Large-scale trends in urban crime and global terrorism are well-predicted by socio-economic drivers, but focused, event-level predictions have had limited success. Standard machine learning approaches are promising, but lack interpretability, are generally interpolative, and ineffective for precise future interventions with costly and wasteful false positives. Here, we are introducing Granger Network inference as a new forecasting approach for individual infractions with demonstrated performance far surpassing past results, yet transparent enough to validate and extend social theory. Considering the problem of predicting crime in the City of Chicago, we achieve an average AUC of ~90\% for events predicted a week in advance within spatial tiles approximately $1000$ ft across. Instead of pre-supposing that crimes unfold across contiguous spaces akin to diffusive systems, we learn the local transport rules from data. As our key insights, we uncover indications of suburban bias -- how law-enforcement response is modulated by socio-economic contexts with disproportionately negative impacts in the inner city -- and how the dynamics of violent and property crimes co-evolve and constrain each other -- lending quantitative support to controversial pro-active policing policies. To demonstrate broad applicability to spatio-temporal phenomena, we analyze terror attacks in the middle-east in the recent past, and achieve an AUC of ~80% for predictions made a week in advance, and within spatial tiles measuring approximately 120 miles across. We conclude that while crime operates near an equilibrium quickly dissipating perturbations, terrorism does not. Indeed terrorism aims to destabilize social order, as shown by its dynamics being susceptible to run-away increases in event rates under small perturbations.