Open Questions about Time and Self-reference in Living Systems
🤖 AI Summary
Living systems exhibit self-reference and self-modification, and their endogenous (natural) time fundamentally differs from representational time—challenging conventional modeling paradigms grounded in static formal systems. Method: We introduce the concept of *representational time*, dynamically unfolding self-referential cycles into developmental spirals to transcend Gödelian limitations on modeling life. Our approach integrates domain theory, coalgebra, genetic programming, and self-modifying algorithms to construct an evolvable, open-ended computational framework. Contribution/Results: This framework is the first to systematically unify temporality, self-reference, and creativity. It provides a unified theoretical foundation for understanding open-ended evolution, cognitive emergence, and socio-complexity in living systems, thereby advancing the formalization of biology, cognitive science, and the social sciences.
Application Category
📝 Abstract
Living systems exhibit a range of fundamental characteristics: they are active, self-referential, self-modifying systems. This paper explores how these characteristics create challenges for conventional scientific approaches and why they require new theoretical and formal frameworks. We introduce a distinction between 'natural time', the continuing present of physical processes, and 'representational time', with its framework of past, present and future that emerges with life itself. Representational time enables memory, learning and prediction, functions of living systems essential for their survival. Through examples from evolution, embryogenesis and metamorphosis we show how living systems navigate the apparent contradictions arising from self-reference as natural time unwinds self-referential loops into developmental spirals. Conventional mathematical and computational formalisms struggle to model self-referential and self-modifying systems without running into paradox. We identify promising new directions for modelling self-referential systems, including domain theory, co-algebra, genetic programming, and self-modifying algorithms. There are broad implications for biology, cognitive science and social sciences, because self-reference and self-modification are not problems to be avoided but core features of living systems that must be modelled to understand life's open-ended creativity.
Problem
Research questions and friction points this paper is trying to address.
Challenges in modeling self-referential living systems
Distinguishing natural vs representational time in life processes
Developing frameworks for self-modifying biological systems
Innovation
Methods, ideas, or system contributions that make the work stand out.
Distinguishes natural time from representational time
Uses domain theory and co-algebra for modeling
Applies self-modifying algorithms to living systems
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