The Earth System (ES) is defined as the conglomerate formed by human civilization and its planetary matrix (i.e., all parts of the Earth that interact with the members and manifestations of our species) (1, 2). Thus, eminently complex systems like the global economy or the human brain are just components of the ES, contributing to its overall evolution. The climate machinery is another formidable subsystem that comprises vast domains of the atmosphere, hydrosphere, biosphere, and pedosphere, involves innumerable intertwined processes, and generates fairly robust dynamical patterns like the Hadley cell. This machinery still operates in the “Holocene mode,” which emerged ≈10 ka ago and is characterized by a distinctive distribution of ice sheets, wind regimes, ocean currents, biomes, and deserts, something that can be perceived as the environmental face of the Earth. Although one of the ES components mentioned above, the global economy, is about to inadvertently transform that face through massive emissions of greenhouse gases (GHGs) and the so-induced planetary warming, one other crucial component, the human brain, struggles to advertently preserve it by constructing clumsy institutions like the United Nations Framework Convention on Climate Change (http://unfccc.int/resource/docs/convkp/conveng.pdf). The ultimate objective of this convention is to avoid dangerous climate change, a target that can be operationalized with the help of recent scientific evidence including the results presented in this Special Feature. Now, what features establish the identity of a face; what distortions erase that identity beyond recognition? The first question can be best answered by cartoonists, whereas the second related one can be addressed in terms of mathematical mapping. An affine (i.e., linear) transformation may stretch or shear the face but cannot wipe out its character. Smooth nonlinear …