Twins have fascinated us since early recorded history. Take the Egyptians, for example. The god Geb was one of the earliest ones to appear, being the son of Shu and Tefnut (where do they get these names?). Shu represented emptiness and Tefnut moisture. So, we are talking primordial here. The sibling and consort of Geb was Nut (really -- that's her name!) who was the goddess of the air. Geb is symbolized by many things, including a snake, a goose, and represented habitable land. There is a drawing of Nut, who is arched, naked, over the earth, represented by Geb. In this image, he has the head of a snake (take a look here). Other than the obvious phallic connotation, the snake also represents a close connection to the earth.
What does this have to do with Twin Souls? Perhaps it points to the fact that our separation goes far back in time and that our longing for our other half is as profound as the earth longing for the sky.