Most systems that try to reference themselves across time, scale, destroy themselves.
The failure modes are boringly consistent:
runaway growth
collapse
phase drift / incoherence
What’s unusual is not that systems fail.
It’s that any survive at all.
The document is an attempt to characterize the survivors.
When you formalize “recursive self-reference without accumulating error,” you get a hard constraint on scale ratios. In the simplest nontrivial case:
λ² = λ + 1
with φ as the only positive fixed point.
I’m not claiming this is a new law, and I’m not appealing to aesthetics, biology, or teleology. This is a structural claim:
recursive systems are extremely fragile, and only a narrow class avoids blowing up, collapsing, or decohering.
The note shows the same constraint and the same failure modes appearing in places that normally don’t talk to each other: fixed points, fluid modes, learning systems, biological loops, and self-models.
If this is wrong, it should be easy to falsify.
A single counterexample — a recursively self-referential system that’s provably stable outside this constraint — would break the entire framing.
Most systems that try to reference themselves across time, scale, destroy themselves.
The failure modes are boringly consistent:
runaway growth
collapse
phase drift / incoherence
What’s unusual is not that systems fail. It’s that any survive at all.
The document is an attempt to characterize the survivors.
When you formalize “recursive self-reference without accumulating error,” you get a hard constraint on scale ratios. In the simplest nontrivial case:
λ² = λ + 1
with φ as the only positive fixed point.
I’m not claiming this is a new law, and I’m not appealing to aesthetics, biology, or teleology. This is a structural claim:
recursive systems are extremely fragile, and only a narrow class avoids blowing up, collapsing, or decohering.
The note shows the same constraint and the same failure modes appearing in places that normally don’t talk to each other: fixed points, fluid modes, learning systems, biological loops, and self-models.
If this is wrong, it should be easy to falsify.
A single counterexample — a recursively self-referential system that’s provably stable outside this constraint — would break the entire framing.
I haven’t found one yet.
Actual Title: "One Equation, ~200 Mysteries: A Structural Constraint That May Explain (Almost) Everything"