The results of seismology and geochemistry for mantle structure are widely believed to be discordant, the former favoring whole-mantle convection and the latter favoring layered convection with a boundary near 650 km. However, a different view arises from recognizing effects usually ignored in the construction of these models, including physical plausibility and dimensionality. Self-compression and expansion affect material properties that are important in all aspects of mantle geochemistry and dynamics, including the interpretation of tomographic images. Pressure compresses a solid and changes physical properties that depend on volume and does so in a highly nonlinear way. Intrinsic, anelastic, compositional, and crystal structure effects control seismic velocities; temperature is not the only parameter, even though tomographic images are often treated as temperature maps. Shear velocity is not a good proxy for density, temperature, and composition or for other elastic constants. Scaling concepts are important in mantle dynamics, equations of state, and wherever it is necessary to extend laboratory experiments to the parameter range of the Earth's mantle. Simple volume-scaling relations that permit extrapolation of laboratory experiments, in a thermodynamically self-consistent way, to deep mantle conditions include the quasiharmonic approximation but not the Boussinesq formalisms. Whereas slabs, plates, and the upper thermal boundary layer of the mantle have characteristic thicknesses of hundreds of kilometers and lifetimes on the order of 100 million years, volume-scaling predicts values an order of magnitude higher for deep-mantle thermal boundary layers. This implies that deep-mantle features are sluggish and ancient. Irreversible chemical stratification is consistent with these results; plausible temperature variations in the deep mantle cause density variations that are smaller than the probable density contrasts across chemical interfaces created by accretional differentiation and magmatic processes. Deep-mantle features may be convectively isolated from upper-mantle processes. Plate tectonics and surface geochemical cycles appear to be entirely restricted to the upper ˜1,000 km. The 650-km discontinuity is mainly an isochemical phase change but major-element chemical boundaries may occur at other depths. Recycling laminates the upper mantle and also makes it statistically heterogeneous, in agreement with high-frequency scattering studies. In contrast to standard geochemical models and recent modifications, the deeper layers need not be accessible to surface volcanoes. There is no conflict between geophysical and geochemical data, but a physical basis for standard geochemical and geodynamic mantle models, including the two-layer and whole-mantle versions, and qualitative tomographic interpretations has been lacking.