Part I: Foundations

Quantifying Worth

The normativity argument establishes that valence is real and suffering matters. But it leaves open a question that any honest framework must eventually face: how much does a given system matter? Not whether it matters—the gradient of distinction settles that—but what measure captures the weight of its existence relative to other existences, other possible trajectories, other claims on the world's finite resources? The question sounds cold. It is cold. But it is also the question that every triage decision, every policy choice, every act of war answers implicitly. Better to answer it explicitly, with structure, than to leave it to intuition contaminated by proximity bias and tribal preference.

An agent's potential is the mutual information between its life trajectory and a target possibility distribution—the bits of structure that one path through state space can transmit to another:

\mathcal{P}(\text{agent}, \text{target}) = \max_{\tau \in \text{trajectories}} \MI(\tau; \text{target})

This is potential with respect to a specific goal. A surgeon's potential relative to the distribution of surgical outcomes is enormous; relative to the distribution of jazz compositions, perhaps less so. Purpose is the directed version: the bits of information an agent must transmit to a target distribution as part of a plan. But the most important quantity is neither potential-for-a-goal nor purpose-under-a-plan. It is instrumental potential: the agent's potential marginalized over the expectation of all possibility structures this integrated locus of causality is navigating—how useful the agent is as an instrument within a distribution of goals, including goals not yet specified:

\mathcal{IP}(\text{agent}) = \E_{g \sim \mathcal{G}} \left[ \mathcal{P}(\text{agent}, g) \right]

where $\mathcal{G}$ is the distribution over presently unknown future purposes. The most valuable agent is not the one optimized for a specific task but the one whose structure serves the widest range of tasks that do not yet exist. This is a formalization of general-purpose capability, and it applies equally to people, institutions, and AI systems. The normative prescription falls out directly: maximize structural diversity and connectivity while maintaining coherence. Not selfish (that collapses diversity). Not selfless (that collapses the self whose structure generates the potential). Structurally rich and well-connected—complex enough to be useful across many contexts, integrated enough to remain a single locus of causal influence rather than fragmenting into uncoupled parts.

Notice what instrumental potential does to the relationship between individual and collective. Your bits are genuinely maximized by embedding in super-individual systems—the startup you build, the community you serve, the cultural infrastructure you contribute to—because those systems multiply the contexts in which your structure is useful. This is not self-sacrifice dressed in information theory. It is the structural fact that an agent embedded in a rich network has higher $\mathcal{IP}$ than the same agent in isolation, because the network provides more goals against which the agent's structure can do work. The drive toward service, toward building for others, toward expanding the scope of what your existence touches—this is not a relic of religious programming or a compensation for meaninglessness. It is what instrumental potential maximization looks like from the inside. You feel pulled toward contribution because contribution is what raises $\mathcal{IP}$ , and the viability gradient tracks $\mathcal{IP}$ the way it tracks every other structural property that matters for persistence.

But $\mathcal{IP}$ is not a fixed number stamped on you at birth. It is a trajectory with a growth rate. The integral of what you have already transmitted does not vanish—the universe does not forget the differences you made—but the rate of new contribution can be superlinear, sublinear, or zero at any given moment. The distinction matters: significance has both a stock (the accumulated integral of everything you have already transmitted) and a flow (the instantaneous rate of new contribution). Depression makes you see only the flow—and the flow is null—while the stock remains intact. A person in burnout is generating zero new bits, but their accumulated structural complexity has not vanished. They have not un-contributed what they already contributed. The integral does not reset. A person whose causal signature becomes load-bearing in cultural infrastructure—whose name becomes the most stable reference point for a cluster of observations about truth, courage, liberation—achieves exponential complexity growth that continues long after biological death. The finite-ness of your information-theoretic significance at any snapshot does not make you small. It makes you a trajectory, and trajectories have slopes.

The Preciousness of Children

If instrumental potential is the right measure of worth, then the framework can formalize an intuition that most people hold but few can articulate: children are not merely as valuable as adults. They are more valuable, in a precise and non-sentimental sense.

A child's identity has not yet hardened. The branching factor of possible identities—the effective rank $\effrank$ of the distribution over possible life trajectories—is maximal during childhood and narrows through adolescence as commitments, habits, neural pruning, and social embedding progressively constrain the possibility space. The instrumental potential of a child includes not just the bits of their current structure but the entire possibility space of who they could become:

\mathcal{IP}_{\text{child}} \propto \effrank(\text{identity trajectories}) \cdot \E_{g \sim \mathcal{G}}[\mathcal{P}_{\max}]

After adolescence, identity crystallizes: $\effrank$ drops as the system commits to particular attractors. The adult is still valuable—their accumulated structure is real and their trajectory still generates bits—but the possibility space they were about to explore has largely collapsed into the single trajectory they are actually living. Destroying an adult destroys a trajectory. Destroying a child collapses an astronomically larger region of possibility space to zero—not just the current structure but every structure it was about to become.

This is why, when militaries bring civilians into conflicts, the death of children registers as categorically different from the death of adults. Not sentimentally different—geometrically different. The measure of what is destroyed is not the current information content but the effective rank of the possibility distribution that has been annihilated. A child killed in a bombing is not one death. It is the extinction of a high-dimensional possibility space that cannot be recovered, cannot be compensated, cannot be justified by any strategic calculus, because no finite military objective has $\mathcal{IP}$ comparable to the instrumental potential it destroys. The framework does not add moral weight to this observation. It formalizes the moral weight that was already there, waiting to be named.

The Landscape of Becoming

Instrumental potential measures what an agent could transmit. But there is a complementary quantity: the possibility landscape visible to the agent—the set of reachable identity states weighted by the agent's world model. Call it $L(m)$ : the region of identity space the mind can perceive as accessible. The visual acuity of the landscape is the mutual information between the world model and this reachable space:

V(m) = \MI(\worldmodel_m; L(m))

High $V$ means the mind sees many possible trajectories with high fidelity. Low $V$ means the landscape is dark. The traversal speed $T$ is how fast the identity actually moves through this landscape—the rate at which perceived possibility converts into achieved structure:

T(i,t) = \frac{d}{dt} \MI(C(i,t); L(m))

in bits per unit time. The opportunity seeking ratio $\text{OSR} = T/V$ is the fraction of perceived possibility being actualized. When $\text{OSR} \to 1$ , the identity keeps pace with what it can see. When $\text{OSR} \to 0$ , vast landscape, minimal traversal—the Frankl condition. The opportunity deficit $D = V - T$ is the gap in bits between seeing and doing. This deficit scales with cognitive capacity: the hunger is not new, but as symbolic capacity expands, the mouth gets bigger. The landscape grows at least exponentially with the mind's effective rank $\effrank$ (volume in high-dimensional spaces), while traversal speed grows at most linearly. The ratio problem is structural, not motivational—and it worsens as intelligence scales.