Hog Nose (was: Massasauga) (Nordhouse Dunes 3)

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The Eastern Massasauga is Michigan’s only poisonous snake. This was my first encounter with a rattlesnake, I didn’t expect to find her at a beach in Michigan.

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The camouflage in the dried sea grass is near perfect, but the human predator trying to get a better picture annoyed her, so she moved.

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Why do us men think of snakes as female, and reserve the male attribute to her larger brother, the dragon (whom I still have to find)? 

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They are beautiful, elegant, hit you when you expect it least, and sneak away when you don’t look.

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Sometimes, they also just sit there thoughtfully and lick their tongue.

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New Eden (New Harmony IV)

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Nested among a garden of fruit trees next to the Roofless Church in New Harmony is another sculpture by Stephen de Staebler, the Angel of Annunciation, which is easy to overlook, despite its tallness.

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A small plaque on the church wall nearby quotes a poem by Staedler that states that arms are for doing, while wings are for being.DSC 1886

This angel is deeply conflicted. The arm sticks out of his head like the wings. The head itself, whose face is just recognizable as such from the side, is split in half when viewed from the front.

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One of the two feet is cemented in, the other free to walk. Where does this leave us?

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There is another sculpture in this garden, without plaque or any indication of authorship: A piece of wood, hanging from a tree.

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It’s not a sculpture. It’s what is left over from binding the branches of an aging tree together to keep it from breaking and falling apart. An attempt can never completely be a failure. Doing and being can still be one.

Verweile Doch (Nordhouse Dunes 2)

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A river with its strict sense of flow is a universally used symbol for the passage of time. Resistance against that is, in contrast, best contemplated by looking at the relentless forth and back of waves along a coast line.

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Time is reduced here to repetition, it seems.

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The weeds and twigs shown are gone. Their only action then was to write on the water, invisibly, and immediately forgotten.

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But there is more. They are defending a territory beyond the water.

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They are also witnesses for an esthetic of complexity beyond the untextured and timeless water.

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And finally, they did leave their traces, elsewhere, in memory.

 

War & War (Nordhouse Dunes I)

For many years we went camping to Nordhouse Dunes at Lake Michigan, and an episode of nostalgia made us revisit this place one last time before my daughter is off to college & life.

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In László Krasznahorkai deliberately cryptic book War & War, the hero György Korin is depersonalized: He just symbolizes a single function of our lives, namely delivering the past into the future, becoming the horizon between the below and the above.

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This happens concretely by carrying an old manuscript to New York, a place that the four inhabitants of that manuscript haven’t seen yet. These inhabitants are cryptic, too, bemoaning the loss of the noble, the great, and the transcendent, this causing also the loss of peace, so that the world now consist of only war & war. 

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Korin realizes however that delivering the manuscript is not enough, he feels the calling to complete it, to find an exit for its inhabitants. There are several attempts for this, one being by writing on water.

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This year, the dune grass that so gracefully used to create sand drawings, is now doing this in the water, thanks to water levels two feet above normal. The water itself leaves very temporary traces on the disappearing beach.

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Is it maybe the author’s dream that his protagonists keep writing the story?

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Noli turbare circulos meos! (Annuli VII)

In science, our goal should always be to present with clarity. Since the discovery of perspective drawings, a realistic representation of 3-dimensional objects has become almost mandatory. However, very often these objects have an appeal beyond their scientific truth which gets lost if its is shown in full clarity.

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This blog has two series of posts titled “Spheres” and “Annuli” that both showcase images of simple 3-dimensional mathematical objects which deliberately forsake clarity in order to convey that other appeal. While accurate perspective renderings are used, the  perspective and textures are chosen as to emphasize the abstract aspect. 

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The example above shows a triply orthogonal system of surfaces. An easy way to create such a system is by taking a doubly orthogonal system of curves in the plane, revolve them about a common axis to obtain two families of surfaces of revolution that intersect orthogonally, and add all planes through the axis of revolution. For instance, we can choose two families of touching circles that pass through a common point, as above.

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A single circle, rotated about the black axis, will revolve into a torus. To spice things up, let’s apply an inversion at a sphere centered at the intersection of the circles. This turns the tori into special cyclids like the one above, which all have the appearance of a plane with a handle. Using both a red and a green circle will invert-revolve in two such cyclids that intersect in a straight line and a circle:

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These are still attempts of realistic drawings, but we already get the feeling that things aren’t completely evident anymore. For instance, the two cyclids above should be equals: but where did the corresponding red handle go?

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Above is the same pair of objects from a different perspective. Now we can see the two handles and the intersection in a line, but where is the intersection circle? Also, where do we need to place the third surface family, which consists of inverted planes, i.e. spheres? The answer to that question is indicated below.

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Other perspectives allow amusing variations:

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For the top image, I have used several cyclids from each family, and several spheres, clipping them between two planes. To appreciate the image, all this knowledge might be irrelevant. To create it, it is essential.

 

Simplicity

We have learned simplicity,
we sing in the choir of cicadas

 

In 2004, the midwest of the USA became the region of the largest outbreak of biomass on the planet. Brood X emerged, the largest of the periodical cicadas, with a life cycle of 17 years.

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They spend most of their life underneath as nymphs, going through several instars, and feeding from root juices of trees. Then, almost all on the same day, they emerge, and crawl up.

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They molt into adulthood, which takes up to an hour. All this takes place above an abyss. If they fall, the soft wings will not unfold properly.

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In the last stage, the wings unfold.

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They hide and rest for a few days. This is supposedly the time they are most delicious.

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Then, they tumble around, with their poor eyesight and clumsy bodies, causing harm to none, and begin their irresistible mating chant, droning sound patterns that move through the landscape like ambient music.

17 years underneath, for a few weeks of a single song. Who will question the meaning of life?

Time and Space

This has been an extraordinary summer. Weather wise, flooding rain falls were followed by torching heat, and now we are enjoying a dry summer weather that would be more typical for Northern Michigan. Time for a visit to the DePauw Nature Park, whose quarry enclosed space I would avoid on regular summer days. 

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It’s as green as it gets, promising a gorgeous fall coloring. Everything seems to take advantage of its given time and space.

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The abundance of vegetation creates patterns that are unusual for this place.

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More typical are the lonely little ones, like the young sycamore trying to make roots in the harsh ground,

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or the singular dandelion, gazing into our future.

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