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Volume One - An Abridged Extract

The Secret Computer of the Ancient Gods




1. Divinatory Readings

Divinatory Readings of the I Ching are normally obtained by use of the Yarrow Stick or Coin Oracle methods, where the random selection of one of the sixty-four readings is determined by the construction of a hexagram symbol. In addition to these two oracle methods, hexagrams may also be created from two trigrams, by simply placing one trigram over the other.  There are eight different trigram symbols and by combining two trigrams together, a combinatory series of sixty-four hexagrams may be formed.

2. Trigram Discs

Two circular trigram arrangements are illustrated in most books of the I Ching. These are known as the Earlier Heaven and Later Heaven Arrangement .  Very little information is given as to their purpose or use.

The consensus of opinion, from a number of authors and researchers of the I Ching, is that they are Magic Charms, which have no real intrinsic or use what so ever. It was thought that they belonged to yet another ancient oracle system which may have employed the use of fixed and spinning discs similar to those used for the Tibetan Prayer wheels or the German Enigma coding machine.

3. The Analytical Model Calculator

In order to prove that trigram discs formed part of an ancient computer system and to determine the technical feasibility of such an arrangement, a model hexagram calculator was constructed which utilized three circular trigram arrangements. The model consists of three individual discs of different radii, attached to each other via a central axis pin, which permits each disc to rotate. The circumference of each disc is segmented into eight equal sections, the periphery of which is inscribed with the following data.

  • The trigram symbol.
  • The respective cardinal compass point position of the trigram.
  • The associated clockwise and anti-clockwise numerical line values of each trigram line.

Each disc represents a different trigram arrangement. The model was so designed so that the respective cardinal compass point alignment of each trigram would enable the practitioner to select two adjacent trigrams each from a different disc, in order to create a hexagram by simply placing one trigram over the other. With the discs in a static mode, a large  number of different hexagrams were created by utilizing various mathematical combinatory movement patterns for the selection of individual trigrams.

4. The Initial Results

It had been anticipated that the hexagram calculator, with the discs in a static mode, would at some point replicate and produce every single hexagram of the I Ching. However, this was not the case. Thirteen anomalous hexagrams had eluded the combinatory series of movement patterns which had been mathematically pre-determined during the initial design of the calculator.

It was obvious that the deficiency of the hexagram production was due to either:

  • A miscalculation of the combinatory mathematics, or alternatively,
  • The use of only three trigram arrangements, where the diverse nature of the sequential trigrams were insufficient in order to replicate the complete series of Sixty-four hexagrams. Therefore an additional fourth disc was considered.

5. Disc Rotation

Disc rotation was considered. It was however initially rejected, primarily because the trigram alignment of each disc to its respective cardinal compass point position was considered to be of some importance for reference purposes. (It should be noted that a disc rotation method would only require one fixed and one moving disc, each inscribed with all eight trigram symbols to effectively create all sixty-four hexagrams by mathematical permutation).

Further research was carried out later, after the Rules for disc rotation and associated logic truth tables had been developed. These rules were applied to the resultant hexagrams produced by the analytical model. The disc rotation method created hexagrams by the instantaneous alignment of two adjacent trigrams  which were selected from two different discs. This instantaneous alignment of trigrams has been termed an instantaneous Causal  Event as change occurs at that moment in time.

Over nine hundred hexagrams were produced in this manner. The prime criteria for an instantaneous causal event was the instantaneous formulation of a hexagram, whose combined binary value of both trigrams matched the binary value of the respective hexagram mentioned in the I Ching text. The number of hexagrams which met this criteria was therefore significantly reduced to sixty-four. These instantaneous hexagrams were then segregated into groups and the resultant pictographic images obtained are as shown herein on Project Data Sheet PD002.

6. The Discovery of a Visual Display Board

A major discovery was made during a review of the research material. I realized that The Key for Identifying Hexagrams, incorporated within the I Ching book, could actually represent an ancient visual display board.

