【Insensible】 ,  【insensitive】 ,  【impassible】 ,  【anesthetic】  mean unresponsive to stimuli or to external influences.

【Insensible】 usually implies total unresponsiveness, and therefore unawareness or unconsciousness such as may result from blunted powers of sensation, obtuseness of mind, apathy, or complete absorption in something else.

【Insensitive】 implies sluggishness in response or less than normal susceptibility; more specifically, it suggests dullness rather than acuteness of sensation or perception, thickness rather than thinness of skin, callousness rather than sympathy or compassion.

【Impassible】  basically and historically implies absence of response because of incapacity for feeling or suffering, but is often used synonymously with impassive or in reference to persons who by discipline have conquered the normal human susceptibility to pain or suffering or in reference to things in contrast with persons or creatures thought of as beings who through necessity of nature suffer pain or are susceptible to injury.

【Anesthetic】 implies a deadening of the mind or senses by or as if by such a drug as ether and therefore an induced rather than a natural insensitiveness.