Theory of Holors: A Generalization of Tensors by Parry Hiram Moon (PDF)

Description

The word holor is a term coined by the authors to describe a mathematical entity that is made up of one or more independent quantities, and includes complex numbers, scalars, vectors, matrices, tensors, quaternions, and other hypernumbers. Holors, thus defined, have been known for centuries but each has been developed more or less independently, accompanied by separate nomenclature and theory. This book demonstrates how these complicated subjects can be made simple by using a single notation that applies to all holors, both tensor and nontensor. The authors consider all possible types of holors and develop holor algebra and holor calculus in the most general sense. Thus the reader will learn to develop a new holor that fits the application, rather than forcing an application onto a holor representation that is known but that does not perfectly describe the application. The discussion includes nontensors having no transformation and holors that transform in more complicated ways than allowed with ordinary tensors. This opens up the possibility to devise a holor for a new physical application, without being limited to a few conventional types of holor. This book should establish a method by which students and teachers can learn vector and tensor analysis via a uniform treatment. Graduate students and professionals in engineering, physics. applied mathematics, chemistry, biology, psychology, and other analytical sciences should find this to be a useful and innovative work.

User’s Reviews

Editorial Reviews: Book Description Establishes a method by which students and teachers can learn vector and tensor analysis by a uniformed treatment.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐While the notation at first seems burdensome, it resolves to be one of the elegant strengths in this groundbreaking but underappreciated text. If you’ve experienced tensors, you will wish you’d started here. While the text is of necessity dense, and rife with formulas, notation, and peculiarly named categories of holors, it is obviously not meant for anyone without a great deal of math already under their belt. It clarifies previously ambiguous distinctions under tensor theory, and leads to many “aha” moments. Rigorous and comprehensive. The only book on the subject, literally.

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