The spiral is born of the desire the point and the circle have to become one, without becoming obliterated or obliterating the other. The force of the will of the originating point is expressed as a line that moves out from the point. The lineʼs successive movement is a loosening outward from the originating point toward the pull of the circle, which causes it to curve in a spiraling action.
There is no such thing as simple stand-alone geometry. Geometry is always about more than simple geo—Earth—and metria—measurement. What geometry really is is a method of describing the way the universe works. Therefore, looking at the origin of the spiral is a way of assessing the conditions of the cosmos.
An Archimedean spiral, also know as an arithmetic spiral, advances in this way as it approaches infinity, or the perfect circle that is the periphery of the cosmos. Of course, it is impossible to actually arrive at infinity and the edge of the cosmos, so the energy of the line moves back toward the originating point, this time in a logarithmic spiral that begins with an angular movement away from the circular curve. This movement is repeated along the lineʼs course back to the originating point. Whereas the Archimedean spiral seeks the circle—and as such represents feminine energy—its inverse, the logarithmic spiral, seeks the straight line and the originating point—representing masculine energy. The two spirals are the paths of an out-and-back motion that represents the breathing out and the breathing in of the universe.