LINEAR VERSUS NON-LINEAR SYSTEMS

Homeopathy has always generated controversy, and will most probably continue to do so for many millennia, since there appears to be an overwhelming need to protect and sanctify ‘the Organon’ with an authority that does little credit to our evolving paradigms of ‘New Physics’ with its concerted efforts to marry consciousness to the acts of observation.

Two facts that lie at the foundations of the ‘classical paradigm’ in homeopathy are:

1. Objectivity – the need to conceptualise ‘the remedy’ as an objective finding that ignores the input of the practitioner, even after the ‘placebo’ effect has been established in the medical literature as an important adjunct to the therapeutic process.
2. We apply our observations as if they were linear systems.

It is to the second fact that I wish to address my discussion, since it is ‘linear systems’ that have preoccupied scientists for the past three hundred years and this has remained an important thread in the thinking that pervades the ‘classical paradigm’ in both homeopathy and science. Hahnemann may well have evolved brilliantly in his insights on the fundamentals of subtle remedies but he was still bound to be deeply influenced by his contemporary scientists.

I would like to quote from a presentation delivered by Paul Davies at the Mystics and Scientists Conference in 1998, which clearly explains the distinction between linear and non-linear systems in Nature and then I will focus on its relevance to the classic model in homeopathy.

‘Roughly speaking, linear systems are those in which cause and effect are associated by some simple proportionality. Let me give an example: a piece of elastic. If you stretch it, then the amount of stretch that you get is in some proportion to the amount of force you apply. It is a linear system, so cause and effect are linearly related. If you plot the cause against effect on a graph, you get a straight line, hence the word ‘linear’.

Many system are approximately linear, and are therefore mathematically speaking easy to describe ……it is often said that linear systems are nothing more than the sum of its parts. Complexity arises in linear systems merely as a result of superposition. If you put a lot of simple things together, you can get a complicated thing. Radio waves are a very good example. A radio wave from a transmitter, which is a familiar linear system, can have a very complicated form when it's travelling from the radio station to the receiver. When the modulated wave is picked up at the receiver, it represents a complicated form all the different frequencies are superimposed and are filtered out by the radio, i.e. broken down or analysed into a simple set of components. You can put the original waveform back together again if you like; linear systems are reversible. The point about linear systems is that they can be taken apart and reassembled; the individual components don't get in each other's way. Linear systems are simple to study, precisely because they can be chopped up and analysed in this way without destroying their essential nature. The philosophy of reductionism therefore works very well for linear systems.

By contrast, a non linear system is more than the sum of its parts. Synthesis in a linear system is mere superposition two or more things put together without interaction. However, in a non linear system, a and b together make more than a + b. The conjunction of two components in a non linear system can lead to novel and very often unforeseen effects. Different parts of a non linear system often interact to produce something totally new. Non linearity arises for a variety of reasons often as a result of feedback mechanisms or from breakdown of the simple proportionality in the action of forces. In reality, all systems are non linear, it's just that many are to a good approximation linear, so that the methods of linear analysis work very well for a wide range of systems.

In a non linear system, complexity is much more than mere complication, more than a lot of things jumbled together. Even very simple non linear systems can display remarkably complex behaviour….
Traditionally, scientists have tended to de emphasise complex systems, treating them as a sort of annoying aberration. This reflects the fact that non linear systems are hard to study. However, by focusing on simple linear systems at the expense of non linear ones, science has developed a strongly reductionistic bias. It used to be argued that complex systems are, in principle, always explicable in terms of their components you just have to chop them up and look at the individual components and then you will understand them as a whole. This purely methodological reductionism became so ingrained that it translated itself into a genuine belief: ………Unfortunately, the entire vocabulary of science has become rooted in this reductionistic philosophy……….Well, many distinguished scientists, including a number of famous Nobel prize winners, have rejected the reductionist picture of the world, although they have tended to be dismissed as sentimentalists or vitalists. I believe, however, that a sea change is taking place in the scientific community due to the rapid progress being made in understanding non linear systems, complexity and self-organization. Across a whole range of disciplines, a new paradigm is emerging. This transformation is due in large part, I might say, to the advent of fast electronic computers, which have made possible for the first time the study of complex non linear systems in great generality. As a result of this explosion of knowledge, a curious inversion of outlook is taking place. Complexity is now seen as the norm rather than as an aberration; most physical systems, as I have remarked, are in fact complex non linear open systems. The simple closed linear systems of traditional science are now recognized as extreme idealizations belonging to a very special class. The strong emphasis accorded to such systems in the past can be regarded simply as a sort of selection effect. When scientists had available only primitive techniques and studied only simple systems.’

