One of the issues, which has made it very difficult for orthodox thinkers to grasp homeopathy, is the concept of the vital force. A unifying field that permeates and imbues material life with energy and health, but which, when limited or blocked, can affect the material well being of the body.

However, this concept is not new and it is not unique to homeopathy. This idea has been written about by many thinkers in other fields, medical and philosophical in the past and in the present.

If we are to try and ascertain how the vital force passes through matter and how it ebbs and flows in health and disease; and how the remedy patterns relate to one another as they mirror these effects and reflect them to us as remedy pictures, then we will have to broaden our perspectives and look at these other theories of the unifying field of Nature.

A MATHEMATICS PERSPECTIVE:

Catastrophe Theory may well help us to understand how the unifying field of vital force actually behaves. Developed by a mathematician, it is used to look at the changes in the behavior of systems, ‘the collapse of a bridge or the downfall of an empire. But it also deals with changes as quiet as the dancing of sunlight on the bottom of a pool of water and as subtle as the transition from waking to sleep’.

These theories are controversial even in mathematics, which has always seen change as slow, smooth and evolutionary. But Nature has catastrophic changes too ‘… the abrupt bursting of a bubble’ or the sudden shift of thought when we get a bright idea!

Catastrophe Theory was developed by a pure mathematician, Professor Thom, to study these sudden events when he was pondering on the order of Nature.

Newton’s calculus enables us to deal with continuous change, and this model of the Universe has molded our thinking for two hundred years. It has allowed us to predict undiscovered planets and to feel certain about the Universe. However, the twentieth century has gone well beyond Newton with the discovery of sudden and discontinuous change in the sub molecular level; electrons have obviously never read Newton!

Professor Thom interestingly believed that though our quantitative grasp of magnitude must not be relinquished, our qualitative grasp of form and geometric order goes much deeper the provision of some kind of picture, at least to the mind’s eye, is of primary importance.

The four fundamental forces science does know about, gravity, electromagnetism and the two forces within the atomic nucleus are ‘mysterious’. Physicists ‘..at best hope for a unifying theory to combine the four mysteries into one’.

Einstein frequently visualized forces as ‘hills’ and ‘valleys’ on a map of space-time. Thom sought to extend our intuitions of form ‘to see that processed and events have a shape of their own’.

Thom believed that we have to grasp the Universe’s ceaseless pattern of evolution and destruction of forms. He developed a topographical representation of this theory, a sort of three-dimensional graph, plus a mathematical formula to express his ideas. Also, he included in his thinking, the expression of continuity of forms of Nature. The branches of a tree, a river delta, a nerve axon and dendrites and the cracks in a wall.

These ‘recurrent identifiable elements’ have what Thom calls ’structural stability’. His goal is to describe the origins of forms, and to do this he has developed a mathematical language. Averages and probabilities founder in attempts to describe life as we see it. Calculus is ‘well behaved’ and ‘obliging’; reality is not.

However, in all aspects of probability and statistical analysis, the appreciation of pattern is fundamental. ‘Something that is not random’ underlies all concepts that require order and determinism for them to have any meaning at all. Science has tried to define a ‘detailed control mechanism’ perhaps located in the genes, ‘but the gap between those first gene products and such complicated end results’ this is the sensitive spot’.

Thom is more interested in their qualitative stability even under quantitative variation. What is striking is the stability, the homeostasis or ecological stability of repeating forms. Thom extends this notion of stability to inorganic systems as well. Based upon internal mathematical consistency, Thom sees Catastrophe Theory generating new forms from other sets of forms, allowing qualitative predictions. He sees it as a language, mathematically correct.

This theory is currently being explored in the social sciences and mathematicians are using Catastrophe Theory to draw graphs to illustrate the difference between sense and nonsense in mathematics.

Thom identified seven qualitatively different types of discontinuity (passing through non equilibrium states) with his new theory, but he states that there are also an infinite number of ways for such a system to change continuously (staying at or near equilibrium). There are other conceivable ways for the system to change discontinuously, but they are unstable and do not contain recurrent identifiable elements. These unstable discontinuous events are only likely to happen once only.

The ’surprising seven’ catastrophic events Thom calls by the colourful names of swallowtail, fold, cusp, butterfly, hyperbolic, umbilic and parabolic.

The stacastic process, which is part of the Law of Large Numbers, depends upon the reliability of large numbers of events, each one based upon the previous event in a cause and effect chain. The pattern emerges with repetition of events and then we can see the pattern within the pattern. Thus pattern is the repetition of events - one implies the other.

The unified field of the vital force and the way this field behaves as it passes through matter must surely occupy our minds from now on.

Source: Catastrophe Theory, a revolutionary new way of understanding how things change, page 9, Alexander Woodcock & Monte Davis Pelican Books ISBN 0 14 02 2250 2.

## Monday, April 20, 2009

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