This key is formed by an eight by eight matrix. It is used by practitioners of the I Ching to determine individual hexagrams from their respective upper and lower trigram components.Each Square is identified by a number from one to sixty-four, in what appears to be a random arrangement. The number identifies the specific divinatory hexagram reading, which has been determined by using one of the oracle method.

The matrix arrangement consists of eight columns and rows. These are individually identified by one of the eight different trigram symbols. The sequential arrangement of trigrams placed horizontally along the top of the matrix (from the 1st left hand column to the 8th column on the right) is the same as the trigram sequence that is placed vertically (from 1st row at the top to the 8th row at the bottom) along the left hand side of the matrix .

This arrangement of "coded" hexagram numbers, which has mystified scholars and philosophers for many centuries, has now been mathematically deciphered!

7. Hexagram Pixels

By employing this matrix board as a visual display unit, a 'pixel' in the form of a single hexagram square could be placed within any one of the sixty-four squares by using either the hexagram identification number or the two associated trigrams.This simple methodology could have enabled the ancient practitioner of the I Ching to create pictographic patterns by utilizing a number of hexagram symbols or their respective trigram components.   

  8. Trial Experiment & Mathematical Exercise  

As a trial experiment and mathematical exercise, the thirteen anomalous hexagrams (mentioned previously) were plotted and positioned onto the visual display board. Amazingly, the position of all thirteen hexagrams formed a symmetrical  pattern either side of an imaginary straight diagonal line, drawn from the top left hand corner to the bottom right hand corner of the visual display board . This arrangement was not coincidental. It was a deliberate design that had been pre-planned by the originators of the I Ching to convey something of importance to the practitioner. How strange it is, when one finds something that has been mislaid or lost for centuries. This pattern represents an enigma.  

9. The Hidden Design  

Looking  more closely at the hexagram arrangement, there seemed to be something hidden in the pattern which mysteriously appeared. Drawing lines to accentuate the hidden design, a right angled triangle with side squares was discovered. The design of this triangle and its associated squares represented the geometrical proposition of Pythagoras i.e., 'The square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the other two sides'. Could it be possible that there was other geometrical and mathematical information hidden in the pattern?

Additional lines were drawn between various points. By trial and error, a unique pentagonal shape was revealed. The result caused quite a sensation and raised more questions than answers. For instance, why would the originators go to so much trouble in designing an encrypted coded system to simply produce just a few geometrical images such as the pentagon.

10. The Pentagon

I realized that this five sided pentagon represented a mystical symbol which was directly linked to a pentagram. The religious significance of this symbol is equally vague, as it is often referred to as the sign of magic or Satan. According to the bible, Satan took the form of a Serpent who gave Eve the apple from the tree of knowledge for Adam to eat. After which Adam 'opened' his eyes and became aware of his nudity. So the pentagon may be attributed to Adam's awareness and the apple which was taken from the tree of knowledge, hidden away from the eyes of the uninitiated.

This seems to be a plausible answer. But why was this particular symbol used?   In addition, one important question remains, as to what was the reason for hiding it? If the knowledge it contained or the ancient message incorporated in its shape was deemed to be sacred, then it must have some relationship with either a Chinese or a Tibetan religious Practice. Indeed, it could well represent a five limbed man within the macrocosm.

11. Measurement of Mathematical Co-ordinates & Discovery of Mathematical Constants

For reference purposes, the individual mathematical co-ordinates of the pentagonal shape were measured, utilizing the side length of one hexagram square as one unit of measurement. What followed was truly amazing. The measured distance  between the apex point of the pentagon and both the right hand and left hand side of the horizontal base was found to be Two Pi units i.e., (2п units).

To obtain more information, two vertical lines were drawn from the base of the pentagon to intercept with the roof, using the corners of the inherent hexagram pattern as a guide. An additional horizontal line was drawn across the apex from one side to the other, to form a rectangular shape inside the pentagon. The measured ratio of the shorter side to the longer side of the rectangular shape was found to be equal to that of the Golden Section Ratio.

Other straight lines were drawn across the inherent hexagram pattern and the value for 'e' epsilon was also determined by direct measurement. In addition a pictographic image of an ancient sun dial plate emerged from the depths of this unique pattern.

