The monoid-now: a category theoretic approach to the structure of phenomenological time-consciousness.

Human consciousness constantly shifts through time, yet each moment is experienced as "now." This duality, called "the standing-streaming now" in Husserlian phenomenology, can be precisely formalized using category theory: the structure of the "now" corresponds to a monoid, while viewing present moments as discrete points on a timeline corresponds to a coslice category. This mathematical framework clarifies differences between ordinary consciousness and meditative states, such as the "eternal now" described in early Buddhist scriptures (Pali Canon) and Dōgen's Shōbōgenzō, which remarkably reflect a monoid structure.

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Abstract

Human consciousness is characterized by constant transitions in time. On the other hand, what is consciously experienced always possesses the temporal feature of "now." In consciousness, "now" constantly holds different contents, yet it remains "now" no matter how far it goes. This duality is thematized in Husserlian phenomenology as "the standing-streaming now." Although this phrase appears contradictory in everyday language, it has a structure that can be clearly understood and formalized. In this paper, we show that this structure can be described as a monoid in category theory. Furthermore, monoids can be transformed into the coslice category, which corresponds to the way of perceiving present moments as juxtaposed in succession. The seemingly contradictory nature of the "now" as both flowing and standing can be precisely structured and comprehended through the monoid, while the perspective of the "now" as discrete points on a timeline can be effectively formalized using the coslice category. This framework helps us more precisely understand the differences between ordinary consciousness and meditative consciousness, specifically the experience of the "eternal now." We illustrate how the meditative states of consciousness presented in the early Buddhist scriptures (Pali Canon) and Dōgen's Shōbōgenzō remarkably reflect a monoid structure.