If, as is widely believed, information is stored in the brain as distributed modifications of synaptic efficacy, it can be argued that the storage capacity of the brain will be maximized if the number of synapses that operate independently is as large as possible. The majority of synapses in the brain are glutamatergic; their independence will be compromised if glutamate released at one synapse can significantly activate receptors at neighboring synapses. There is currently no agreement on whether "spillover" after the liberation of a vesicle will significantly activate receptors at neighboring synapses. To evaluate the independence of central synapses, it is necessary to compare synaptic responses with those generated at neighboring synapses by glutamate spillover. Here, synaptic activation and spillover responses are simulated in a model, based on data for hippocampal synapses, that includes an approximate representation of the extrasynaptic space. Recently-published data on glutamate transporter distribution and properties are incorporated. Factors likely to influence synaptic or spillover responses are investigated. For release of one vesicle, it is estimated that the mean response at the nearest neighboring synapse will be <5% of the synaptic response. It is concluded that synapses can operate independently.