We show that if actors are defined as more knowledgeable when they possess more information, and if actors are defined as more powerful when they can extract greater surplus while exchanging resources, there is a fundamental trade-off in the social structural foundations of power and knowledge. This trade-off derives from the opposing implications of having redundant (i.e., directly or indirectly linked) contacts. Insofar as egos alters are nonredundant, ego can be expected to become more knowledgeable more quickly. And such nonredundancy can also be the basis for great power as ego monopolizes the flow of resources (including information) between egos alters. However, the very same mechanism that is behind egos power as a provider of resources - i.e., the possession of nonsubstituitable resources on the part of disconnected contacts also implies that that egos alters will themselves be monopolists, thus weakening ego as an acquirer of resources. Furthermore, while the surplus earned from providing resources on monopoly terms is potentially much greater than the surplus earned from acquiring resources on competitive terms, the former strategy carries the risk that socially distant actors will not value one anothers resources. Beyond elucidating the trade-off in the social structural foundation of knowledge and power, our framework also shows how the opposing implications of redundancy are the basis for a broad family of well known trade-offs (cosmopolitanism versus localism; exploration versus exploitation; insider versus stranger; robust versus simple identities) whose relationships with one another and with power and knowledge have not been appreciated. For all such trade-offs, the greater potential returns afforded by nonredundancy are balanced by the surer returns available from redundancy.