The Coastline Paradox

By one measurement, the Earth has 217,490 miles of coastline.

For comparison, the average distance between the Earth and the Moon is roughly the same (238,854 miles). 217,490 miles is a large, but comforting measurement.

Humans have an affinity for naming and measuring. From measuring grows understanding. Yet measurement also gives us a deceptive sense of mastery.

There's more.

The edge of the sea is a strange and beautiful place.
~ Rachel Carson

Measuring coastline is not as simple as it appears. The aggregated length depends on the size of the ruler.

The smaller the measurement, the more coastline.

How can that be?

Measured length increases without limit as the measurement scale decreases towards zero.

Mathematician Benoît Mandelbrot discussed self-similar curves, laid groundwork for fractal dimension, and examined the Coastline Paradox in a 1967 paper published in Science.

The Coastline Paradox is that the measured length of a stretch of coastline depends on the scale of measurement. Empirical evidence suggests that the smaller the increment of measurement, the longer the measured length becomes. If one were to measure a stretch of coastline with a yardstick, one would get a shorter result than if the same stretch were measured with a 30cm (one-foot) ruler. This is because one would be laying the ruler along a more curvilinear route than that followed by the yardstick.

~ Wikipedia, How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension.

Resources

1. Benoît Mandelbrot, 1967, How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science, New Series, Vol. 156, No. 3775. (May 5, 1967), pp. 636-638. doi:10.1126/science.156.3775.636, JSTOR.
2. Coastline Paradox, Wolfram Math World.
3. The Coastline Paradox, Wikipedia.

Tectonics & Lucy In the Sky

The Afar Region in Eastern Africa is renowned for stunning evidence of plate tectonics and for a famous fossil named after a song by The Beatles.

The Afar Triangle, in Eastern Africa, is a nearly barren rockscape at the junction of three pieces of the Earth's crust.

Centered about the Afar Depression, at 509 feet / 155 meters below sea level, this junction of tectonic ridges, known as the East African Rift, is splitting apart and pulling away.

The junction consists of the Arabian Plate to the North and East, and the African Plate to the West and South. The African Plate is subdividing into two new tectonic plates, or protoplates, known as the Nubian Plate and the Somali Plate.

Geologists believe the pulling apart of these plates will eventually form a new ocean basin.

The Afar Depression - where 3 plates are pulling apart

The junction is shown in this image above (from NASA’s Terra satellite). The pulling apart stresses the rock which causes cracks, faults, volcanoes, fumaroles (gas vents), escarpments, and hot springs. The river-like feature that transects the image is a graben. This graben is a depression caused by the sinking of the ground when earth on either side pulls apart.

Lucy in the Sky with Diamonds

Lucy Reconstruction

The fossil of a young adult female was discovered in the Afar region by a team of paleoanthropologists in 1974. The team called her "Lucy" because The Beatles song Lucy in the Sky with Diamonds played on the radio as they examined the find.

Picture yourself in a boat on a river,
With tangerine trees and marmalade skies
Somebody calls you, you answer quite slowly,
A girl with kaleidoscope eyes.
~ The Beatles

Lucy's scientific name later became Australopithecus Afarensis. Australopithecus Afarensis is an extinct hominid that lived between 3.9 and 2.9 million years ago.

When you're riding in a time machine way far into the future, don't stick your elbow out the window, or it'll turn into a fossil.
~Jack Handey

Lucy was a bipedal hominid about a meter tall with a small brain and a primitive face. Radiometric dating of the surrounding rocks suggest Lucy's age is about 3.2 million years.

Patterns in Perpetual Wind

We feel the wind, but we don't see it. Perhaps that's what makes this wind map from data visualization researchers at HINT.FM so compelling.

Snapshot of Wind Vectors in the United States

Wind Map Source - HINT.FM data visualization website by Fernanda Viégas and Martin Wattenberg who lead Google's "Big Picture" visualization research group.

In its current form, the wind map depicts a satellite view of wind paths and intensity within the outline of the United States. There are plans to extend the map over the entire earth.

