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Sphere Spirals

In October 1958, Escher created one of his most beautiful, but also most complex objects. He did extensive research for Sphere Spirals, searching for a solution to show the open ribbons that form this sphere in a three-dimensional form.

Sphere Spirals is part of a series of prints that demonstrate Escher’s fascination for difficult constructions. He sees it as an enormous challenge to visualize complex, three-dimensional objects in such a way that the eye of the viewer understands how they are put together. He often ‘opens them up’ so that there are views of the inside or the back, parts that would normally be invisible to the eye. Other prints with this property are Two Intersecting Planes, Concentric Rinds, Spirals, Three Intersecting Planes, Rind, Bond of Union, Sphere Surface with Fish, Four Regular Solids and Knots. They are extremely detailed representations of complex and remarkable shapes. But they are also prints that are regarded by many as atypical work for Escher. They are not illusions, the shapes are not impossible. They also appeal to the intellect more than to the heart. Yet these are prints in which Escher’s genius clearly manifests itself. He visualizes constructs that might exist, but which without his efforts would probably never have come to life. He’s showing us something we’ve never seen before.

M.C. Escher, Concentric Rinds (Concentric Space Filling/Regular Sphere Division), wood engraving, May 1953
M.C. Escher, Three Intersecting Planes, woodcut in green and black, printed from two blocks, June 1954

Sphere Spirals is complex not only because of its shape. Escher needed four wood blocks that had to fit together exactly to form the end result in four colors. The first wood block, with which he made the proof, also formed the basis in gray for the print Spherical Surface with Fish. In addition, he not only had a hard time with the print itself, he also had a hard time on a personal level. His son George and his wife Corrie had recently emigrated to Canada, and on October 12, 1958, he wrote to them:

‘The large flocks of starlings always fly up from the tops of the high beeches, swing around and settle down again in another top. On this quiet Sunday morning, Mother and Arthur are not up yet, I keep seeing them swinging by, high above my studio window. They feel the autumn pull within them, they are being called somewhere, their group consciousness is restless.
These days it is very difficult for me to accept my fate when I think about you. That is why I buried myself in sphere spirals.’*

In another letter to George and Corrie he wrote on October 25:

‘Ever since you left, I’ve been chugging my spherical spiral woodcut. After a first proof, my high expectations were – as always – very disappointed. Now, with a little despair in my heart, I am going on steadily, at least to achieve a result that is acceptable.’**

The print was finished shortly after that, but he was not satisfied, something that happened to him quite often. The perfectionist in him kept seeing how it could have been even better.

M.C. Escher, Sphere Surface with Fish, woodcut in grey, gold and reddish brown, printed from three blocks, July 1958
M.C. Escher, Knots, woodcut in black, green and brown, printed from three blocks, August 1965

In The Graphic Work of M.C. Escher (1959) he confines himself to a sober description of the print:

‘Here, just as in no. 18 (Sphere Surface with Fish), a sphere is shown with a network of longitudinal and latitudinal circles. Four spirals coil their way around the spherical surface, infinitely small at the poles and broadest at the equator. Half of its yellow exterior is visible. Through open channels in its side the red interior can be followed to the opposite pole.’

If you take a longer look at this print, you will see the sphere start to revolve before your eyes. Just like the revolving red, white and blue spirals barbers used to display outside their shops. Sphere Spirals is above all a testimony to Escher’s incredible mastery of his craft and his persistence to bring a complex shape to life.

Although Escher’s Sphere Spirals are unique, the concept of ‘spirals’ is certainly not. In fact, it is a very common form, both in nature and in culture. Think of a snail shell or the shape of galaxies. Peel an apple or an orange and see how the peel is like a spiral circling the spherical fruit. It is also a frequently recurring form in mathematics and architecture. The closest to Escher, however, are the seafarers. When a ship travels across the ocean, the shortest route between A and B is a curved line. The line between the two poles corresponds to the lines on Sphere Spirals. In navigation this is called a rhumb line (or loxodrome), a curve over the earth’s surface along which the course remains the same.

Nautilus shell. Photo: Jitze Couperus, CC BY 2.0
Staircase in the Sagrada Família, Antoni Gaudí. Photo: Wenchao Wang, CC BY 3.0

[*] J.W. Vermeulen, Maurits C. Escher, een eigenzinnig talent, Kok Lira, 1995, page 151-152
[**] Wim Hazeu, M.C. Escher, Een biografie, Meulenhoff, 1998, page 404

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