System fields, intense fields and virtual fields are three interlocked concepts of the field. In his essay From Object to Field, Stan Allen primarily discusses the concept of a system field. I am using this term to describe a large group of objects that relate to each other in a systematic way and might produce emergent behaviors. An example of such a field is an ant colony as discussed by Steven Johnson in his book Emergence. In fact, a field is really just a set of relationships between objects. It can be hierarchal, unlike what Steve Allen implies, but does tend to be more of an intertwined mesh of objects, homogeneous or heterogeneous. Still a set of relationships between objects is hardly a clear way to describe a field. To be a field those relationships must be specified in a more exact manner. In fact, those relationships can not be a static “pattern” but are behavioral. The key to understanding a field is that each object inputs its behaviors, or its capacities and potentials to affect and be affected, into relation with other capacities and potentials. In a systems field the capacities are extensive properties of the objects. Examples of extensive properties are length, mass and energy.

DeLanda describes quite convincingly in his book Intensive Science & Virtual Philosophy, that extensive properties are produced by the process of symmetry breaking from intensive properties, which in turn were produced from virtual differences. A symmetry break happens when an “object” becomes no longer invariant to a transformation or behavior. For example a sphere is invariant to all rotations about its central axis, but if the sphere where stretched into a cube, only rotations of 90° would be invariant. A symmetry breaking process is said to have occurred. DeLanda’s most common example of a symmetry breaking process is the phase transitions of water from gas to liquid to solid.

So an intensive field is one of temperatures, pressures, densities, etc. Differences across a field will drive the becoming of the extensive. Like heat flowing from a hot object to a cool, energy and matter will flow from intensive differences and produce the behaviors and capacities of extensive reality in which we live. The weather is an excellent example of a highly intensive process. Yet within an intensive field exist certain singularities called attractors and repellers. These singular points don’t actually exist but are virtual. By virtual, I mean that these points can not be occupied as actual states of the system, but they have a profound actual effect on all the states around them. These special singular points in turn change over time. Allowing the system to adapt and evolve. As the intensive field changes and additional energy and matter flows are added, additional singularities unfold from the old ones. This is what DeLanda refers to as a bifurcation. It is at these bifurcations that symmetry breaking will occur.