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Escher and Two Dimensions?

Is the pebble two-dimensional and drawn onto the paper, or is it a three-dimensional pebble sitting on top of the sheet as a paperweight?

Escher explored the interplay between our perception of dimension versus reality and how readily we accept the representation of something three-dimensional in a two-dimensional work when it really could be a two-dimensional representation of something two-dimensional! If that last sentence has your head spinning don't worry, Escher illustrates the concept perfectly in his woodcut Three Spheres I.

Escher knows our eyes start at the top of the page, we are trained to read from left to right, top to bottom. So immediately our brains jump to the conclusion that the top "sphere" is the two-dimensional representation of a three-dimensional sphere. How could it not be?

But as soon as our eyes drift downward we hit confusion. What is that crease? What happened to the "sphere"? It is clearly deformed, but the perspective is warped. That second "sphere" is simply the top 1/4 of the printed paper you are looking at folded over to 90 degrees. Given this is a valuable original, you'll have to imagine it as I'm not about fold a woodcut just for learning purposes.

The bottom "sphere" is that same flat piece of paper sitting on a table. Did Escher convince you that your first impression of dimensionality was wrong? The sphere is flatter than you think, and that has nothing to do with misconceptions about our Earth.

If you are still puzzled, Bruno Ernst destroyed the illusion by looking at if from a different angle. This image is in the book "The Magic Mirror of MC Escher." Does looking at Escher's art from a different angle explain the illusion for any of Escher's other artworks? You bet!

Check to see if Three Spheres is available HERE.

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