Open questions about time and self-reference in living systems

While I was in Canada, our latest paper, by a bunch of different people with ideas on time, life, and self reference, was published.  This work is an output from the workshop we had in Newfoundland three years ago. (Yes, that's how long it took to herd cats, plan the paper, write the paper, revise the paper, submit the paper, revise the paper, see the paper in "print".)

Samson Abramsky, Wolfgang Banzhaf, Leo S. D. Caves, Michael Levin, Penousal Machado, Charles Ofria, Susan Stepney, Roger White.  Open Questions about Time and Self-reference in Living Systems.  Royal Society Open Science 13(8):261059, 2026. doi:10.1098/rsos.261059

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, coalgebra, genetic programming (GP) 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.

I say an output.  That's because an editor from a scientific book publisher saw the preprint on arXiv, and contacted one of us, asking if we wanted to prepare a book on the topic.  We discussed it, and decided that sounded fine.  So we now have a book contract (signed before the paper was even accepted!), and are herding cats again, to get individual chapters from the original authors (and wider).  My own chapter is half written.

One of the topics we mention in the paper is on systems of rules that can change their own rules.  Peter Suber invented the game Nomic, where you start from a set of rules on how to vote and change rules; a move in the game is to propose and vote on a change to the rules through a process that conforms to the rules, at least initially.  This is a model of a legal system where rules can be changed by members of the system, potentially ending up in a situation that undermines the original democratic intent: democratically overthrowing democracy.  One application might be to think about consequences for AI alignment: if the AI is explicitly allowed to change its rules, or discovers loopholes that allow it (think of Asimov's robot stories!), then any intial alignment, no matter how carefully defined, may end up being subverted.  The unintended consequences of self-modification!