beyond_turbulence

We model the dementia caregiving experience as a topological manifold M whose points represent care states and whose paths encode caregiving trajectories.

Drawing on ethnographic data from the NPR report by Ashley Milne-Tyte, we formalize concepts of caregiver burden, crisis points, wandering behavior, and memory care transitions.

The framework uses theory (topological groupoids) to model the relational dynamics between caregiver and care-receiver. We prove theorems concerning crisis manifolds, wandering as geodesic deviation, and the phase transition from home care to institutional care.

The analysis reveals that caregiver exhaustion corresponds to curvature singularities, while memory care facilities represent attractor basins with lower metabolic cost. All constructions are implemented in minimal Scheme and λ-calculus.

culture

Abstract. 

We model the dementia caregiving experience as a topological manifold M whose points represent care states and whose paths encode caregiving trajectories. 

Drawing on ethnographic data from the NPR report by Ashley Milne-Tyte, we formalize concepts of caregiver burden, crisis points, wandering behavior, and memory care transitions. 

The framework uses theory (topological groupoids) to model the relational dynamics between caregiver and care-receiver. We prove theorems concerning crisis manifolds, wandering as geodesic deviation, and the phase transition from home care to institutional care. 

The analysis reveals that caregiver exhaustion corresponds to curvature singularities, while memory care facilities represent attractor basins with lower metabolic cost. All constructions are implemented in minimal Scheme and λ-calculus.