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SHAPE Special Issue 26
Mathematical Chaos I:
A Basis For Understanding
1. Introduction: Mathematical Chaos
2. What is Mathematical Form?
3. Abstracting From The Form/Content Amalgam
4. What is Mathematical Chaos?
5. Historical Papers: Introduction
The Secret Life of Chaos (Reviews)
6. Masters of Another World
7. Where is their World?
8. A Postscript
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Welcome to the 26th Special Issue of the SHAPE Journal, compiled to address one of the Key Questions in both Philosophy and Science, while seemingly residing solely in the most esoteric regions of Pure Mathematics.
It attempts to find an alternative to the currently universally accepted formalism, and also the basis for all theories in Science, which is dependant upon the usually unstated Principle of Plurality, but turns decisively away from this now standard approach, to the alternative that sees Reality as more properly characterised as deeply holistic.
It has become a truly major undertaking, not only because of the difficult problems that have been encountered, but also because of the significant breakthroughs that have already been achieved with this alternative approach.
And, these gains have been primarily in what is usually termed Mathematical Chaos. These achievements have been primarily philosophical, for they have questioned the usually agreed ground for this area of Mathematics, by a careful study of the implications of iterative assumptions and methods, NOT, as is usually the case, in pragmatic assemblies, but in the generation of the now renowned Chaotic Forms that they can be persuaded to produce.
But, its status here is not solely dependant upon these researches, but also, and perhaps even more importantly, upon extensive resonances with these forms both in Physics and in Philosophical studies too.
The crucial and revealing studies have been in tackling the need for a scientific methodology, based upon the assumption that Reality is not pluralist but most definitely holistic, yet though this is often conceded, NO feasible methodology or formalism has so far been achieved.
Holism, though probably the more correct view of Reality, seemed incapable of providing Science with any means to rival those delivered by the assumption of Plurality.
Yet, in this relatively small group of papers, a possible way has been devised.
It may not be what mathematicians want to hear, and the vast majority of physicists, immersed up to their necks in the now consensus Copenhagen Interpretation of Quantum Theory, will certainly be directly opposed to these ideas. But, in the opinion of this theorist, these papers represent a significant contribution, and lay down a sound basis for further research, and, maybe even a Major Revolution!