The Law of Field Scale — A Dynamical Model of System Scale, Conservatism, and Innovation Capacity

Why do large-scale systems tend to become more stable but less innovative? Why can small-scale systems generate new structures more easily, while often lacking long-term stability? Why do organizations, languages, cognitive systems, and civilizations become increasingly conservative as their scale grows? This work proposes a dynamical model of the relationship between system scale and structural evolution. The framework argues that scale is not merely a measure of system size. It systematically changes the effective ranges of compression strength, openness, resolution availability, and path dependence. Under sustained input and long-term operation, large-scale systems tend to accumulate deeper historical structures, producing higher compression, lower openness, stronger familiar-path locking, and greater resistance to new structural differentiation. Small-scale systems, by contrast, tend to preserve higher openness and greater capacity for novel differentiation, but with lower structural stability. The work further distinguishes scale from hierarchy: hierarchy refers to vertical structural depth, while scale refers to horizontal capacity. These two dimensions are independent. The model aims to provide a unified explanation for organizational conservatism, cognitive rigidity, linguistic stabilization, civilizational path dependence, innovation difficulty in large systems, and the openness of small-scale adaptive systems. This work belongs to the Field Chapters of On Self-Manifestation and focuses on how system scale modifies structural formation, openness, compression, and innovation capacity.