This talk explores the emerging field of multivariate information theory and the phenomenon of higher-order, synergistic interactions in complex systems: dependencies between three or more elements that are irreducible to the sum of their parts. In it, I make an analogy to the idea of “dark matter” in cosmology: dark matter forms the majority of the apparent mass of the Universe, but our understanding of its nature is limited by our inability to detect or interact with it. Similarly, “dark information”, being composed of the combinatorially vast space of possible polyadic interactions in a complex system, may form the vast majority of the computational “structure” of a system - but existing statistical tools are almost completely blind to these interactions. Using computational neuroscience as a case-study, I show how two foundational techniques in modern neuroscience (correlation networks and manifold learning algorithms) are insensitive to higher-order synergies, and instead only provide a narrow window into a small slice of the overall structure brain activity. This large space of higher-order interactions in the brain has therefore gone almost completely unexplored, and may contain novel insights into how the interaction of large numbers of components gives rise to emergent features of cognition and consciousness. Finally, I end by arguing that “dark information” is almost certainly not unique to the brain, but instead is a feature of any complex system.