The previous section contained a lot of ideas. It would be useful at this time to illustrate in a pictorial way some of the ideas that were proposed. Firstly, let us think about a soliton moving down a canal.

The simplified vector diagram above shows the direction and velocity of water at various points in the soliton dynamic. One of the boundary conditions for this type of soliton is the canal bottom. We notice that the soliton is continuous with this surface; the motion of the water is in the same plane as the bottom of the canal where they come into contact. From this we may gain an insight into the robustness of the soliton. The fact that the soliton is continuous with the canal bottom means that there is no turbulence. It is clear that the regular depth of the canal is an example of symmetry or invariance. In fact, symmetry or invariance is necessary for solitons to exist at all. To contextualize this example in terms of the general thrust of the hypothesis, i.e. that 'life makes explicit the implicit order in the environmental survival space,' we can consider the regularly flat plane of the bottom of the canal as an example of an implicit order and the dynamic of the soliton as making this implicit order explicit as an aspect of the continuous wave form. Thus, the persistence of the soliton is dependent upon the implicit order of the canal bottom. We may go a stage further and suggest that life is a continuous solution to a set of discrete boundary conditions in space and time.

Let us now apply this idea to a cognitive problem. In order for this to be done we have to alter our perception of the soliton moving down the canal slightly. Normally, we perceive the soliton as moving and the landscape (including the canal) as stationary. With a little imagination we can choose to see things in a different way; we can imagine the landscape moving in the opposite direction, such that the soliton remains fixed in a single position. All things being relative, this is an equally valid way of understanding the situation. Again, with a slight shift of perspective we can imagination that the moving landscape represents time and that the soliton is preserving its dynamic structure and persisting by making explicit the implicit order (the symmetry or invariance of the canal bottom) in its spatial/temporal environment as an aspect of its dynamic. From this perspective, the canal bottom actually represents a set of transformations. In this case the transformations do not change any of the spatial relationships.

Now, let us imagine that we are looking at a triangle. As is instanced above, we should imagine that the triangle is actually a set of simple transformations in time and space. Again, this is a simple transformation in that none of the spatial relationships change:

Now, let us imagine the problem faced by a brain state that corresponds to the recognition of the triangle. Just like the stationary soliton that maintains its coherence and structure as the canal moves past, any brain state associated with the recognition of the triangle is faced with a similar problem, a set of transformations in space and time. The problem is further compounded by the fact that the brain is a highly dynamic process where feedback and feed forward interactions contribute to a highly complex set of dynamics. Previously, we examined the way in which the brain preserves the relative spatial and temporal relationships of the world as an aspect of neural activity. Thus, a triangle in the field of view translates to a triangle of neural activity in the visual cortex. Now, let us imagine a child who is too young to recognize a triangle. If we were able to look into the child's visual cortex we might see something like this:

We note that the energy released by neurons that are stimulated by the retina is highly chaotic. There is no sense in which the invariance that comprises the 'implicit' triangle has been made explicit. Feedback relationships may be spontaneously formed between neurons that form part of the triangle or with other objects in the visual field. However, imagine that moment when the child recognizes the triangle for the first time. I suggest that this is the moment when the previously chaotic and discrete set of neural events suddenly forms a coherent dynamic that unites the neural activity that forms the implicit triangle and makes it explicit as a unified dynamic in space and time:

So, a soliton moving down a canal is able to maintain its dynamic structure because there are implicit orders in the regular depth and the regular flat surface at the bottom. So, too, the triangle, as it is imposed upon the visual cortex, forms the boundary conditions for a soliton comprised of many interrelated neurons to move through time and space, making the regular features of the triangle (invariance or symmetries) continuous with each other as aspects of the dynamic of the soliton. At first this may seem puzzling. A triangle contains discontinuities (angles) that are usually thought to be a hindrance to the formation of continuous wave like dynamics. However, recent work with travelling wave formation in excitable mediums clearly demonstrate that such waves may have shapes with sharp corners as depicted above (Jinguji, et al, 1995).

Also, to correctly appreciate this as essentially a catalytic process, we must bear in mind that cells in the visual cortex may not immediately fire as a consequence of stimulus from the retina. I suggest that they may be 'primed' to fire, and it is the action of the macroscopic soliton that catalyzes them to do so. It is important to bear in mind that what is described above is a very basic recognition of a triangle. No reference is made here to what might be described as a 'conceptual' triangle. There are no concepts here. In order to understand this basic level of cognition, one has to imagine what it is like to able to recognize an object without being able to refer to that object using language. Also, the diagram is a little misleading; we cannot observe an object without the relationship between our own point of view relative to the object being an aspect of the experience; so, the example is a simplification.

This represents a significant departure from how we usually think of cognition. How, one might ask, could something like a soliton, albeit, in the shape of a triangle, correspond to a personal experience of a triangle? I suggest, that far from being counter to intuition, this interpretation of cognitive processes gives us a greater insight into the subtle 'qualities' of perception. When we observe a triangle we do not see the set of discontinuous events that would correspond to the discrete and separate neural firings, as when the cells in the retina are triggered to fire. We experience the triangle as a whole, each part given significance in terms of its relationship to the rest of the triangle. The soliton is a unified non-linear dynamic in which each part plays an essential 'role' in maintaining the overall dynamic. I suggest, that it is this aspect of the soliton that allows us to understand the intrinsic 'content' of our perceptions. Of course, this claim brings into relief an important question related to our observation of objects and the 'information' embodied by those objects. It is often assumed that the brain must perform some sort of calculation in order to determine the nature of the object before we can we can recognize it. I suggest that the dynamic of the soliton must embody the information implicit in the triangle for it to persist. The question then becomes, 'What form must information take before it can be considered appropriate for cognition?'

This gets to the heart of the ontological component of this hypothesis. I suggest that the soliton combines two very necessary properties for life -- information (invariance or symmetries) and robustness. Instead of performing innumerable calculations in order to determine that there is indeed an object to be observed and then applying the information in such a way as to ensure that it is recognizable in the future, the soliton's robustness is directly related to the information that is implicit in the object. And because synaptic junctions are strengthened as a consequence of stimulation, the consequence of a soliton is to promote its own existence as a consequence of future exposure to the stimulus of the object.