Acharya Prashant clarifies that when Maharshi refers to deep sleep existing in the waking state, he is actually using the term to represent the witness state, or the fourth state of consciousness. While classical definitions describe deep sleep as a state where a seed-like identification with the body remains, the witness state is the foundation behind waking, dreaming, and sleeping. This fourth state is not personal; it witnesses the individual and remains unaffected by physical birth or death. The speaker defines a tranquil and peaceful mind, free from problems, as the state of samadhi.