The thirty-first path joins Hod, Splendour, to Malkuth, the Kingdom, descending the left side of the Tree to the material world. It carries the letter Shin, whose name means "tooth", and which is one of the three mother letters of the Sefer Yetzirah, the primal trio Aleph, Mem and Shin, from which the alphabet and the basic divisions of the cosmos proceed. The three mothers are assigned to the three elements: Aleph to air, Mem to water, and Shin to fire.
Shin is thus an elemental letter, carrying the formative power of fire, the consuming, transforming and purifying element; its three-pronged form is often read as a triple flame. Its position and its fiery attribution come directly from the ancient Jewish source, where the three mother letters are the fundamental principles holding the cosmos in balance, fire and water at the extremes with air reconciling them, and Shin the letter of the flame at the base of the Tree.