Topological Ethics Paper 1

This concept paper proposes Topological Ethics, a way of organizing AI alignment constraints as a landscape over an agent's possible behaviors: cooperative outcomes form low-cost "wells," harmful trajectories become high-penalty regions, and cultural change acts as a slow input that reshapes the landscape within protected bounds. The geometry, borrowed from metric-affine physics, is an organizing analogy rather than a formal mapping. The paper then tests the simplest version of the idea, a penalty that protects a simulated human's options, in four small gridworld experiments. The penalty kept agents from trapping a stationary human, but with a goal-seeking human it achieved safety mainly by keeping the agent away, and cooperation appeared only when the penalty encoded a precise forecast of the human's next moves. The paper concludes that the hard problem in this approach is not shaping the landscape but knowing what the human intends, and it sets out the open problems as a research agenda. Code and data are archived at doi:10.5281/zenodo.23841251; full experimental details are in the companion technical report. AI disclosure: The experiment code, analyses, and editing were carried out with the assistance of Claude (Anthropic).