The third eye of Shiva indicates transcendental wisdom. Implicit in the idea of desire, is the idea of choice. Desire means the quest for one thing over another. To want something one must not want another thing. In other words, one needs two eyes, one that selects and the other that rejects. When both eyes are shut it means nothing is selected or rejected, nothing is approved or disapproved, nothing is included or excluded. Everything is the same. The third eye therefore embodies absence of discrimination and choice, hence absence of desire.
