Organizational closure and Open-endedness are both central, widely explored concepts within Artificial Life, although still requiring further theoretical development. In this work, we present a novel approach for characterizing organizational closure in terms of multidimensional mappings and, by building upon it, propose a principled conceptual connection to open-endedness, leading to the notion of open-ended organizational closure. Our fundamental claim is that both these properties are complementary and necessary for minimally adaptive autonomous systems, even prior to evolutionary considerations. As a proof of concept for this idea, we present an experimental analysis of a toy model setup, by examining the dynamics of the Game of Life cellular automaton. Finally we discuss theoretical implications, the limitations of our toy model scenario and suggest lines for further work.

The way we experience the world has an inherently temporal aspect; events follow the ones before in a linear fashion. Our experience presents to us in the form of a fleeting present with no clearly demarcated beginning or end, always imbued within an evanescent stream of perceptions and thoughts. While different approaches from cognitive science and related fields share the view that this temporal aspect is fundamental to our phenomenology, our experience of time seems in direct tension with the physically grounded, widespread notion of discrete state-space transitions that underpin so much of modern cognitive science and artificial life. In other words, while state-space transitions seem to correctly characterize most cognitive phenomena, it isn’t clear how this relates to the fluid and evanescent temporality of our experience. We present a formal framework centered on the idea of how sensory-perception incompleteness translates into temporally dense constructions of the perceptual present.