Hierarchy of knowledge

The Hierarchy of knowledge is the idea that the basic fields of the sciences and mathematics can be organized linearly from its most basic pure form to its most derivative manifestation, at least as a convenience of discussion.
In brief, the hierarchy is as follows:
Math→Physics→Chemistry→Biology→Psychology→Sociology
According to this approach, Mathematics is the most basic and abstract form of knowledge. Math cannot be broken down into lesser elements or underlying factors or patterns. The application of math onto the real world is Physics, which attempts to explain the happenings of the universe through mathematics. Chemistry is the science of using physics to understand the constituent particles that make up all matter. Biology is the study of how chemistry manifests itself as life. Psychology is the study of mind and behavior based on biological context. Sociology is the study of human systems and social interaction.
Each step cannot exist or be understood properly without a firm understanding of the step that lies before it. One cannot understand biology without first understanding molecular biology and how DNA encodes the proteins that make life possible. One cannot understand DNA unless he first understands how the chemistry of atoms allow them to form covalent bonds and intermolecular attractions. One cannot understand atoms unless he first understands physics and the nature of particles. One cannot understand particles without math. However, in going down the hierarchy, the necessary degree of mastery of the primary level is less.
In some respects, each level in the hierarchy is simply another level of complexity imposed on the prior. Looked at differently, each successive step is a higher degree of generalization,dealing with increasing levels of organization. As the hierarchy implies there is not set division between levels and instead it forms a gradient as each level blurs into its neighbours. A more fleshed out hierarchy may appear as:
Mathematics→Physics→Physical Chemistry→Chemistry→Biochemistry→Biology→Ecology→Neurobiology→Psychology→Sociology.

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