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In order to understand the concept of the earth systems science, we need to take a quick look at the basis of systems theory. Systems theory views an "organism" in a holistic manner, which is different from the reductionist approach where components are broken down individually and described by basic principles of chemistry, physics, and mathematics. It also allows for system behaviors such as self-organization.
The Earth Systems Science Educaiton Program of the Universities Space Research Assocation website offers some materials on what earth system science is.