Time-Logic Computation and Nonlocal Sampling Cognition: A Topological Framework for the Emergence of Intelligent Motion

We present a unified theoretical framework---Time-Logic Computation (TLC)---that explains the emergence of life-like, intelligent, and aesthetically graceful motion as a consequence of nonlocal synchronization acting through temporal--topological modulation. In TLC, dynamics are not governed primarily by local energetic gradients but by a time-modulation field that aligns phase relations across many spatially distributed micro-units (e.g., hydrogen bonds, sensory pixels, motor units). We formalize nonlocal synchronization as a spatiotemporal point-set endowed with phase, introduce a temporal modulation operator and coherence indices, and show how macroscopic behavior follows topological minimization paths rather than classical energy minima. Four conceptual exemplars (sequenced explosions, protein--water interaction, plastic-bag drift, Jellyfish swimming) motivate the theory and sharpen testable predictions. We propose measurable indicators (THz/2D-IR coherence peaks, persistence-diagram dynamics, cross-coherence EEG/MEG signatures, behavioral fractal spectra) and outline experiments and simulations to falsify the framework. Time-logic computation provides a parsimonious explanation for recognition, decision, and aesthetic judgment as resonance phenomena between observer and observed, implemented by nonlocal sampling cognition.