The accelerating development and deployment of AI technologies depend on the continued ability to scale their infrastructure. This has implied increasing amounts of monetary investment and natural resources. Frontier AI applications have thus resulted in rising financial, environmental, and social costs. While the factors that AI scaling depends on reach its limits, the push for its accelerated advancement and entrenchment continues. In this paper, we provide a holistic review of AI scaling using four lenses (technical, economic, ecological, and social) and review the relationships between these lenses to explore the dynamics of AI growth. We do so by drawing on system dynamics concepts including archetypes such as "limits to growth" to model the dynamic complexity of AI scaling and synthesize several perspectives. Our work maps out the entangled relationships between the technical, economic, ecological and social perspectives and the apparent limits to growth. The analysis explains how industry's responses to external limits enables continued (but temporary) scaling and how this benefits Big Tech while externalizing social and environmental damages. To avoid an "overshoot and collapse" trajectory, we advocate for realigning priorities and norms around scaling to prioritize sustainable and mindful advancements.