Not all references to the circle are benign. Dante Alighieri, in the Inferno, from his La Divina Commedia, described the circles of Hell. For two centuries, the dark side of the search for knowledge has been associated with Goethe’s Faust [26]. In one scene, a witch draws a circle to cast a spell:

                                When the miller got home, his wife said, "Tell me, from whence 
                                comes this sudden wealth into our house?" He answered, "It comes 
                                from a stranger who promised me great treasure. I, in return, have 
                                promised him what stands behind the mill; we can very well give
                                him the big apple-tree for it." "Ah, husband," said the terrified wife, 
                                "that must have been the devil! He did not mean the apple-tree, but 
                                our daughter, who was standing behind the mill sweeping the yard."

                                The miller's daughter was a beautiful, pious girl, and lived through 
                                the three years in the fear of God and without sin. When therefore the 
                                time was over, and the day came when the Evil-one was to fetch her, 
                                she washed herself clean, and made a circle round herself with chalk. 
                                The devil appeared quite early, but he could not come near to her.

Just as did the ancient Greeks, the philosophers of the seventeenth century used the circle as an example of mathematical idealization, to distinguish between an idea and an actual item. Consider that, in 1690, Locke wrote the following [28].

                                Hence the reality of mathematical knowledge.... The mathematician 
                                considers the truth and properties belonging to a rectangle or circle 
                                only as they are an idea in his own mind. For it is possible he never 
                                found either of them existing mathematically, i.e., precisely true, in 
                                his life. But yet the knowledge he has of any truths or properties belonging 
                                to a circle, or any other mathematical figure, are nevertheless true and 
                                certain, even of real things existing: because real things are no further 
                                concerned, nor intended to be meant by any such propositions, than as 
                                things really agree to those archetypes in his mind.

Although the mathematically pure circle doesn’t exist in the tangible world, it is present in aspects of many parts of life, as Walt Whitman wrote in Leaves of Grass [29]

                                 Facing west from California's shores,
 
                                 Inquiring, tireless, seeking what is yet unfound,

                                 I, a child, very old, over waves, towards the house of maternity,

                                 the land of migrations, look afar,

                                 Look off the shores of my Western sea, the circle almost circled;

                                 For starting westward from Hindustan, from the vales of Kashmere,

                                 From Asia, from the north, from the God, the sage, and the hero,

                                 From the south, from the flowery peninsulas and the spice islands,

                                 Long having wander'd since, round the earth having wander'd,

                                 Now I face home again, very pleas'd and joyous,
 
                                 (But where is what I started for so long ago?

                                 And why is it yet unfound?)

To us, the poet here is seeing circles in many aspects of life. He is connecting the end and the beginning of his own travels, of his lifetime, of geographical longitudes, and of the spread of human migration and cultural diversity. He is commenting on his own aspirations and those of all people. The goals and activities of life do not always go forward in a straight line, but can circle one back to the start. Whitman’s poem interweaves many of the ideas we see connected to circles.

The philosophy of living in harmony with circular patterns was expressed more recently by Black Elk (Hehaka Sapa, 1863-1950), a holy man of the Oglala Sioux Native Americans [30].

                                 Everything an Indian does is in a circle, and that is because the 
                                 power of the world always works in circles, and everything tries 
                                 to be round. In the old days when we were a strong and happy 
                                 people, all our power came to us from the sacred hoop of the nation, 
                                 and so long as the hoop was unbroken the people flourished. . . . 
                                 Everything the Power of the World does is done in a circle. . . .

                                 Even the seasons form a great circle in their changing, and always 
                                 come back again to where they were. The life of a man is a circle 
                                 from childhood to childhood and so it is in everything where power 
                                 moves. Our teepees were round like the nests of birds, and these were 
                                 always set in a circle, the nation’s hoop, a nest of many nests, where 
                                 the Great Spirit meant for us to hatch our children.

The circle has been used throughout history, and is still incorporated into new works, such as this feathered snake eating itself (Figure 26) [31].
 

The circle remains an intimate part of human culture, from math and science to art and human views of the world. Edwin Markham (1852-1940) expressed this in his best-loved poem [32].