I have always loved the art of Mourits Cornelis Escher¹ because it plays with our minds and preconceptions. He had an inventive mind which constructed the extraordinary from assemblies of the ordinary as in his pictures of infinitely ascending staircases² and brilliant tessellations³. You can see many of these images online at the Escher Art Collection⁴ and buy them online at the World of Escher⁵.

In many of his works, Escher interwove images in patterns (tessellations) which showed one object slowly transforming into another as with his picture Sky and Water I ³. In others, with similar visual tricks, he challenged our emotions as with the white angels which tessellate with black devils in Heaven and Hell ⁶. That picture can be seen in miniature form at the left of this essay.

The mathematics (or geometry) of Escher's drawings is just as interesting as the images themselves. Roger Penrose⁷ describes the geometry of Escher's circle drawings like Heaven and Hell as being "fine and accurate representations of Lobachevskian (or hyperbolic) geometry" - a geometry which differs from conventional Euclidean geometry by having the sum of the angles of any triangle as less than 180^o rather than exactly equal to 180^o.

I don't know for sure what Escher intended Heaven and Hell to say. I have one book in which he describes this woodcut by saying "Here, too, we have the components diminishing in size as they move outwards. The six largest (three white angels and three black devils) are arrange about the centre and radiate from it. The disc is divided into six sections in which, turn and turn about, the angels on a black background and then the devils on a white one, gain the upper hand. In this way, heaven and hell change places six times. In the intermediate, "earthly" stages, they are equivalent."⁸

That description is mainly technical but carries a hint of an underlying explanation in the suggestion that here on earth good and evil are equivalent. My faith rests on something very different from that suggestion. In my reading of the Bible, good has already defeated evil. Jesus, risen from the dead, has won the final victory over the devil and the power of sin over my life.

I may struggle with sin in my life from time to time, I may experience a continuing battle between good and evil (as did St Paul) - but provided I call on the name of Jesus and trust in his saving power, I can share in the final victory of Jesus.