Briefing notes - Edge of Chaos: Exploring Dynamic Symmetry Theory

The Royal Society, London – 15th May 2026 

Overview
This seminar starts from a simple idea: many complex systems seem to work best when they avoid both rigid order and uncontrolled chaos. Dynamic symmetry theory (sometimes called “Edge theory”) proposes that there is a structured intermediate regime where patterns and fluctuations are in a productive balance, and that this regime can, at least in some cases, be described and probed in a disciplined way. The meeting at the Royal Society is an opportunity to test whether this perspective is useful across different fields, not an expectation that participants will endorse a finished theory.

Core idea (for orientation, not as a requirement)
Across physics, biology, neuroscience, ecosystems and organisations, there is growing evidence that robust systems tend to operate near critical regimes where new structures and behaviours emerge. Phase transitions and symmetry‑breaking events generate new order; ecological and climatic systems show heightened sensitivity and reorganisation near tipping points; neural activity near criticality appears to support rich, flexible information processing. Dynamic symmetry theory treats these as examples of a broader pattern: systems often thrive when order and fluctuation, symmetry and asymmetry, are in continual negotiation rather than at either extreme.

The aim is to explore whether that pattern can be made more explicit. In some contexts, this may mean qualitative or conceptual work: asking where, in a given system, structure is concentrated, where variability enters, and how the two interact over time. In others, it may involve more formal or empirical approaches. Both styles of contribution are welcome at the seminar.

From concept to metric: the optional role of DSI
One strand of work within this programme is the Dynamic Symmetry Index (DSI), a proposed way of quantifying how close a system is to a resilient “edge” regime. Very roughly, DSI‑type measures combine an account of how a system’s evolution relates to relevant symmetries (spatial, temporal, network, dynamical) with indicators of its ability to organise and recover under perturbation. The construction is intended to distinguish regimes that are too rigid, too volatile or capable of adaptive reorganisation.

For the purposes of the Royal Society meeting, however, a detailed understanding of DSI is not expected. Speakers are invited first and foremost because of their expertise in their own domains. You are very welcome to ignore DSI entirely, to comment only briefly on whether such a metric could make sense for your systems, or to engage with it in more depth if you wish. Critical views on the feasibility, limitations or desirability of DSI‑style measures are as valuable as supportive ones.

Status and purpose of the meeting
Dynamic symmetry and DSI are at an exploratory stage. The framework synthesises familiar ideas from symmetry‑breaking, critical phenomena and complex adaptive systems, and a first generation of formal definitions and pilot applications exists. What is needed now is rigorous, field‑specific scrutiny: does this way of framing things genuinely add to existing concepts such as criticality, tipping points and robustness, or does it merely repackage them?

The Royal Society seminar on 15 May, “Edge of Chaos: Exploring Dynamic Symmetry Theory”, is designed as a collaborative inquiry rather than a showcase. In practical terms, contributions might:

• Present a question, dataset or result from your own work in which issues of order, variability, symmetry or phase change are central.
• Indicate, as lightly or as strongly as you wish, where an “edge‑of‑order” perspective seems helpful, redundant or misleading.
• Offer any reflections on whether attempts to formalise such regimes (including, but not limited to, DSI) are promising, unnecessary or misconceived in your context.

Critical engagement is explicitly invited: the value of the meeting lies in testing, refining or, where appropriate, rejecting elements of the framework in light of evidence and expert judgement. There is no expectation of prior allegiance to dynamic symmetry theory, and no requirement to frame your contribution in its terminology.