This book is an introduction to the simple math patterns that can be used to describe fundamental, stable spectral-orbital physical systems (represented as discrete hyperbolic shapes, i.e., hyperbolic space-forms), the containment set has many dimensions, and these dimensions possess macroscopic geometric properties (where hyperbolic metric-space subspaces are modeled to be discrete hyperbolic shapes). Thus, it is a description that transcends the idea of materialism (i.e., it is higher-dimensional so that the higher dimensions are not small), and it is a math context can also be used to model a life-form as a unified, high-dimension, geometric construct that generates its own energy and which has a natural structure for memory where this construct is made in relation to the main property of the description being, in fact, the spectral properties of both (1) material systems and of (2) the metric-spaces, which contain the material systems where material is simply a lower dimension metric-space and where both material-components and metric-spaces are in resonance with (and define) the containing space.

This book is an introduction to the simple math patterns used to describe fundamental, stable, spectral-orbital physical systems (represented as discrete hyperbolic shapes). The containment set has many dimensions, and these dimensions possess macroscopic geometric properties (which are discrete hyperbolic shapes). Thus, it is a description that transcends the idea of materialism (i.e., it is higher-dimensional), and it can also be used to model a life-form as a unified, high-dimension, geometric construct, which generates its own energy and which has a natural structure for memory, where this construct is made in relation to the main property of the description being the spectral properties of both material systems and of the metric-spaces that contain the material systems, where material is simply a lower dimension metric-space and where both material components and metric-spaces are in resonance with the containing space.

This book is an introduction to the simple math patterns used to describe fundamental, stable, spectral-orbital physical systems (represented as discrete hyperbolic shapes). The containment set has many dimensions, and these dimensions possess macroscopic geometric properties (which are discrete hyperbolic shapes). Thus, it is a description that transcends the idea of materialism (i.e., it is higher-dimensional), and it can also be used to model a life-form as a unified, high-dimension, geometric construct, which generates its own energy and which has a natural structure for memory, where this construct is made in relation to the main property of the description being the spectral properties of both material systems and of the metric-spaces that contain the material systems, where material is simply a lower dimension metric-space and where both material components and metric-spaces are in resonance with the containing space.

This book is about a fundamental re-organization of language which is used, in regard to describing the stable many-(but-few)-body spectral-orbital systems, from nuclei to planetary systems, which, now, have no valid descriptions, based on, what are called, the laws of physics. The current description, based on partial differential equations, results in: non-linear, non-commutative, and an improperly identified and improperly used random basis for physical description. The result is that the properties of stability, which are observed for these systems, have not been describable in such a context. On the other hand, the already identified math patterns of geometrization, along with E Noether's symmetries, which allow the stable set of discrete hyperbolic shapes to be identified with energy-spaces, as well as the many-dimensional structure in which these stable shapes (of any size) are defined, as identified by D Coxeter, are patterns which can be used to form a new context for physical description. This is what this book is about, forming such a new context, wherein, the stable many-(but-few)-body spectral system is formulated and accurately described, ie it is solved. In such a new context, partial differential equations come to play a subordinate role to stable shapes and their relation to defining a finite stable spectral-set, which is a property of the, new, many-dimensional containment-set, a property which determines which stable patterns can exist. But there are many social forces which oppose such a discussion. These opposing social forces are also discussed.t

Includes reports of the Society's meetings.

Proceedings of a NATO ASI held in Corfu, Greece, June 25-July 7, 1994