Viewed in hypnotizing real-time visualization, the paths of perpetual wind suggest a focused but random purpose. Black areas represent regions of calm, while curvilinear white lines are high winds. The spectrum of wind intensity is represented in shades of gray.

The commonality between science and art is in trying to see profoundly - to develop strategies of seeing and showing.
~ Edward Tufte

On a given day, one might see winds pouring down from Canada, a highway of gulf air flowing into the nation's mid-section, or the western slope of the Rockies getting buffeted by an eastward flow.

What causes wind?

Differences in earth's atmospheric pressure are perpetually driving toward equilibration. Wind is air moving from high pressure peaks to low pressure valleys. From physics we know,

Higher energy states move toward lower energy states.
~ The Second Law of Thermodynamics

The downhill movement of air from high to low pressure is the driving force behind wind, but wind is also deflected by the earth's rotation around its own axis. Wind is deflected to the right in the Northern Hemisphere and deflected left in the Southern Hemisphere.

Most of earth's physical phenomena, including wind, demonstrate cause and effect.

...nature's laws are causal; they reveal themselves by comparison and difference, and they operate at every multivariate space/time point.
~ Edward Tufte

The 5-Whys is a question-asking technique to explore cause-and-effect relationships. Sometimes this technique converges to a root cause. A variation of The 5-Whys is 5-Whats.

5-Whats of Wind

Starting with What cause of wind? asking the 5-Whats of Wind seems like a promising tack, but soon diverges from root cause to the cosmological.

1. What causes wind? Pressure differences. Air flowing from high atmospheric pressure to low atmospheric pressure.
2. What causes atmospheric pressure differences? The warming and cooling of air changes its density, which increases or decreases pressure.
3. What causes the warming and cooling of air? Warming occurs from incident solar energy; the highs of the day to the cool of nights, also known as diurnal temperature variation, are caused by the earth's rotation.
4. What causes the earth's rotation? The earth spins because of the way it was formed -- a huge cloud of gas and dust that collapsed under its own gravity. As the cloud collapsed, it started to spin by inertial force (like when a skater pulls in his arms then spins faster). The earth spins because there are no forces acting to stop it.
5. What causes the huge cloud of gas and dust that coalesces into the planet earth? The early development of the universe, also known as the Big Bang theory.

The answer of wind, and its patterns, lies somewhere between invisible variations in atmospheric pressure and the Big Bang.

If you reveal your secrets to the wind, you should not blame the wind for revealing them to the trees.
~ Khalil Gibran

System Earth

Ocean Currents

Have you ever considered the earth a single living system? The concept of a living, self-regulating earth is known as the Gaia Hypothesis.

Gaia Hypothesis
The Gaia Hypothesis proposes that all organisms and their inorganic surroundings on Earth are closely integrated to form a single and self-regulating complex system, maintaining the conditions for life on the planet.
~ Gaia Hypothesis, from Wikipedia.

NASA's Scientific Visualization Studio produced a visualization of ocean surface currents around the world from June 2005 through December 2007 titled Perpetual Ocean (shown below). This stunningly beautiful animation seems to communicate to us like a living organism.

This visual representation of surface currents was produced from the output of an ECCO2 model. ECCO2 uses a general circulation model known as MITgcm to synthesize satellite and in-situ data. The level of detail in the data enables the resolution of ocean eddies and currents.

We are tied to the ocean. And when we go back to the sea, whether it is to sail or to watch - we are going back from whence we came.
~ John F. Kennedy

The Gaia Hypothesis was formulated by scientist and futurologist James Lovelock and co-developed by American microbiologist Lynn Margulis in the 1970s. The Gaia Hypothesis, initially met with hostility in the scientific community, is now a widely accepted field of study in geophysiology and Earth System Science.

The massive whirlpools of ocean currents are reminiscent of the luminous swirling stars in the painting The Starry Night by Dutch post-impressionist Vincent van Gogh.

Ocean Currents

The Starry Night (detail)