The basis of all brain activity is the propagation of neuronal excitations. In the cortex, which forms the highest subsystem, the signals from most receptors arrive in the form of neuronal excitations in the input neurons of the fourth layer. Via axons of the neurons and interneurons, the incoming excitations propagate in the cortex layer and overlap additively. This results in a distance-dependent damping of the neuronal excitation, which corresponds to a concave transfer function. This is concave for each individual input neuron and has a negatively definite Hessian matrix in a sufficiently large environment. The additive superposition of any linear combination with positive factors (firing rates are positive!) again results in a concave overall excitation function, which always has a global maximum within a certain superposition area. This global excitation maximum moves back and forth when the firing rates of the input neurons change, i.e. the strength of the primordial variables that excite the signal-providing receptors change. Thus, changes in joint angles in circular movements lead to the rotation of cortical excitation maxima around a fixed centre. Similarly, movements of inclined straight lines lead to excitation maxima that are arranged windmill-like around a centre and whose neuron populations are called orientation columns.
In the cortex, many signals are represented by maximally excited populations of neurons, and the location of the maxima encodes the parameters of investigation involved. Maximum coding is a basic principle of the brain. The application of extreme value methods enables the determination of the parameters that cause these maxima. Differential calculus provides the tools to understand why researchers observe excitation maxima at the cortex surface, and it provides the relationship between the maximum excitation and its cause. Only then can we understand how the brain internally represents and processes signals. The basis of signal processing in the cortex are divergence modules, in which the input is distributed partly vertically, partly in the plane and partly spatially, overlapping and leading to excitation maxima. The output represents maximum-encoded signals whose maxima represent new modalities, e.g. brightnesses, colours, joint angles, line elements, etc.