Gradients are spatial differences of some system’s property that form directed flows of system’s components (matter), energy or information. Properties can be scalars or vectors. If the property at each spatial point can be expressed as a sole number it is called a scalar field. The spatial distribution of energy-mass temperature, pressure, humidity, concentration, height, density are examples of scalar fields. The only known fundamental scalar field to date is the so-called Higgs field which provides masses to elementary particles. The gradient of these scalar fields produce flows or vector fields which generate directional motions at each spatial point. If the scalar field is homogeneous (has the same value) all over the space then no flow emerges. It is symmetric because each point in space is the same as any other. There is always a gradient when some property is unevenly distributed in space. Then, the previous symmetry breaks and directed motions as well as forces are formed.
Gradients are important context forming constraints on the system’s behavior. A velocity of a fluid at each spatial point is an example of a vector field. Gravitational and electrostatic forces are spatial gradients of gravitational and electric potentials. They are vector fields. For example, if there is more gravitational potential at some place than on another, a force exists that pulls the system toward the place of lower potential and creates motion. The directed collective behavior of water molecules forming rain, snow, rivers and waterfalls is formed because of gravitational gradients, i.e. vector fields. The differences of electric charge in some places form a gradient, as well. Then a flow of the electricity toward the lower electron concentration follows. An electric current as a directed collective behavior emerges. Batteries in our mobile phones, computers and vehicles must contain gradients for these devices to work. The collective flow we call – lightning – uses the same gradient between clouds and ground to emerge. Temperature and pressure gradients form the directed collective behavior of air molecules that we call a wind.
Gradients are of utmost importance for life. To see this it is enough to recall that the evolution has discovered and stabilized the use of sodium and potassium pumps to allow maintaining electrochemical gradients across cell membranes. Electrochemical gradients are crucial also for the metabolic processes in our cells. Pressure and concentration gradients in our cells enable the gas and nutrient exchanges across the capillaries. The differences between our current state and the intended states form gradients that put us in action. Food, wealth and quality of life gradients form migratory flows of bacteria (chemotaxis) and human beings. For example, akin to food gradients and bacteria, the financal and quality of life gradients create migratory flows of human beings from countries, sport clubs, universities and scientific institutes with low towards those with high economical status. Informational gradients form the information flows from the sources containing the information toward those who are information hungry. All these flows tend to erase the differences, nullify the gradients and form spatial homogeneity. Fortunately, so far, there are always processes that form contexts in which new gradients are formed at different spatio-temporal scales (as shown through the previous examples). These gradients enable the life flow on the Earth.
Robert Hristovski 07.12.2015