The human brain needs distributed, time-critical computation to efficiently solve complex problems. Turbulence provides such highly efficient spacetime information processing and transmission across widespread brain networks, yet we have been missing a mechanistic understanding of the interactions of turbulent vortices underlying human cognition. Here, we build the first whole-brain model of turbulent vortices as defined by the levels of local synchronization in brain signals quantifying turbulent interactions in vortex space. Specifically, using large-scale human neuroimaging data, we found that the interactions of turbulent vortices is an excellent framework for understanding cognition and brain computation. In particular, we show that when combined with connectome-based predictive modeling, this significantly predict the g-factor and the scores on the underlying tasks. In addition, turbulent vortices also distinguish the detailed spacetime dynamics of rest and cognition—and can even distinguish between subtle subcomponents of cognitive tasks, where manipulation of vortices can be shown to change cognition. Overall, this whole-brain framework creates a natural vortex space for the brain computation underlying cognition, as well as potentially providing novel ways of controlling turbulent interactions in disease.