Table of Contents
Life and persistence
Function and Metabolism
The Thought Experiment
Life as a dynamic system
What is catalysis?
What are solitons?
Solitons in biology
Scale invariance in biology
Structure, energy, unity and resonance
Application of catalysis 1
Application of catalysis 2
Life as catalysis
Ontology of consciousness
Fractal catalysis and autopoiesis 1
Fractal catalysis and autopoiesis 2
How can catalysis be applied to provide
a model of cognition? Part 1
Before we explore the relationship between catalysis and cognition in detail, a few words should be devoted to defining conscious states as a physical process within the catalytic model. If conscious states correlate to a process of macroscopic catalysis then we can locate the phenomena of consciousness at the transition state:
Locating living processes at the transition state of a macroscopic process of catalysis is, I suggest, entirely consistent with the fact that life is a far-from-equilibrium process. Additionally, we may now cast in a slightly different light commonly accepted phenomena of mental 'processing'. The concept of 'association' is commonly used to describe the way in which we may 'jump' from one set of circumstances to another if each shares something in common. For example, if someone mentions 'shoes' you may be reminded that you must take your shoes to be repaired. Normally, we think that two independent pairs of shoes have been associated. I suggest, that actually, 'shoes' represent a 'fixed point' or symmetry and are the transition state by which we may get from one set of circumstances to the other. Also, there would seem to be a close relationship between 'association' and metaphors, analogies, similes; even puns. All these mental phenomena may be closely linked and suggest that the brain utilises points of commonality - transition states.
Usually, we consider cells that form part of a larger organism to have well defined functions - functions that are determined by the requirements of the organism. However, this raises an interesting question: Given that any biological process should be robust enough to last the lifetime of the organism, is there a necessary relationship between function and robustness? The function of a bone, for example, is to be both strong and durable, and therefore illustrates an instance where this is true. However, when we consider the brain, it is difficult to explain in a simple way why its 'functions,' when considered as processes, should be necessarily robust. Also, if we consider the fantastic complexity and variety of neural functions: perception, co-ordination, conceptuality, etc., we might justifiably ask how such a complex and interrelated set of processes don't compromise each other.
Not withstanding recent developments in PDP (Parallel Distributive Processing) and connectionist models that represent a movement away from the idea of symbols, the pervading paradigm considers the brain as a computer of some sort which usually involves the use of symbols and/or representations. Given this, we expect there to be a logical schism between the brains functions and the material substrate which supports those functions. To illustrate the point, it does not matter whether we make a computer out of silicon or Coke cans -- what is important is the relationships effected. We attribute the durability of an ordinary computer to the materials from which it is made and to the inherent strength of its rigid structure, not to the functions of the programs that run on it. However, unlike a computer, the brain is a highly dynamic process where 'functional' changes are linked to structural changes of the material substrate, suggesting that there is an intimate entanglement between 'function' and structure.
It has been previously argued that 'functionality' as it is applied to living processes is a redundant term, that all living processes are processes of catalysis. The challenge, then, is to show how a scale invariant catalytic process can give rise to a stable and integrated set of apparently functional neural processes. Let us remind ourselves of the major factors involved in a chemical reaction:
In the case of the brain, the major thermodynamic consideration stems from the energy gradient that is created as a result of glucose being provided by the bloodstream. The structural hindrance, I suggest, corresponds to the spatial/temporal pattern of neural firings stimulated by the body and the senses. So, how the available energy moves through the brain is constrained by spatial and temporal structural aspects of the body and the environment as they are sensed.
This constitutes a significant departure from how we usually think of the role of neurons. It is commonly thought that a neuron firing is significant in that it 'communicates' via some, as yet, undiscovered code. I suggest, on the other hand, that the significance of a neuron firing is that it takes place at a certain place and at a certain time within an overall context where neural events are taking place in space and time. To support this idea let us examine the visual system:
'...the retina connects overwhelmingly to one distinct part of the brain... the striate or primary visual cortex, also known as area V1. This connection is made with high topographic precision: V1 effectively contains a map of the entire retinal field.' (Zeki, 1992)
It seems that in at least two places the brain preserve the spatial relationships of the visual stimulus as a physical aspect of neural activity. The relative spatial relationships of the stimulus are preserved at the retina and the V1 layer in the visual cortex. The brain also preserves temporal properties; cells in the audio cortex collectively fire at the frequency of the stimulus.
