Wikipedia
Thaumiel (twins of God) is the name of one of the Qliphoth in the Kabbalah, the shadow side of the Kabbalistic Tree of Life. It is the shadow of the Sephirah Keter (the crown). While Keter is concerned with the unity of God, Thaumiel represents the dual contending forces, struggling, and it is represented by two giant heads with bat-like wings.
The Qliphoth are not the opposite of the Sephirot, but the shadow. They are the chaotic forces that are unleashed when one of the Sephirot is not in balance with the others. Therefore, although Keter is concerned with unity, implicit in its existence is the concept of duality. It is the first emanation from the Ein Sof, the point of consciousness that crystallises out of the vast emptiness. Without the forces of the other sephiroth to balance it, specifically Malkuth below, it would exist as something apart from the Ein Sof, God in his totality. However, since all the paradoxical and contending forces unleashed through Keter find their eventual rest and resolution in Malkuth, balance and the unity of God are maintained.
The ruler of Thaumiel is Satan. Satan in legend was the chief of the angels, holding a position similar to that of Kether. According to Islamic legend, after God created man, Satan and his angels refused to bow down before Adam. Ralph Austin describes that in the thought of the Islamic mystic, Ibn Arabi, the diabolical principle is that "which resists the Self-Realizing urge to create the own-other object (creation) and insists in the sole right of pure spirit and transcendence, this being the reason for Satan's refusal to obey God's command to prostrate himself to Adam, from jealousy for the integrity of pure spirit." Seeing this in a kabbalistic way, this means the refusal of Kether, the pure spirit, to find completion and self-realisation through the act of emanation and creation, terminating in Malkuth. Satan therefore represents spiritual pride and arrogance.
"Second, it is also that principle which insists on the separate reality of cosmic life and substance and which denies all primacy to the Spirit. In other words, it is that principle which would seek to insist on the separate reality of either pole, at the expense of the other, and thus to impair the original wholeness of the divine experience as the Reality by trying to sever the all-important link between "own" and "other" and consign each to mutually exclusive isolation in absurdity". Which neatly fits with the kabbalistic description of Satan as the master of 'The Dual Contending Forces'.