In his introduction to the great work of Thomas Taylor entitled "The Theoretical Arithmetic of the Pythagoreans," Manly P. Hall writes "Through the study of mathematics Pythagoras invited all men to a communion with the gods." As an individual working in the field of theoretical mathematics, I have been fortunate to know fleeting moments reminiscent of "a communion with the gods." And as a woman, I was thankful to find out that Pythagoras invited all men and women to pursue this communion. In fact, it was a woman, Theano, who took charge of the Pythagorean school after his tragic death. Throughout history individuals have pursued the study of mathematics as a means to understand things that matter. It is not the only means to such ends but it is far more valid than commonly recognized during this day and age. In "The Republic" Socrates states "the eye of the soul which is blinded and buried by other studies, is alone naturally adapted to be resuscitated and excited by the mathematical disciplines."
I have found great satisfaction in the study of numbers. I have also made many discoveries in the way of pure mathematics, discoveries that lend themselves to theoretical interpretation. Now when I look at the famous Fibonacci sequence, I no longer see "one plus one equals two," and "one plus two equals three," and so on. I have found that this procedure is missing an important step, a step that places the sequence among a limitless number of sequences composed in the very same manner. And when I look at the procedure for calculating phi, I no longer see "sq rt of 5 + 1 over 2." These procedures have become obsolete. In their place are universal procedures whose components exist within a greater framework of a hidden mathematical structure that composes all numbers and number patterns from under their surface-level appearance. It matters to me to know what is behind the procedure for calculating phi and to know that there is another step in calculating the Fibonacci sequence.
I invite those who may be interested in learning more to review the free PDF file introducing my greater body of work entitled "The Composition of Number." I will not compare my work to the profound works brought forth throughout history by more learned men and women but I do deliver this work to you in acknowledgement of its purity of existence and its substantial influence on my understanding of things that matter.
Barbara Mae Brunner
I offer this introduction for those individuals interested in learning more about "The Composition of Number." Click the link below to download the PDF file. The first two pages of the Introduction, describing its content, are presented below. Correspondence is welcome.
Copyright © 2002, Barbara Mae Brunner, All Rights Reserved
The concepts presented in this summary, and in the greater body of work entitled "The Composition of Number," are a result of my personal exploration into numbers and number patterns. The popular view that the perfection of the Fibonacci sequence is in its tendency to move toward a phi ratio between progressing consecutive numbers had always felt incomplete to me--not quite reaching the truth of the matter. I felt that there must be perfection, somehow, within the entire series of numbers right from the beginning. Exploring this thought catapulted me quickly into the concept of the composition of numbers and number patterns.
I found that perfection did exist from "the beginning" when looking at that which composes the Fibonacci sequence from under its surface-level appearance. Furthermore, I found that the Fibonacci sequence is composed in the same manner as an unlimited number of other sequences just as perfect, and that the phi ratio acts in the same manner as an unlimited number of ratios within the composition of similar number sequences. The common procedures used to calculate phi and the Fibonacci sequence appeared as incomplete versions of more universal procedures--procedures whose components represented different aspects of a greater mathematical mechanism.
I was beginning to see the hidden nature of numbers and number patterns through the study of their composition. However, without an education in mathematics, I faced the challenge of how to convey my discoveries in a language consistent with the subject matter. I was also unaware of how much of what I discovered is already known by other individuals. In the end, I have opted to let my work stand on its own as the result of a personal discovery process, and to express it as such. This approach may make its content more accessible to others who are not formally educated in mathematics but who, nevertheless, are seeking to know perfection through the study of numbers.
A mathematical structure, which I call the "ratio-based fabric," exists under the surface-level appearance of all numbers and number patterns. The operations of multiplication, addition, subtraction, and division applied to the structure initiate a process of composition for all numbers and number patterns. The ratio-based fabric is comprised simply of points in space. A point references a location within space and is represented by a numerical value. Every number represents both an A and B point. A and B points are not duplicated throughout the ratio-based fabric but, instead, stand in relationship to all other points through ratios and resonance. Space itself becomes defined when held between points. Spaces of the same quantity exist throughout the ratio-based fabric and, under specific conditions, become organized into fields.
Multiplication, addition, subtraction, and division are seen as natural forces that bring this limitless underlying mathematical structure to life--enabling and sustaining the composition of numbers and number patterns of many different types. The composition process occurs when points are connected into mathematical formations--as presented in the Introduction pdf file. Relationships between numbers and number patterns that would otherwise be undetectable or difficult to detect become visible when working with the ratio-based fabric.
In essence, the unique nature of a number or a number pattern is revealed when exploring its hidden composition through the study of the ratio-based fabric.
To download the entire Introduction click here: