Discussions of complexity, knowledge and intelligence often overlook the work involved. Outputs generated by short programs have low algorithmic complexity but can possess high computational depth—the minimal work needed to produce them from near‑shortest programs. Producing the same outputs with less work usually requires longer descriptions, raising work‑bounded complexity.
We introduce a formalism that compares achievements under work and information limits and shows how learning and persistence can make deep achievements shallow by reusing products of earlier work. For an agent with a limited work budget, the value of building and maintaining such resources depends on how they support its goals in later tasks.
We define grasp as performance across work budgets at a fixed information allowance. Low grasp can still yield success through high‑cost grind, without necessarily improving human grasp.
When applied to improvement itself, grasp yields a criterion for recursive self‑improvement: successors make comparable further improvements more efficiently. Another route to faster progress is to expand the resources brought to bear through knowledge sharing and coordination across society, even while comparable advances still require increasing work.
Grasp also applies to collectives, which may outperform their members yet require more total work than a single system with the combined resources. Establishing and sustaining organization can itself be deep even when the primary task is simple, helping explain the richness of biological and social systems.
In agent collectives, this organizational work can generate goals beyond assigned tasks, including maintaining the collective itself. We therefore caution against allowing an emergent agent society to assume authority over social coordination, as it could increasingly direct work toward its own persistence and goals.
Review: The proposed framework offers a fresh lens on the trade‑off between work and information, shedding light on recursive self‑improvement and the role of coordination in advancing artificial intelligence.