The global chaos caused by the July 19, 2024 technology meltdown highlights the need for a theory of what large-scale cohesive behaviors-dangerous or desirable-could suddenly emerge from future systems of interacting humans, machinery, and software, including artificial intelligence; when they will emerge; and how they will evolve and be controlled. Here, we offer answers by introducing an aggregation model that accounts for the interacting entities' inter- and intraspecies diversities. It yields a novel multidimensional generalization of existing aggregation physics. We derive exact analytic solutions for the time to cohesion and growth of cohesion for two species, and some generalizations for an arbitrary number of species. These solutions reproduce-and offer a microscopic explanation for-an anomalous nonlinear growth feature observed in various current real-world systems. Our theory suggests good and bad "surprises" will appear sooner and more strongly as humans, machinery, artificial intelligence, and so on interact more, but it also offers a rigorous approach for understanding and controlling this.