"There is a room in the Department of Mysteries that is kept locked at all times. It contains a force that is at once wonderful and more terrible than death, than human intelligence, than the forces of nature." - Albus Dumbledore
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The High Priestess, along with The Magician, encompass the base energies of the world. While the Magician represents outward power, the High Priestess is the deepest, most secret knowledge, the feminine Yin to the Magician's masculine Yang. It is a card filled with the mystery of the unconscious and unknown, an invitation for meditation and intuition.
The incredible force Dumbledore refers to is the unseen power of Love, one of the most ancient, powerful forms of magic. It is Lily's abundant love which creates the undefeated protection over Harry, as well as giving him a spiritual weapon that Voldemort's shattered soul could never comprehend. Harry's understanding in the secret of love is what separates him from the cold-hearted, power-hungry Tom Riddle, ensuring that he never wavers from the path of good.
In the Rider-Waite tarot, the High Priestess holds a half-concealed scroll, containing the mysteries of both things that are spoken as well as those that are implicit. This is represented by the bundle in Lily's arms - it bears her infant child, the source and expression of her motherly love, and the one thing that most confounds and eludes Voldemort. The High Priestess is depicted seated before a veil, which conceals, yet hints at, the secrets of her knowledge. She is also associated with the "underworld" - the dark, unconscious realm. These aspects are together embodied in the ancient veil from the Department of Mysteries, which seems to be a sort of gateway to "the other side". Finally, weeping willows frame this card because in Druidic belief, the willow tree represents water, the moon, and psychic energy - all common aspects of the High Priestess card - and also because it is the wood of Lily's wand.