In the cerebral cortex, membrane currents, i.e., action potentials and other membrane currents, express many forms of space-time dynamics. In the spontaneous asynchronous irregular state, their space-time dynamics are local non-propagating fluctuations and sparse spiking appearing at unpredictable positions. After transition to active spiking states, larger structured zones with active spiking neurons appear, propagating through the cortical network, driving it into various forms of widespread excitation, and engaging the network from microscopic scales to whole cortical areas. At each engaged cortical site, the amount of excitation in the network, after a delay, becomes matched by an equal amount of space-time fine-tuned inhibition that might be instrumental in driving the dynamics toward perception and action.