This simple and very clear exposition emphasizes clearly that science has functioned over the past two centuries on extreme idealizations that are approximately linear but to quote Paul Davies again: ‘In reality, all systems are non linear, it's just that many are to a good approximation linear, so that the methods of linear analysis work very well for a wide range of systems.’

This important distinction becomes extraordinarily important when we begin to study the views of some of the present day masters of homeopathy and how they seem to differ in how they define and delineate their own interpretations of the actions of good remedy. But before entering this discussion, let me make a very clear point regarding how we engage with the classic model of homeopathy. It is clear that we have extrapolated a model of homeopathic therapeutics that has until now been a very linear model: the ‘simillimum’ acted curatively and the individual came to rest within the parameters of his ‘constitutional remedy picture’. This was at least in the early days of the homeopathic community; the great masters built on this premise, and we seemed to have clear pictures that corresponded to clear remedy states. This was and is today how the classical model is still taught at most of our colleges. The trouble with this elegant approximation is the rather neglected fact that all systems, including our own systems, are part of Nature, and Nature has suddenly been found not to approximate with such elegance anymore. It is obvious that the model needs to reach out to a greater and more dynamic system that brings into existence the mathematics of chaos theory and complexity, and we cannot continue to abide by the dictates of a subtle medical model that is still adhering to some of the outdated Newtonian paradigms that are functionally useful but bear little resemblance to the complexity of the human ‘ecosystem’.

Let us examine two contrasting masters of homeopathy today who I think clearly bring out the distinction made between linear and non-linear systems. Firstly, Massimo Mangialavori. Mangialavori sets up very rigorous standards insisting that a remedy must continue to work for a period of two years, it should work if repeated in an acute, it should reduce the severity of the patient’s symptoms and the patient should experience some fundamental shift at a deep level. Furthermore, Massimo describes the correct prescription as part of a process with ups and downs but with an upward movement towards cure over several years.

These standards are truly rigorous and fall into a linear paradigm of classical homeopathy. It assumes certain parameters of proportionality, the single remedy defined as the closest to the ‘simillimum’ and that this will behave in a particular manner. Yet this rigorous approach needs to be examined. Although one cannot deny the quality of his results, Mangialavori states in an interview published in The Homeopath: ‘In my practise I have a lot of failures……I think you can roughly divide my practise in three. One third are very good cases, one third are not good enough, and in one third there is nothing .’ In other words, his stringent standards apply in only one third of his cases - an idealisation that approximates to the reductionist model of a linear system. His results obviously encourage him to search for ever better approximations to this ideal, but his problems in producing such brilliant cures do not lie in learning ever greater tomes of materia medica but in the ‘modus operandi’ of Nature itself!

The other modern master who has contributed enormously to the growth of the homeopathic model is Jan Scholten. His views on the ‘correct remedy’ are somewhat different, for not only does he state that a remedy can create a rapid and visible shift in the perceptual life-patterning of an individual but this change can be irreversible and immediate. He further makes the point in his book Homeopathy and the Elements that a patient is not a remedy, for if someone was, his problem then would be that he could never be cured. In other words, remedy pictures are frozen patterns that effectively manage the ecosystem of the patient for a duration of time and this is called a remedy picture. Nevertheless, states are dynamic processes which are potentially fluid, and therefore no one can be restricted to ‘constitutional states’ as it suggests a state for life and this clearly only applies to certain idealized situations. Scholten’s model of the homeopathic process seems to fall far more succinctly into the category of a non-linear system. He does not restrict the possibility or the search for new homeopathic states to part of a ‘time-line’ that have to fit certain stringent parameters that enable idealized states of a remedy picture to be clearly defined as a clear case of that remedy. It is not to detract from the brilliance of Massimo’s cases that I comment on his strict adherence to ideal remedy pictures, and his contribution to the homeopathic community is overwhelming, yet at the back of my mind, I still ask the question: if his patient remains the same remedy picture over a period of two years and the identical pattern is potentially still present in his cured patient, where is the effective cure?

