The diagram does not describe things in the world. It describes the condition under which things can appear as things at all.
Inside the enclosing oval are two distinct systems. They are deliberately drawn as different. Each contains a trace of the other inside itself, but never the other as such. Between them is a bidirectional arrow. Neither comes first. Neither is foundational. What matters is the relation.
The oval enclosing them is labelled cobordism. In mathematics, cobordism names a situation where two distinct spaces are not identical yet belong to the same higher-dimensional continuity. Here the idea is used more generally. It says that these two systems are part of a single situation without being reducible to one another. Their unity does not lie in sameness, but in coexistence.
Crucially, the arrow labelled “cobordism” points downward into the system. The enclosing relation is not built out of the parts. The parts exist within it. The whole precedes the pieces, not in time, but in structure.
This already marks a departure from familiar logic. Most logical systems begin with identities and then describe relations between them. This diagram begins one level deeper. It begins with difference that cannot be eliminated.
Each system depends on the other for its definition, but neither can absorb the other without destroying the situation altogether. If they collapse into identity, the system disappears. If they separate entirely, it disappears. Stability lives in the maintained distance.
This is the orbit frame.
An orbit is not a line and not a balance point. It is a structured motion sustained by tension. Two bodies remain distinct while continuously constraining one another. The orbit is neither object. It is the condition that keeps both in play. Collapse the distance and the orbit vanishes. Push the bodies infinitely apart and it vanishes again. Persistence exists only in between.
The orbit frame generalises this idea beyond physics. Communication, cognition, language, governance, and even scientific modelling itself work this way. There is always a system and a counter-system: signal and noise, model and world, rule and exception, self and other. None of these pairs can be resolved into a single term without destroying what they are doing. What persists is the structured relation between them.
That structured relation is what the diagram calls H.
H is not an object and not a substance. It is a constraint. Its job is to prevent collapse. It regulates how close the systems can come without becoming identical, and how far they can separate without losing coherence. It is what keeps feedback loops open rather than closed. It is what limits certainty, precision, and control.
This is why the equation at the bottom matters:
H(f, g) = −H
This is not algebra. It is a structural statement.
It says that the binding function cannot be represented as a stable, positive entity. The moment you try to define it directly, it flips orientation. It becomes its own inverse. Any attempt to fully capture the relation from within one system distorts it. The structure is real, but it cannot be fixed without being broken.
This is not a paradox for effect. It is a statement about limits.
In physics, perfect closure would require infinite precision or zero dissipation. In economics, costs displaced from one domain reappear elsewhere as externalities. In language, meaning is inseparable from ambiguity. In control systems, total control produces instability. In each case, what keeps the system alive is not resolution, but regulated incompleteness.
H is the name for that regulation.
This brings us to the logical orbit.
Classical logic, including Aristotelian logic, operates effectively inside bounded domains. It assumes stable identities and evaluates relations between them. That power is real and indispensable. But it depends on a deeper condition it cannot itself describe: every logical system requires a boundary it cannot formalise from within.
The logical orbit names that condition. It recognises that every system defines itself against what it excludes, that the exclusion is active rather than passive, and that the excluded element returns as uncertainty, error, surprise, or novelty. Systems do not fail because of this. They exist because of it.
What this framework is pointing to is not a new competing logic. It is not an alternative formalism. It is the structural field within which all formalisms operate.
Aristotelian logic works inside this field. So do probabilistic, modal, and computational logics. They are tools for navigating regions of the orbit. They are not the orbit itself.
What lies “under the underneath” is not another rule, but a constraint: maintained difference, regulated tension, structured absence.
If this level is missed, systems appear broken when they are functioning normally. Ambiguity looks like failure instead of fuel. Contradiction looks like error instead of structure. Control is pursued where balance is required.
Seen clearly, different things come into focus.
Stability appears as motion.
Meaning appears as a property of distance.
Continuity appears as something sustained, not solved.
The diagram is not abstract decoration. It is an attempt to draw the shape of persistence itself.
Not the thing.
Not the rule.
But the condition that keeps things possible.
Daedelus Kite 