it’s a start). You finish, and you come up with a total costal length of 2800km. And you’re pretty happy. Now, you have a friend who also for some reason wants to measure the length of the coast of Great Britain. And she goes out and measures, but this time using straight lines of the length 50km and comes up with a total costal length of 3400km. Hold up! How can she have gotten such a dramatically different number?
It turns out that due to the fractal-like nature of the coast of Great Britain, the smaller the measurement that is used, the larger the coastline length will be become. Empirically, if we started to make the measurements smaller and smaller, the coastal length will increase without limit. This is a problem! And this problem is known as the coastline paradox.
By how fractals are defined, straight lines actually do not provide as much information about them as they do with other “nicer” curves. What is interesting though is that while the length of the curve may be impossible to measure, the area it encloses does converge to some value, as demonstrated by the Sierpinski curve, pictured above. For this reason, while it is a difficult reason to talk about how long the coastline of a country may be, it is still possible to get a good estimate of the total land mass that the country occupies. This phenomena was studied in detail by Benoit Mandelbrot in his paper “How Long is the Coast of Britain” and motivated many of connections between nature and fractals in his later work.
Dubbed terrorists, Mayans fight back against Guatemalan mining projects September 8, 2014
The road between the Guatemalan towns of San Miguel Ixtahuacán and Quetzaltenango is guarded by a dozen thin, young, Mayan men in baseball caps and hooded sweatshirts, who mill around a truck parked across the road. “If you are from the mine,” the ringleader says, “you can’t come through.”
A mile or so away, the land falls away into a dust bowl, picked at by heavy machinery – the Marlin gold mine. All along the road, orange cliffs have collapsed onto the tarmac and the air is heavy with the stink of burnt clutches from the trucks that labour up the slope through the mountains, around 50km from Guatemala’s border with Mexico. The volcanic peaks are swaddled in gunsmoke drifts of cloud and patrolled by vultures; scattered settlements of adobe houses overlook a deep green patchwork of maize and coffee fields laid out across the ghosts of old Mayan terraces.
The Mayan Mam village of Agel hangs precariously over the edge of the pit. Crisanta Pérez’s house on the edge of the settlement clings to a steep slope that runs down to a long, turquoise tailings pond.
An intense, soft-spoken woman, “Doña Crisanta” is the figurehead of a peaceful resistance in San Miguel Ixtahuacán that has formed to protest the mine’s continued presence. Dubbed terrorists and enemies of progress by the state, the Frente de Defensa Miguelense is one of several Mayan-led protest groups across Guatemala that are facing down assassinations, detention and intimidation to stop their land becoming part of a continent-wide rush for resources.
“My family and I have been intimidated and criminalised,” Pérez says. “But I won’t give up. Who is going to do it, if not me?”
Pérez and her fellow community leaders say that the Marlin mine has contaminated the water sources that they use to wash and irrigate their crops and that the subterranean explosions have caused houses to collapse – charges that the mine’s owners, the Canadian firm Goldcorp, deny. Newsweek was shown evidence of skin conditions and severe neurological diseases that local health workers believe are the result of heavy metal poisoning, but, without independent medical assessment, their claims are hard to verify.
For the majority, the economic opportunities that the mine promised never materialised. Many, like the men manning the roadblock, sold their land and bought trucks, hoping to haul for the mine – their vehicles, daubed with religious icons, sit idle by the road. The Mayans’ anger goes deeper than individual grievances, however. The Mam, one of several Mayan nations in Guatemala, make up the majority in San Marcos. They number around 650,000 in the western highlands. On the other side of the mine, another nation, the Sipakapa, are also actively resisting the development. Both groups say that they were never consulted before work began on the pit, that their land was simply taken by a central government that does not represent them. This, they say, marks the continuation of centuries of marginalisation and discrimination – what rights they have won have proved secondary to the demands of commerce.
The Mam and Sipakapa see the mine, the government and private security firms as one entity that work together against them. “They have created a social monopoly. The mine comes to divide us, it causes conflict, psychological trauma, social repression,” says Rolando Cruz, a leader of the Movimiento de Resistencia Sipakapense, a resistance group in nearby San Isídro. “And they did not consult us.”
Téodora Hernandez was shot in the head and left blind in one eye by two men who came to ask her why she would not let a road pass through her land. Francisco Javier Hernandez Peréz, a leading voice opposing the development, was doused in petrol and set alight in 2011 by hooded men who identified themselves as supporters of the mine. His wife, Victoría Yóc, witnessed the attack; her neighbours heard her screaming across the mountains. Others have stories of near misses: Miguel Angél Bámaca, a health worker who has documented cases of suspected poisoning, was shot at in his home.The Mayans’ response has been escalating levels of protest and direct action. They have blocked roads, seized mine equipment and led demonstrations against company activities. Their campaign has been met with startling levels of violence.
Often, the violence is perpetrated by members of their own communities. The limited opportunities that the mine offers have created a powerful incentive for the few beneficiaries – Cruz calls them “traitors” – to crack down on dissent. The brutality has only hardened the resistance’s resolve.
“I’m never going to shut up,” says Victor Vicente Pérez, a Mam community leader. “I know I have the right to speak the truth … The [mineworkers] have tried to intimidate me with rumours that one day soon I’ll disappear, but I know I’m fighting for my rights and I’m willing to die for that.”
Marlin is one of over 100 metal mines currently operating in Guatemala. There are close to 350 active licences for exploration or production, with nearly 600 pending as the government, supported by the international financial institutions, promotes the sector as a way to raise revenues. Only 2% of the country’s gross domestic product (GDP) is based on mining, and the government hopes that the sector may offer a chance at rapid economic growth. Around 75% of the population lives below the poverty line. Infant and child mortality rates are high, and around 50% of children are malnourished.
The largest, and capital city of Roman Dacia, this city was founded by Terentius Scaurianus about 108-110, during the reign of Roman emperor Hadrian.
Situated less than 50km away from the former capital of the Dacians, Ulpia Traiana Sarmizegetusa was built on a strategic point between where the battle of the Dacian troops and Roman legions took place. This site is on the ground of what was a camp of the Fifth Macedonian Legion, and was settled by veterans of the Dacian wars.
Later destroyed by the Goths, this large cosmopolitan centre remains in ruins today. The site features temples, gladiator schools, a large forum, and an amphitheater.
While researching I also found these virtual reconstructions of what features of this site would have once looked like:
Es una capa de la atmósfera que se encuentra entre la troposfera y la mesósfera, se extiende entre los 10km y 50km de altitud, la temperatura allí varia entre 10C y -60C, en la parte baja de la estratosfera la temperatura es relativamente estable y en la capa hay poca humedad.
Cerca al final de la estratósfera se encuentra la capa de ozono que absorbe la mayoría de los rayos ultravioletas del Sol.
Today’s NASA image of the day is of the atmospheric layers of Earth. Captured by astronauts on the International Space Station, the distinction between the troposphere (orange-red) and the stratosphere is quite distinct.
Several satellites are dedicated to researching the chemistry and dynamics occurring within, and between these two atmospheric layers.
The troposphere starts at the Earth’s surface, and extends to about 20km. It contains almost all of the Earth’s “weather”. The stratosphere sits above the troposphere, extending to about 50km from the Earth’s surface. It holds about 19% of the atmosphere’s gases.
Perhaps an even more striking example of this image is this one: [x]
Image Credit: NASA/JSC Gateway to Astronaut Photography of Earth (July 21, 2011) More information: 1, 2