Let me expand with a couple of examples from my own practice. I have seen wonderful cases which responded beautifully to Mangialavori’s particular rules of a ‘classical case’. One such case concerned 68 year old man suffering from chronic insomnia who responded beautifully to the remedy Aurum arsenicum given over two years. The remedy fitted his whole totality and he may well have responded to this particular remedy at any time in his life. This would correspond to a ‘linear case’; the remedy and its totality covered all psycho-environmental situations that this individual might have met in his lifetime. There was a direct relationship between this remedy and the psycho-neuro-immunological ecosystem of that individual. Every eventuality that this individual might meet, would probably respond to Aurum arsenicum in various potencies.

Another case was that of a woman who responded firstly to Calcarea bromatum but who shifted within six months to an entirely different state and returned to the clinic presenting a different state or layer of her past which had surfaced. This state concerned possible abuse from her step-father and her feeling of entanglement together with feelings of profound antipathy towards him. For this state she was given Python, a recently proved remedy, which resolved the situation very clearly. This individual is now happy and pregnant, and may need another remedy, but I am unclear what the next remedy is and will watch with anticipation! The point to be made is that this was clearly a non-linear case, similar in many ways to some of Scholten’s cases; the individual changed from one state to another, and then another, and she may continue to evolve through different states that may possibly explore even more facets of her psycho-immunological individuality. To argue from the classical point of view that there may have been a even more profound remedy that covered the whole totality is to argue from an idealised point of view that insists:

1. Individuals cannot explore more than one remedy state
2. Individuals cannot change dramatically from one state to another state
3. Individuals are remedy pictures

IS A RESOLUTION POSSIBLE?
One way to accommodate the obvious tensions between the two aforementioned models, is to accept that Massimo adheres to a model that is linear, and idealized, and that his intention and the sheer elegance of his cured cases motivate and drive his intention towards a linear model that actively encourages him to seek further evidence for his methodology. Yet, and this is my point, today science and its methods of perceiving reality have moved on with the advent of super-computers, and have found such ideal linear models to be only approximations to non-linear systems which fundamentally are constantly evolving towards ever greater level of complexity broken up by chaotic interludes. It is not time to set aside such idealized models but to realize that ultimately Scholten’s model is actually a lot closer to the reality of science and to try and evolve a model of homeopathy, where accommodating the idealizations of Massimo’s work is but one step towards creating a model of homeopathy that can encapsulate both models yet with the insight gained from ‘New Physics’ that linear models can only sit within the greater totality of their non-linear denouement.

Ultimately, most of homeopathy falls under the category of the experiential interface, and how one has evolved in one’s use of remedies and the cures elicited. My own preference and observations have fundamentally led me to accommodate my experiences within the domain of a non-linear system. It is hard for me to adhere so closely to Massimo’s model since his model is based on how long the remedy pattern is frozen in time i.e. how invariant or solid the entire process is embedded in the patient’s ecosystem, with the concomitant premise that having found this acceptable level of invariance at the core of the patient’s psyche, that repetition must be continued until this pattern is finally cleansed or eliminated from the ‘ecosystem’. What I fail to understand is why such ‘temporal’ limits have to be put on change; it seems limiting in the extreme and even ‘unhealthy’. One of Hahnemann’s stipulations was the uniqueness of the homeopathic process and the fact that different people were uniquely configured to receive different remedies, so why do people not have equally unique curative time-lines which indicate different rates of change and cure!

In the final analysis, it is not to detract from the quality or brilliance of the linear model that I am writing this article, but if we are to mention science and homeopathy in the same context, and it is difficult to remain purist in a society which is undergoing such phenomenal changes, then we must accommodate or create more dynamic models of the ‘human ecosystem’ that encourage active explorations in the field of non-linear systems.

My own feelings can be succinctly summarised by Umberto Eco, in an interview when he said that ‘there is a sense today that the past is restricting, smothering and even blackmailing us.’