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reed magazine logoMarch 2010

Capturing Infinity continued

Day and Night

Day and Night (1938) is the most popular of Escher’s works.

Capturing Infinity

In 1959, Escher described, in retrospect, a transformation of attitude that had occurred at the midpoint of his career:

I discovered that technical mastery was no longer my sole aim, for I was seized by another desire, the existence of which I had never suspected. Ideas took hold of me quite unrelated to graphic art, notions which so fascinated me that I felt driven to communicate them to others.

The woodcut called Day and Night, completed in February 1938, may serve as a symbol of the transformation. By any measure, it is the most popular of Escher’s works.

Prior to the transformation, Escher produced for the most part portraits, landscapes, and architectural images, together with commercial designs for items such as postage stamps and wrapping paper, executed at an ever-ris­ing level of technical skill. However, following the transformation, Escher produced an inspired stream of the utterly original works that are now iden­tified with his name: the illusions, the impossible figures, and, especially, the regular divisions (called tessellations) of the Euclidean plane into potentially infinite populations of fish, reptiles, or birds, of stately horsemen or dancing clowns.

Of the tessellations, he wrote:

This is the richest source of inspiration that I have ever struck; nor has it yet dried up.

However, while immensely pleased in principle, Escher was dissatisfied in prac­tice with a particular feature of the tessellations. He found that the logic of the underlying patterns would not permit what the real materials of his work­shop required: a finite boundary. He sought a new logic, explicitly visual, by which he could organize actually infinite populations of his corporeal motifs into a patch of finite area. Within the framework of graphic art, he sought, he said, to capture infinity.

Serendipity

In 1954, the organizing committee for the International Congress of Mathe­maticians promoted an unusual special event: an exhibition of the work of Escher at the Stedelijk Museum in Amsterdam. In the companion catalogue for the exhibition, the committee called attention not only to the mathematical substance of Escher’s tessellations but also to their “peculiar charm.” Three years later, while writing an article on symmetry to serve as the pres­idential address to the Royal Society of Canada, the eminent mathematician H.S.M. Coxeter recalled the exhibition. He wrote to Escher, requesting per­mission to use two of his prints as illustrations for the article. On June 21, 1957, Escher responded enthusiastically:

Not only am I willing to give you full permission to pub­lish reproductions of my regular-flat-fillings, but I am also proud of your interest in them!
Figure A

Figure A

In the spring of 1958, Coxeter sent to Escher a copy of the article he had written. In addition to the prints of Escher’s “flat-fillings,” the article contained the following figure, which we shall call Figure A:

Immediately, Escher saw in the figure a realistic method for achieving his goal: to capture infinity. For a suitable motif, such as an angel or a devil, he might create, in method logically precise and in form visually pleasing, infinitely many modified copies of the motif, with the intended effect that the multitude would pack neatly into a disk.

reed magazine logoMarch 2010