Triangular Array and Hexagonal Firing Patterns

The model that, in Calvin's account, provides the stage for the simulation of such behavior, is an idealized triangular grid that hosts a neuron-type constituent at every intersection. The triangular grid models the particular way in which pairs of neurons that are in mutual re-excitation mode tend to entrain sub-threshold neurons that sit equidistant from the members of the pair. Furthermore, adjacent edges of excited triangles may co-opt a fourth and a fifth cell to complete a large hexagonal synchronous patterns of triangular arrays. This creates a kind of hot spot that can potentially excite entire structures through its influence over nearest neighbour interactions - interactions with nearest surrounding constituents. Figure 7.1 illustrates Calvin's model.

  

Figure 7.1: Calvin's model: The triangular grid models the particular way in which pairs of neuron that are in mutual re-excitation mode tend to entrain sub-threshold neurons that sit equidistant from the members of the pair. Furthermore, adjacent edges of excited triangles may co-opt a forth and a fifth cell to complete a large hexagonal synchronous patterns of triangular arrays. This creates a kind of "hot spot" that can potentially excite entire structures through its influence over nearest-neighbour interactions - interactions with surrounding constituents. Here, the green and red hexagon represent competing patterns for neural territory.

These hot spots are sometimes referred to, particularly in physics, as attractors. An attractor is usually a small critical number of constituents in a system, that are in a particularly stable state, that is, a strongly defined pattern that can induce into its own state neighbouring constituents that are inactive or in a relatively indeterminate state. Activation in a neuron can occur in two ways: from direct sensory input and from feedback^7.2 or reentry in which initially stimulated neurons activate neighbouring neurons and then, are re-stimulated from the activity in the neighbours.

As neural cells are co-opted into a particular pattern that extends into a net-like structure, it is likely that this structure will encounter another set of synaptic patterns along its edge. The other pattern has its own attractor. Sometimes these attractors can be easily disrupted so that one structure will overrun the other. At other times, attractors are very stable so they get into competition with each other. These structures may be the result of some sensory stimulus. The competition may arise from choices to be made and may resolve with time or additional information. The resolution may occur in different ways but it usually implies that a territory overtakes a competing territory. However, sometimes territories can somewhat overlap and the boundary of overlapping territories can develop its own attractors. Calvin thinks this resulting territory can give rise to what we would cognitively recognize as categories. An overlap of structures corresponding to apple, orange and banana can create a coherent superposition experientially rooted in a shared sensory experience such as sweet, tree-borne, and so on. These stable points may resonate sufficiently to generate stable attractors that can co-opt neurons throughout the overlapping territory. This new territory may be akin to a process of schematization that, one might surmise, could be the neural basis for a derivative category such as that of fruit.

In Calvin's model, these structures are not merely syntactic; in fact, syntax is rooted in the sensory experience of being and moving about in the world. Syntax evolves from perceptual and motor functional structures that are activated during vocal transactions.

The perceptual (those involved in the experience of an apple) and motor-functional structures (those involved in the utterance of apple) are intertwined. The neurons involved on the edge of the structural landscape tend to alternate between spatio-temporal attractors, one for the motor-functional structures and one for the perceptual structures, until recognitional competitions are resolved. Once resolution is achieved, the attractors merge into one structure that constitutes the immediate experience of apple.