Physics has been haunted by coincidences. The Sun and Moon appear almost exactly the same size in our sky. Certain physical constants seem delicately balanced so that atoms, stars, and chemistry can exist at all. When confronted with these near-matches, we usually reach for one of two explanations: sheer luck, or the anthropic idea that we could only observe a universe where things happened to work out.
In a new paper, I argue for a simpler and more structural explanation: persistent things don’t live just anywhere — they live at the edge of what’s physically allowed.
The idea is straightforward. Any structure that lasts must satisfy constraints: forces holding it together must beat forces trying to tear it apart; coherence must exceed noise; order must survive disturbance. These requirements define an admissible region in parameter space — a zone where persistence is possible at all. But systems don’t spread out evenly across this zone. They migrate to its boundary: the point farthest from disruption while still remaining viable. This isn’t fine-tuning or design. It’s simply where survival closes.
Crucially, the edge does something special. Deep inside the allowed region there is slack — many configurations could work, and the system’s identity is underdetermined. At the boundary, that slack disappears. Constraints saturate. The system is forced into a single, repeatable configuration. In a time-free sense, this is where facts become consistent. Stable structures don’t just prefer the edge; they require it to exist as definite things.
Once you see this, many “coincidences” stop looking mysterious. When multiple constraints apply at once — for example, orbital stability, tidal disruption, and long-term coherence — their admissible regions intersect in a narrow window. Quantities that depend differently on those constraints are squeezed into similar numerical ranges. The numbers line up not because the universe is lucky, or because observers demand it, but because that’s where persistent structure is geometrically forced to live.
The paper develops this idea mathematically, shows how it reproduces classical limits like the Roche boundary for moons, and reframes them using a time-free information-capacity principle. It also makes concrete predictions — for example, that Sun–Moon-like eclipse matching should be impossible around the smallest stars, a claim future exomoon surveys can test. Just as importantly, it predicts where coincidences should not appear: in systems dominated by extreme hierarchies.
The broader message is a shift in perspective. Instead of asking “Why do these numbers happen to match?” we should ask “Where can structure persist at all?” Often, the matching isn’t something that needs explaining away — it’s a visible signature of living at the edge.