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M.C. Escher

Integral is often described as the ability to hold multiple perspectives at the same time.

As we evolve and experience shifts in our perspective we are forced to leave behind us the illusion of dualistic self-centered experience.

One man who bridged the gap between art and science and demonstrated anything but flatland is the graphic artist M.C. Escher.

Known for his interlocking shapes, transforming creatures and impossible architecture, Escher challenges us to question our perception of reality.

His mathematical approach to the creation of art or put otherwise, his artistic expression of mathematical concepts makes the study of his work fascinating for those interested in integral concepts.

The increasing ability to take perspectives is illustrated in his artwork.

His ability to turn the real into the unreal, to represent infinity on a two-dimensional plane and to demonstrate metamorphosis, makes the study of his work fascinating for those interested in integral concepts and possible integral art.

In Islamic art the spiritual world is reflected through geometry and rhythm.  After his visit to the Alhambra, Escher began to experiment with spatial imagery and symmetry.  He became fascinated with the idea that timeless truths could be found through repeated forms.

He covered an entire surface with geometrical patterns and his artwork can be appreciated for its aesthetics and its symbolic meaning and it can be used for contemplation.

I first discovered Escher when teaching symmetry in my mathematics classes, and recently this fascination was rekindled when visiting the Escher Museum in The Hague.

The concept of reality and illusion took on new meaning as I studied his works.  The illusion of independence was challenged through his metamorphic representations. That emptiness is form and form is emptiness shifted before my eyes.

Here are a few of his works:

 

Are there any other Escher fans out there?

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Up for adoption

Will you adopt me?  I will make you this sort of art, I promise!

Mommy!!

I am not joking btw. My life is to cause.

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Double Planetoid

 

In “Double Planetoid” by Escher there are two regular tetradrons which pierce each other as a star tetrahedron and float through space as a planetoid.  One is inhabited by human beings who have transformed their region into an area made up of houses, bridges and roads.  The other tetrahedron is in its natural state, with rocks on which plants and prehistoric animals live.  The two fit together into a whole but seem to have no knowledge of each other.

I have posted this for Brendan and Christophe who are discussing this shape in Wilber 6???

Please note that this work was created in 1949 without any computer aid.

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Mosaic II

Mosaic II

Mosaic II


I first found Escher's Mosaic II when reading Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid.

One afternoon when I had a few friends at my house, I projeted this image on my wall and began to hand-out artist's pencils so we could "make our mark."  As the shapes began to burn into the wall via graphite and charcoal, I read aloud from GEB the “Sonata for Unaccompanied Achilles.” This is a dialogue between Tortoise and Achilles about figure and ground: how, by defining one subset of a given set, you implicitly define another subset of that same set -- the part that is not included in the first subset. In the visual arts, this is best exemplified by Escher's Mosaic lithographs, where the shapes that form the background for a group of black “phantasmagorical beasts” define another set of figures, in white. The musical example that Hofstadter uses is Bach's Sonatas for Unaccompanied Violin, where the listeners' imagination fill in “between the notes” as the violin plays, and one often imagines hearing the accompanying piano. But the form of the dialogue pulls the very same trick, as the reader can easily imagine the Tortoise answering Achilles at the other end of the line!
(excerpted from http://tal.forum2.org/geb)

Our we-space was enveloped by image and action--a breathing holograph... and the scar was left on my wall to greet me each day thereafter.

 

 

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Relativity

“That means that the phenomena brought forth by various types of human inquiry will be different depending on the quadrants, levels, lines, states, and types of the subjects bringing forth the phenomena.” (from Excerpt B: The Many Ways We Touch -Three Principles Helpful for Any Integrative Approach by Ken Wilber)

As seen in Escher's "Relativity" we can all walk around the same place, but we will all look in different ways often incapable of seeing what others see.  Remember too, that the viewer of "Relativity" will have yet another perspective and will be able to see something of the structure that could be invisible to its occupants. 

 

Sounds rather like the concept of “Kosmic addresses” (i.e. altitude + perspective) wouldn’t you say?