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
Structure, energy, unity and resonance
In the classical world, we find that energy and matter are discontinuous. If we apply a sudden force to a structure the energy will quickly dissipate and will not follow the lines of the structure. A soliton is different. The point can be best made by referring the Davydov model of muscle function again. As we saw previously, the soliton was proposed as a possible mechanism for muscle function because Davydov noted the fact that Myosin filaments were comprised of extremely structured molecules. He realized that the regularly spaced molecules could support a soliton. The important point here is that for the soliton to exist at all there must be structure in the boundary conditions - in this case, this corresponds to the regularly spaced carbon and oxygen atoms. The regularly spaced carbon and oxygen atoms constitute a symmetry or invariance. The soliton, therefore, dynamically involves the symmetry or invariance 'implicit' in the structure such that energy and structure become continuous - they work together. Consequently, the 'implicit' structure (invariance) of the actin molecule is made 'explicit' as a unified non-linear dynamic - a soliton wave.
Following on from this, I suggest that a major effect of a soliton is to unite structures by 'utilizing the invariance that they embody. Earlier, a potential problem concerning the relationship between function and persistence was addressed by demonstrating the possibility that 'apparent function' and metabolism (as a process of catalysis) were identical. A similar problem arises when we consider that biological processes require energy. Energy almost invariably imposes stresses upon structures. However, if energy in biological processes utilizes the symmetry (invariance) implicit in biological structures via a solitonic mechanism, then there is a continuous relationship between energy and structure.
Again, we can use the analogy of an arch to illustrate the point:
To get a more intuitive feel for this idea I would like to use another analogy - resonance. We have all run our finger around the lip of a wine glass to make it 'sing'. This is an example of resonance. Objects that have a high degree of symmetry are liable to resonate if energy is 'tuned' to the resonant frequency of the object in question. Soldiers are required to 'break stride' when passing over a bridge because if the regular step of their march matches the resonant frequency of the bridge then it may shake itself to pieces.
Although solitons are not strictly speaking resonant phenomena, there are, nevertheless, similarities. Solitons can only exist if there is a high degree of invariance (structure or pattern) in the medium and/or boundary conditions. Also, a particular medium and set of boundary conditions will only support a soliton of a particular structure and energy. If solitons are indeed a principle biological mechanism then they are 'utilizing' the symmetries of the environment such that energy and structure come together.
Considering these points in the light of the main theme of this paper - robustness, may give us an insight into the nature of the living process. Conventionally, we think of an organism as some sort of machine within an environment. The exact manner of functionality (or 'how' the organism works) being contingent on the particular evolutionary steps that the organism took. So, there is no necessary relationship between an organism and the environment. The structure of the organism is arbitrary and the manner by which the environment is utilized by the living machine is also arbitrary. All that matters from the Darwinian perspective is what survives - not how it survives.
Given this, we must conclude that all living processes represent a sort of compromise, between the 'functionality' of the living machine and the forces and stresses imposed upon it by the environment. This is because the environment cannot be considered to be 'in tune' with the requirements of the organism. That is to say that there is a discontinuity between the organism as a self-generating machine and the contingencies of an environment the properties of which have nothing to do with the needs of a self sustaining machine. Furthermore, these destructive forces need not necessarily come from the environment. The living process is itself an environment for more microscopic functional living processes. So, from a simple Darwinian perspective, 'the environment' is not only the source of energy and raw materials that enable a living process to perpetuate itself, but, is also a sort of obstacle course that the evolving life form has to negotiate; full of discontinuities and stresses that are potentially destructive.
Let us now consider the same problems from the fractal catalytic point of view. Immediately, the environment is perceived in a different way. Instead of being an 'obstacle course' the environment is understood to be a set of transitions that the living process mediates as a process of catalysis. Therefore, there is no discontinuity between the organism and the environment. The persistence of the organism can be directly attributed to the properties of the environment. There is a necessary relationship between the environment and the organism. Also, there is a necessary relationship between invariance in the environment and invariance in the organism. That is to say that the persistence of the organism is directly related to the persistence of those factors in the environment that the organism mediates.
Furthermore, if the process of catalysis necessarily involves the coming together of energy and structure in the form of solitons and that this is achieved as a result of the fact that solitons utilize symmetries or invariance then we can see also how life avoids the potential problems associated with the discontinuity between energy and structure. There is a close relationship between symmetries or patterns and what are termed mathematical 'fixed points'. A mathematical 'fixed point' is a point that does not change under transformation. The process of catalysis clearly involves a fixed point between the reagents and products - the transition state:
This is a subtle idea and is best conveyed by use of an analogy. Let us suppose that we wish to build a machine, and the environment in which we wish to build this machine happens to be a spinning wheel. At first we try to build the machine on the rim of the wheel. However, because the wheel is spinning we run into all sorts of problems. After several attempts we finally hit upon the idea of building our machine at the axis of the wheel. The axis of a wheel is a mathematical 'fixed point' (a point of symmetry) that does not change under the transformation of rotation. Life, I suggest, occurs at 'fixed points', or points of symmetry between transformations. At such points the stresses endured by living systems are lowest because these points do not change. Furthermore, life is able to mediate transitions via 'fixed points'. In a sense then, life exists at the axis of its environment.
Having argued that life is a phenomena that unifies structure and energy I would go further and suggest that life also unifies various aspects of the survival space. Yet, there would appear to be a problem. If life is essentially a 'transition state' process, then how can we claim that it also unifies. This is a question that is difficult to answer precisely because as yet we cannot 'see' into the word of the individual catalytic event. However, increasingly it is claimed that quantum coherence and tunneling effects play a role in the catalytic process. I am of the opinion that this coherent state includes the probability wave functions of both the reagents and the products and therefore represents a state of unification.
So, the persistence of the life process can be understood to arise, not because life actively maintains its own structure, but rather, as a consequence of the unique position that it occupies in the environment - a point where the usual discontinuities between energy and structure do not exist.