                                                           12. Initial Conclusion

I concluded that this inherent and unique pattern of hexagrams had revealed not only the existence of the geometrical proposition of Pythagoras, but had also indicated the values of the irrational mathematical constants that governed the Mathematical Laws of the Universe, together with the means to measure Time!

This in itself represented a truly magnificent mathematical achievement, which had been conceived by an ancient and advanced civilization some 3000 years ago.

I considered that the visual display board, together with the individual and specific series of hexagrams, could form an important educational tool. In order to obtain additional information, the nine hundred plus hexagrams (previously mentioned) were carefully re-examined and segregated into separate groups. From which it became apparent, that a significant effort had been made by the originators of the I Ching to pass on their own thoughts,  ideas and images of their ancient civilization.

 13. Investigation of Combinatory Methodology

An investigation, conducted on the initial combinatory methodology, showed that a considerable amount of hexagram repetition had occurred, which had been not only time consuming but unnecessary. A simpler and more accurate calculating model was therefore envisaged. After several weeks work, together with additional research on the inherent binary code within the I Ching text, a new model hexagram calculator emerged from the design board. This new model, now rearranged as a central processing unit, can compute and select trigrams in a specific manner. It is so designed, that it can easily perform the same function as required by an ancient I Ching Computer System.

14. The Creation of a Universal Set of Numerical Hexagram Tables

The physical CPU is re-programmable and the series of hexagrams it creates are formed in a mathematical and scientific manner which is repeatable. The new model calculator has led to the creation of a universal set of numerical hexagram tables, which are being used in conjunction with analytical sheets. The methodology employed is currently being synthesized, to create a modern day software program, so that every possible pictographic image may be recovered from this unique ancient combinatory computer system. To-date a large number of trigram discs have been deciphered. The resultant pictographic images have been reviewed and their inherent meaning interpreted.

15.  The Visual Display Board - Numerical Code Decipherment

The visual display board was found to incorporate a numerical coded system, which was thought to be undecipherable. However, a study of the information contained in a silk manuscript recovered by archaeologists from the Ma Wang Tui tomb in China, has lead to the decipherment of this numerical coded system and the mysterious encrypted code used by the originators of the I Ching.  The technical details, logical operations and mathematical methodology which was incorporated within the ancient I Ching Computer System is now known.

16. Final Conclusion

Research has conclusively proved that the originators of the I Ching:

  • invented, developed and used the Binary Digital Code over 3000 years ago.
  • understood and had an in-depth knowledge of Amino Acids and the Genetic Code.
  • knew the basic components of Nuclear Physics.
  • developed a mathematical system of numbers which encompassed everything in the Universe.

The I Ching is a book that relies on self knowledge. It gives mankind an insight into the minds of the scribes of an ancient civilization, by showing us in a pictographic manner their thoughts, ideas, inventions and wisdom.

It is concluded, that a considerable amount of mathematical information is encoded within the strange symbolic trigram discs. The examination of a number of acquired archaeological discs and other religious artefacts, has shown that it is not necessary for the practitioner to obtain every disc, in order to complete the project work.

With the exception of a few unique and different discs, which incorporate two or more than two trigram symbols of the same type (by omitting other trigrams), all trigram disc arrangements can be determined by using combinatory mathematics.

The Computer System of the I Ching, has revealed an ancient time capsule of pictographic images. It will take many years to decipher the thousands of images which lay hidden within its mystical symbolism.



Important Note:

The Appendix Pages shown herein form part of the I Ching Project Documentation and are presented in this document for reference purposes only.

No part of these Project Data Sheets or appendices may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by an information storage and retrieval system without the permission in writing from the Author.

                            Appendix 1: Flow Chart of The I Ching Computer System

                            Appendix 2: I Ching Project Data Sheet - MS.001

                            Appendix 3: I Ching Project Data Sheet - KC.001

                            Appendix 4: I Ching Project Data Sheet - PD.001

                            Appendix 5: I Ching Project Data Sheet - PD.002

                            Appendix 6: I Ching Project Data Sheet - PD.003

                            Copyright John C. Compton - 2006 - 2013