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For 200 years it has been assumed that the sciences are arranged in a hierarchy, with developed natural sciences like physics at the top and social sciences like sociology at the bottom. Sciences at the top of the hierarchy presumably display higher levels of consensus and more rapid rates of advancement than those at the bottom. A distinction is made between two classes of knowledge: the core, or fully evaluated and universally accepted ideas which serve as the starting points for graduate education, and the research frontier, or all research currently being conducted. Data are presented from a set of empirical studies which show that, at the top and at the bottom of the hierarchy in either cognitive consensus or the rate at which new ideas are incorporated. It is concluded that in all sciences knowledge at the research frontier is a loosely woven web characterized by substantial levels of disagreement and difficulty in determining which contributions will turn out to be significant. Even at the research frontier, however, minimal levels of consensus are a necessary condition for the accumulation of knowledge. Consensus in all sciences is maintained by sociological processes such as the evaluation and reward systems.