Analogical Geometry - Book I

domenica, 15 maggio 2022

A few months after publishing Science & Perception, I met up with my friend, Francesco, who works as a mathematical modeler for a large university in Stati Uniti. Somewhat curiously, Francesco asked whether I might be able to port the ideas in my first book to mathematics. And so the idea for this book was born. At the time, I had no idea that I would end up writing a book about Geometry, let alone breathing life back into an ancient form of Geometry that didn't involve numbers or calculations.

Few people, even scientists, realize how much the assumption of particles has permeated not only science, but mathematics as well — especially a form of mathematics that replies upon an initial assumption of parts. Even at the most basic level of counting, people make an assumption of parts by first counting one piece or part, and then another. With that said, what other approach is there?

Well, it is also possible to take "one thing" and partition it into fractional parts. Thus, each "part", rather than being completely independent, can be seen as an integral aspect of the original whole. One has to go back several hundred years, to the time of Newton, and even the time of Descartes to find a branch of mathematics that progresses from an initial whole to its parts. This branch of mathematics is Geometry.

Ancient Geometry, however, is distinctly different from the modern "calculation-based" approaches to geometry developed by Descartes, familiar to many as the branch of mathematics referred to as Analytical Geometry. Analytical Geometry, however, employs very different methods than those of Classical Geometry. For Geometry, in its most ancient form, operates completely without calculations or numbers. As odd as this might sound, there are no need for numerical calculations since everything is based upon relations.

This relational approach, without numbers, is the topic that I have chosen to explore in my work, Analogical Geometry, with many surprising results. This book contains a wide range of constructions and explorations with Geometric relationships, illustrating a very different approach to mathematics — one which eliminates the need for numerical calculations.

Yours in inspiration,
Michael Weaver