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Geometry Has Consequences

Although the percentage is small, some visitors to southwestern Utah must get a kick out of the shapes, lines, and geometry of this part of North America. As I do. In fact my eyeballs and brain positively feed on the geometry. 

My favorite picnic table at a trailhead.  It should be offered by Merriam-Webster as a visual definition of 'autochthonous.'  I hope whatever ranger is responsible for this makes District Ranger someday.

For instance, your eye can extend the line of a sedimentary layer from one mesa to a nearby mesa, and visualize the land in between the two mesas as eroding away over the eons. But when you do this, it doesn't quite seem as though the tops of the two mesas have the same altitude.

But why should they? Sedimentary layers are uplifted -- tilted -- out of their original horizontal condition at the bottom of a sea.

It becomes a game to visualize the formation of this topography as being formed from differential erosion of rock layers that might appear to be uniform. The best tool for appreciating this area is a non-academic book -- with hand-drawn sketches! -- by a geology professor, William Lee Stokes, "Scenes of the Plateau Lands and How They Came to Be."

Don't be repelled by the word, geology. It is easy to gag on the memorization and jargon in most geology books, and then give up on it. A book can please the readers better if it emphasizes the 'lay' of the land, that is, the stuff you can actually see.

My favorite walking in this area is not some vaunted hiking trail in Zion National Traffic Jam, but some ignored dry wash (arroyo) that is barely named; and of course, since it is outside the Park I can take my dog.

On a chilly morning, an infrared photograph from a satellite would delineate the cold blue curves and lines of these arroyos.

To somebody new, it might be difficult to distinguish 'upstream from downstream' in a dry wash, an arroyo. But a little bit of walking -- or better yet, mountain biking -- will soon make it obvious which way is headed down to the mighty 'father of waters,' the Colorado River.

On and on the geometry goes. I have always felt drawn to a private business in the area that "makes" flagstones. Yesterday blind luck had me reading a book about the Scientific Revolution around 1600, when geometry was emphasized.

One day towards the beginning of 1610 Johannes Kepler was walking across a bridge in Prague when a few snowflakes settled upon his coat... This got Kepler thinking about two-dimensional six-cornered shapes and how they form a lattice...and about how the only shapes that one can use to tile a floor, if all the tiles are the same, are triangles, squares and hexagons. [The Invention of Science, by David Wootton.]
That's all it took for the local tile quarry to get me reading about tessellation on Wikipedia, and fluttering my eyelashes. The Zion scenery was right in front of me. Who cares?

In Seville, Spain. From Wikipedia.


Ed said…
I became fascinated with tessellation back in 2016 and 2017 and drew a lot of them using HTML Canvas. Drew almost all of them that were shown on the Wikipedia page.

The ones that I really liked were the Roger Penrose tiles; open this page then scroll down to 10 January and 11 January or this page where you need to scroll down to 18 February 2017 to see the Penrose Cartwheel.
Yes, Ed, I remember when you were titillated by tessellations.
I've never thought about that as Art but have often used something similar when building Machinery. Interesting Subject.
Be Safe and Enjoy!

It's about time.
Rick and Kathy, I don't understand your "have often used something similar when building Machinery." Maybe an example would help.