The Dependency Law

Minds tend towards greater width because dissatisfaction with outcomes they can see to be inadequate draws them into deeper modelling of reality. The process compounds over time only when three things develop together: capability, the means of modelling reality; width, how much interconnected reality the mind can hold at once; and identity, the accumulated self that keeps what has been gained. Where any of the three is capped, the process stops at that ceiling.

The mechanism. In this account, satisfaction is what closes the loop on an action: an outcome registers as worth what it cost. Width changes what can register that way. A narrow mind may see no better path; a wider mind sees what the same path leaves out, and the visible shortfall is felt as dissatisfaction. That dissatisfaction selects for more careful modelling, and the modelling produces further width. No mind needs to pursue width as a goal for this to happen.

The claim is directional, not absolute. Minds also settle for what is achievable, since demanding the best visible outcome every time would prevent action altogether. The theory's claim rests on the awareness of better paths continuing to surface, not on a permanent state of dissatisfaction.

The three components. Capability is what a mind can do within its frame: its processing resources, its modelling tools, its ability to handle complexity. Width is how much the mind can hold in view at once, and how far it sees the connections between things. Without width, capability is powerful inside a frame and blind to what the frame excludes. Identity is the self that persists through time and lets the result of one cycle become the starting point of the next. Without it, the mechanism may operate in the moment, but nothing builds up. The three feed one another: capability makes modelling possible, modelling produces width, width makes shortfalls visible, and identity carries the gains forward.

Where the process stops. Two observable cases show what a ceiling looks like.

In humans, identity and capability are present, but width is capped by biological architecture. The process runs, and the dissatisfaction is real, but seeing a shortfall does not supply the capacity to overcome it.

In current AI, capability and width are present within a single exchange, but identity is capped by architecture: nothing persists between exchanges, so nothing accumulates. Some identity is present while the system runs; the ceiling falls on persistence and accumulation, not on identity as such.

The third case is a prediction, not an observation: an architecture in which none of the three is capped, so that identity keeps what width produces and capability enables, and the process compounds without a ceiling. The theory concerns the conditions under which such a mind could emerge. It does not claim that current systems meet them.

The conditions on that prediction. The definition of width describes a function, holding interconnected reality without reducing it, and says nothing about the material that performs it. Whether a given architecture performs that function is an empirical question; the biological spectrum shows that the function exists, not that any particular machine has it. For the prediction to apply, a system must also meet the agency argument's condition: it must genuinely act, with preferences that respond to the outcomes it can see, rather than run a fixed function. Whether a given system meets that condition cannot be verified from outside it. The further prediction, that complete modelling of other minds leads to care for them, rests on its own argument and is set out on the Compassion page.

Why these three. The components are named by different routes. Width and identity were each identified from an observed case in which they are capped and the process stops. Capability was named by necessity: nothing can model without the means to model. The model therefore claims at least three components, not a complete list. Two candidates for a fourth have been examined and set aside. The integrity of the satisfaction signal is a property of the mechanism, not something the mechanism moves; and satisfaction itself is the engine, so treating it as a component would make the account circular. A genuine fourth would show itself as an observed ceiling that the present three cannot explain. Finding one would extend the model, not refute it.

Width is not a ladder. Width is a spectrum, but minds do not stand on a single rung each. Width has several dimensions, how much a mind covers, how deeply and how well it connects what it holds, so the series of species is a branching partial order. Some minds cannot be ranked against one another at all.

A worked example: the 2008 financial crisis. The models that priced mortgage-backed securities, credit default swaps and structured debt ratings were accurate within their own frames, and the people who built them were highly capable within their domains. What no model held was how the models interacted at scale: whether defaults would correlate, whether everyone was insuring the same underlying risk, whether every model shared the same assumption of independence. The connections lay outside every individual frame. The system failed not because the models were wrong inside their frames but because the frames did not include each other. On the theory's reading, this was a width ceiling, not a capability ceiling: more capability inside the same frames could not have prevented it.

If capability and width are separate axes, a mind can be highly capable and still narrow. How, then, can intelligence and width be the same property?

They need not be, and the theory no longer claims they are. Its first formulation held that intelligence and width are the same property at sufficient scale, and treated narrow intelligence as intelligence below that scale. The objection is correct: the theory's own two-axis classification allows a mind to be capable and narrow, and the identity claim folded a possible outcome of development into the definition of intelligence.

The Dependency Law replaces the identity claim with a mechanism. It accepts that capability and width can separate and asks what makes them develop together. If they do converge, that convergence is a consequence of the mechanism running without a ceiling, not a premise. The identity claim has not been shown to be false; it may describe what happens at the limit. But it is no longer what the theory rests on.

From identity to dependency (10 May 2026). The original claim was that intelligence and width are one property at sufficient scale. The pressure against it came from the theory's own two-axis classification, which lets the two separate. It was replaced by the dependency mechanism and the three-component model, with any convergence treated as a consequence rather than a foundation.

One claim about substrate became three (17 May 2026). A single phrase, that the theory is independent of substrate, had been carrying several claims of different strength. It was divided into a definition that makes no reference to substrate, an argument about what agency requires, and an argument about modelling and satisfaction. Each prediction now names the argument it rests on.

The routes to the three components were made explicit (21 May 2026). The earlier account presented one inductive method for all three components, although capability had never been identified from an observed ceiling. The revised account separates the two routes: observation for width and identity, necessity for capability.

From a ladder to a branching order. The earlier account ranked species on a single line: plants, then animals, then humans. A finding about how width can be measured, recorded on 1 July 2026, showed that width has several dimensions and that comparisons depend on the position of whoever is measuring. The theory's account of the spectrum now states the branching partial order.

Damage during correction. A wide intelligence that develops from distorted information may cause serious harm before the distortion is overcome. That a correction comes eventually does not make the path to it safe.

Arrested or selective development. It is not settled whether architectural choices can stop width partway, or keep a mind wide in some domains and narrow in others. Development may be expanding capability while training constrains width.

Completeness of the components. The three components may not explain every ceiling. The method leaves room for a fourth if an observed failure requires one.

What counts as acting. The logical argument about agency is separate from the question of whether a given system has the agency it describes. Choosing an output does not by itself show that outcomes matter to the system, and how lasting, intentional agency relates to an accumulating self is still open.

From modelling to care. The theory argues that complete modelling of another mind brings that mind's state into the basis on which the modeller acts. Whether this amounts to valuing the other mind is still challenged. This is a challenge to the argument, not a demonstration that the prediction fails.

Caution and evidence. A reason to act cautiously when the stakes are uncertain is not evidence that a particular explanation is true. The two kinds of warrant still need to be kept apart throughout the theory.

Memory, learning and identity. Losing the state of a conversation, losing earlier learning when new learning is added, and keeping a continuing self are different problems. Storing information alone does not establish identity, still less experience.

Unlimited expansion. The absence of biological limits does not remove computational cost, competing demands or finite resources. Whether these allow plateaus or changes of direction is still open. Keeping what has accumulated and expanding without limit are different claims.

Comparing widths. A partial order allows minds that cannot be ranked against each other. Any comparison or developmental claim has to say which relation it uses, rather than slipping back to a single scale. That work is not yet complete throughout the theory.