As we have mentioned, Calvin's model offers a finer grained description of dynamics similar to the ones we have used in our description of the evolution of language. We think that our description is compatible and must be reflected in the dynamic of neural interaction. Calvin's approach allows us to do so. We think that by using a description of Calvin's model that includes phase transitions we can add details that Calvin's description lacks, specifically in relationship to what could be the synaptic event of syntax and more abstracted forms of vocables such as functional vocabulary.
Calvin's model does not strictly model phase transitions, though the concept is not incompatible with it. He does mention that a resolution of competition is the result of a phase transition. However, no detailed description is given of the kinds of structure that can result from a phase transition. Phase transitions could explain much in the activation of structure in low-connectivity or ``hurry up'' time. I suggest that this finer grain mechanism can help along the cloning procedure. Dynamical equilibrium can be reached in a low-connectivity system - where limited energy is available - through a phase transition.
Percolation is a good example of a phenomenon leading to a phase transition that can further the description level of Calvin's model. To re-iterate, percolation theory deals with the properties of clusters of occupied sites that form into a lattice. Percolation refers to the possibility of having a cluster spreading over an entire lattice. Percolation usually demonstrates second-order phase transition defined by the connectivity between sites. This state change is usually the result of a critical number of connections between clusters. Percolation is a description of low-connectivity stuctures. For example, given two metal plates separated by some physical distances, say 100 cm, that hold an electrical charge, percolation would describe the creation of a path for current flow when coins are randomly thrown down between them. The definition of connection here is a conductive path, the nature of the medium is round coins that can overlap one another, and the nature of the medium evolution is random dropping. The function of these variables give rise to a particular percolation behaviour. Also consider the Kerplunk! example given in the introduction.
In Calvin's model, locked states can emerge in hexagonal arrays that are highly synchronous, from constant activation. A situation that requires a fast response could be described as a low-connectivity system in which percolation may occur. The high synchronicity of stable hexagon structures, despite being minimal, will successfully clone without the benefit of competition.