Movement, Field, and Resonance: Description without Causation (Ugoki to Ba to Kyoushin: Inga naki Kijutsu)

This paper proposes a hierarchical structure underlying the universality of the Stuart-Landau equation: movement, eld, attraction, resonance, and synchronization/collapse.Drawing on the historical connection between Hiroshi Shimizu's eld research and YoshikiKuramoto's synchronization theory at Kyushu University in the 1970s, we argue that thishierarchy is not merely conceptual but historically grounded. Furthermore, we propose thatthis structure can be described without invoking causationas covariation rather than cause-and-eect relationships. The authority of causation may be unnecessary for understandingcomplex phenomena in both physical and semantic spaces. We extend this framework tosemantic space, identifying a unique property: the observer undergoes an irreversible phasetransition upon acquiring knowledge. Despite this fundamental dierence from physicalsystems, the hierarchical structure remains valid. This work builds upon our unied theoryof dynamic emergence (Ishibashi, 2025a) and connects to applications in nancial systemanalysis (Ishibashi, 2025b).