To support this idea we may refer to the work of Adamatzky (Adamatzky, 2001). Perhaps the most striking evidence that the formation of travelling waves involves the structure in the environment is instanced by his empirical experiments. A variation of the Belousov-Zhabotinsky reaction in which a photosensitive excitable medium is used. Basically, light is used to 'activate' or 'suppress' areas of an excitable BZ medium. An image is projected onto the medium and the BZ reaction is initiated. It is found that the evolution of the spatio/temporal dynamics of the reaction performs basic image processing. Using this technique broken contours can become continuous, edges become defined and contrast can be enhanced. One very significant aspect of this methodology is the lack of any sort of representation. The processing is being performed in 'the plane of the problem'. That is to say that the relative spatial relationships of the image are physically preserved as an aspect of visual processing. This is very significant: the visual cortex preserves relative spatial relationships as an aspect of visual processing. I suggest that what we may be observing in this type of process is a two-dimensional example of what the brain does in three dimensions. The brain may well be an excitable medium and cognition is the consequence of the 'evolution' of spatio/temporal dynamics in the form of solitons where the boundary conditions are determined by the senses.
Previously, we examined the role that solitons play in the process of catalysis. It was also noted that the persistence of solitons depended upon structure in the form of symmetries or invariance in the boundary conditions. Given that there is a necessary relationship between structure and the robustness of solitons, then we can propose a possible mechanism for mental development.
Current thinking suggest that the action potential that results from a nerve cell firing is a soliton. Also, nerve cells may behave collectively like coupled oscillators. Coupled oscillators may also give rise to solitons. Whatever the exact mechanism, I suggest that it is possible that the interactions of very many neurons may give rise to macroscopic solitons in the brain. Now let us suppose that a stimulus embodies no order at all - no structure or pattern. Energy is released as action potentials as nerve cells fire, but, because there is no pattern (and therefore no symmetry) implicit in the stimulus, the energy interacts in a chaotic way and quickly dissipates. However, if there is an implicit pattern in the stimulus, then that pattern will embody aspects that are invariant, aspects which remain the same under a transformation in space and/or time. If solitons somehow 'utilise' the invariant aspects of the stimulus to sustain themselves then two things will happen. A soliton (or an interacting complex of solitons) will persist by utilising the invariance in the stimulus and will unite (or make explicit) the invariant aspects of the stimulus as a continuous dynamic. Also, the synaptic junctions that form the material substrate supporting those solitons will be strengthened. This mechanism may be compatible with the proposals, in the areas of perception and cognition, that humans abstract 'invariants' or 'prototypes' through a process involving resonance (Changeux & Dehaene, 1993; Gibson, 1979; Lashley, 1942; Ratliff, 1983; Shepard, 1984).
Again we have identified a possible union between energy, matter and 'order.' The eventual structure of the brain and its robustness are necessarily related to the robustness of the soliton. Also, the robustness of the soliton is related to the symmetry implicit in the stimulus. What this implies is that the structure of the brain is ultimately determined by a wave form.
We can take this idea a stage further. Imagine a child that is learning to speak. The child's mother uses certain words very often. At the early stage of the child's development there is no conceptual distinction to be made between stimuli, be they visual or auditory, that the child learns to recognise. A word, I suggest, is simply a sequence of events in space and time. If it embodies sufficient implicit order in its frequency components and the repetition of its use, then it may become 'explicit' as a soliton-unified neural event, an object of recognition. However, there is a second level of order or symmetry implicit in the occurrence of word-objects and other 'objects' of experience. For example, the child's mother creates the word-object 'cat' whenever the child sees a cat. I suggest that the implicit relationship between word-objects and other objects of experience is made explicit as language and conceptuality.
We can now understand, not only how the brain develops, but also, how its many processes co-exist in a stable way.
Again, we can use the analogy of an arch to illustrate the point: