The term "outer being" is adopted from Sri Aurobindo. In Vedanta (based on the Mandukya Upanishad) the equivalent might be the Gross or Waking state, and in Sant Mat the physical or Pinda region (see tables here), but that refers more to physical reality and the physical body, and there can be non-physical "outer" or "gross" regions as well.
This is the region of dualistic separative reality. As with all the gradations of being, this is divided into subdisions. So in this case there is an Inner Reality aspect (inner Outer Being), representing ordinary consciousness (the "inner world") which includes the mundane, impermanent personality, ruled by the self-seeking ego; and an Outer Reality aspect (outer Outer Being), representing reductionist matter on the physical level, and various chaotic orders of existence on the hylic and the psychic, and which finally merge with the "Outermost" or Klippotic aspect, representing even further chaotic orders of existence on the different planes.
The psychological distinction between Introvert and Extrovert pertains to the above-mentioned inner division, so the introvert, who lives in his or her own world and is uncomfortable in social situations, is inner-inner Outer Being, and the extrovert, who depends on and interacts with external stimulii, and is uncomfortable when left to him or herself, is outer-inner Outer Being.
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