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Subspace (also sub space, headspace, flying, or floating), in the context of a BDSM scene, is the psychological state of the submissive partner. The term is unrelated to the mathematical term subspace.
Subspace is a metaphor for the state the submissive's minds and bodies are in during a deeply involving play scene. Many types of BDSM play invoke strong physical responses. The mental aspect of BDSM also causes many submissives to mentally separate themselves from their environment as they process the experience. Deep subspace is often characterized as a state of deep recession and incoherence. Deep subspace may also cause a danger in newer submissives who are unfamiliar with the experience, and require the dominant to keep a careful watch to ensure the submissive isn't placing him or herself in danger. Many submissives require aftercare.
During the scene, the intense experiences of both pain and pleasure trigger a sympathetic nervous system response, which causes a release of epinephrine from the suprarenal glands, as well as a dump of endorphins and enkephalins. These natural chemicals, part of the fight or flight response produce the same effect as a morphine-like drug, increasing the pain tolerance of the submissive as the scene becomes more intense. Producing a sort of trance-like state due to the increase of hormones and chemicals, the submissive starts to feel out-of-body, detached from reality, and as the high comes down, and the parasympathetic nervous system kicks in, a deep exhaustion, as well as incoherence. Many submissives once reaching a height of subspace will lose all sensation of pain, as any stimulus causes the period to prolong.