# A SYNERGETIC PERSPECTIVE ON NUMBER DYNAMICS

### A GRAPHIC NUMBER THEORY FOR THE MILLENNIUM

Abstract:  SYNDEX identifies and demonstrates various properties of the base ten number field, such as the symmetrical distribution of prime numbers.  The continuum can be viewed as both progressive and regressive.  The key to the comprehensive analysis of general number behavior is found in the concept of "circular unity."  Synchrographics has been systematically contrived to formally illustrate behavioral patterns that have successfully led to a general understanding of the fundamental elements of the geometrical nature of the base ten system.  The graphic importance of the Holotomic Sequence is that circular symmetry is being conserved and may be enlisted as the fundamental reference key in the graphic investigation of number behavior.  The primes are deployed in symmetrical interface only within these specific Holotomic domains.  Here, the enigma of prime number distribution has been solved.

Synchrographics regards symmetry as a primary analytical aspect of reference, making the Syndex archetypal system of classes of numbers possible.  The foundation of this system is palindromes and transpalindromes, yielding 12 classes of number.  Palindromes, or binomial reflection numbers are neither purely accidental nor without significance.  Transpalindromes are the reversal of any particular number exceeding a single digit (for example, 16 and 61).

Numeronomy, the laws relating to the essential structure and dynamics of number, is a new word for an extremely ancient science.  This science, (based on the knowledge that the continuum contains a definite structural order with general laws that describe the nature of that order), has laws that relate to the general behavior of nature itself.  Each number has both a geometrical and numerical identity.  It is the outcome of Synchrographics: numbers speak for themselves through structure and behavior.  The first concern of Synchrographics is maximum information expressed via minimal graphic elements.  Correspondences, such as those between geometry, numbers, colors, and frequency of divisibility form an integral part of the system.

All mandalogs (number wheels) are the product of the systematic generation of the exact sequence of minimax factorization.  They have the perfect retrograde feature by which the patterns generated in the first half of the spiral are reversed at midpoint and are reflected as a mirrored image in the second half of the spiral.  Comprehending the universal nature of the transpalindromic function of number behavior is not easy.  We tend to see the number chain as a unidirectional continuum, which is too linear  for a synergetic perspective.

Revisioning the number continuum with the concept of simultaneous counterflow yields a more accurate picture.  Remember, this is also happening in Post-quantum Physics under the rubric of quantum backflow.  With large spans of number, the complex interrelationships become difficult to visualize without good graphics.  Because of the octave nature of the base cycle there cannot be more than four consecutive transpalindromic pairs in a single symmetrical sequence, regardless of the amount of digits in each individual number.

We cannot contemplate numeracy without an automatic involvement with geometry.  A triangle is an expression of the number three and a square is an expression of number four, i.e. number and geometry are two sides of the same coin.  Therefore, Synchrographics was contrived to analyze the geometrical properties of number and conversely the numerical properties of geometry.  In the proceedures that will be explained in the text, we discovered the key sequence (Holotomic Sequence) which consists of a series of key numbers or circular unities in the rhythmic wave.

Buckminster Fuller was very excited, and "filled with joy" over these revelations, and we hope you will be also.  After all, numbers are what they are, not what we wish them to be.  They will not do what they cannot do, i.e. show symmetries where none exist.  Nor can they hide their inherent qualities forever from the astute devotee.  Using a general systems theory approach, we employ metaphors from many disciplines to demonstrate how this perspective can be employed in other fields of investigation.

"2520 Mandalog"

### DEDICATION

to EROS...
and CHARIS...

Electra...

and Tesla...

### ACKNOWLEDGMENTS

R. Buckminster Fuller for his mentorship;  Jack Garvey for early attempts at verbal descriptions; Jaime Synder for networking; Vickie Webb for cyber-ingenuity (graphic support and web page design).

Special  thanks to Susanna Abbott for introducing Bob and Iona in the late 70s, and for her continued moral and graphic support.  Susanna also holds the distinction of being the very first teacher to use Synchrograph C, #108 as a study tool in her Middle School classes, in the Bay Area, California.

: Robert Marshall, Master Numeronomist  : Iona Miller