A previous paper described a network of simple integrate-and-fire neurons that contained output neurons selective for specific spatiotemporal patterns of inputs; only experimental results were described. We now present the principles behind the operation of this network and discuss how these principles point to a general class of computational operations that can be carried out easily and naturally by networks of spiking neurons. Transient synchrony of the action potentials of a group of neurons is used to signal "recognition" of a space-time pattern across the inputs of those neurons. Appropriate synaptic coupling produces synchrony when the inputs to these neurons are nearly equal, leaving the neurons unsynchronized or only weakly synchronized for other input circumstances. When the input to this system comes from timed past events represented by decaying delay activity, the pattern of synaptic connections can be set such that synchronization occurs only for selected spatiotemporal patterns. We show how the recognition is invariant to uniform time warp and uniform intensity change of the input events. The fundamental recognition event is a transient collective synchronization, representing "many neurons now agree," an event that is then detected easily by a cell with a small time constant. If such synchronization is used in neurobiological computation, its hallmark will be a brief burst of gamma-band electroencephalogram noise when and where such a recognition event or decision occurs.