The article departs from the Teilhardean opposition of the inside (le dedans) and the outside (le dehors), notions of reflection and self-enclosure (enroulement sur lui-même), and an experimental law of recurrence (une loi expérimentale de recurrence). The author supplements them with his own apparatus of simplex-complex transformations as an epistemic principle and a set of related practices. The article starts with quantum emergence, forging its inside and outside by an interface and an alternative way to represent it as Diracean membrane, branes of the string theory, and the eigenform. The interface instrumentality for operating the inside and outside of the quantum allows their structured totality to enact agency potential. Simplex-complex transformations allow to represent an evolutionary series of agency transformations as modules of a single model up to a developed human self. The article discusses the recurrence, enclosure, and other trickeries of emergence as well as their representation with the help of cognitive metaphors likme Ouroboros or mathematical formalisms like the Moebius strip. It proceeds to chemical catalysis and autocatalysis, further to emergence of autopoiesis, and finally to biogenesis. Forms of life internalize environmental productive factor (Umwelt) by duplication, recursion, enclosing, folding, etc. to evolve a series of codes, making up integral genetic agency and genome as its key vehicle. The article considers organismic symbiosis and respective autocatalytic recursions, addresses the emergence of signal systems and cognition, which is parallel to and duplicating neural processes. It discusses primary cognitive abilities and their further autocatalytic transformations into a range of more advanced capabilities, along with the emergence of higher levelhigher-level signal systems. Finally, it ends up by discussing anthropogenesis and stepwise emergence and advancement of human language and thought in a series of internalizations of communicative contexts (frames, typical communicative settings, mementoes and typical remembrances, etc.) into codes of the first, second, and further orders.