## Introduction to The Numerical Structure

#### Note to Readers

##### Please understand the following things about this research and the website

##### It is under constant development but once you have paid for access to a section of the site you will see all further updates as they are made. From time to time I may also need to move info from one section to another. My apologies for any inconvenience caused.

##### By anyone’s standards this sorting out how the universe works and the nature of reality is a gargantuan undertaking and which was not my initial aim. Things have just turned out this way. I can honestly say I started with no personal axe to grind. I was brought up Catholic and seriously disillusioned in formative years to the point of rejection of Catholic doctrine but not the rejection of the God that resides in me (and that resides in us All), and which connection had always been felt very strongly in me as a child.

##### I am not a scientist. I am simply very curious, with a wide range of interests.

##### I have always been attracted to Numbers, but not the mathematics I was taught. I was never exposed to Pythagoras and Plato during my education and thus had no appreciation of the quality of numbers until 2010.

##### I have worked in financial markets for 20 years using a Harmonic Grid to help time global asset markets. (See www.marketharmony.com for details)

**The Harmonic Grid**

##### The Harmonic Grid methodology suggests emphatically that there is in fact an innate order in the universe and that this order permeates all financial markets as it is ubiquitous throughout the universe. It brings order from chaos.

##### However, this is really hard to swallow for most people. You see, we are conditioned by modern science and doctrine to accept that we are all here by chance, existing in a chaotic universe, evolved from some primordial soup, that was at one moment inanimate, and the next alive.

##### Nothing could be further from the truth!

##### This thinking is at the absolute fundament of the world’s problems. We must work with the Universe and not seek to obviate it.

##### In this effort I have pieced together the work of many great men and women and it is by standing upon their shoulders that this theory of everything can come to you at all.

##### Otherwise, I have simply let intuition be my guide and have been rewarded by a flow of incredible synchronicity that has allowed me to progress the theory to this stage.

##### This theory is a work in development and the physical book will be extricated from the contents of this website, hopefully later this year, depending on how fast things come together.

#### Setting the Scene for The Numerical Universe

##### To set the scene for the whole of this work I can think of no better introduction than the one written by John Michell in his brilliant book, The Dimensions of Paradise, with which all of my work is strongly aligned.

*From Dimensions of Paradise*

*INTRODUCTION: IN QUEST OF THE CANON *

*INTRODUCTION: IN QUEST OF THE CANON*

*Ancient science was based, like that of today, on number, but whereas number is now used in the quantitative sense for secular purposes, the ancients regarded numbers as symbols of the universe, finding parallels between the inherent structure of number and all types of form and motion. Theirs was a very different view of the world from that which now obtains. They inhabited a living universe, a creature of divine fabrication, designed in accordance with reason and thus to some extent comprehensible by the human mind. *

*The special regard paid to mathematical studies in the ancient world arose from the understanding that number is the mean term in the progression from divine reason to its imperfect reflection in humanity. At some very early period, by a process quite beyond explanation, certain groups of numbers were brought together and codified. Thus was created that numerical standard, or canon of proportion, which was at the root of all ancient cultures and was everywhere attributed to some form of miraculous revelation. It was taken to be the nucleus and activating principle of number generally, a summary of all the types of progressions and relationships that occur within the field of number and thus a faithful image of the numerically created universe. *

*In the known civilizations of antiquity, such as China, Babylon, and Egypt, the canon of number was venerated as the source of all knowledge and a guide to rightful conduct. Its influence extended from art and music to affairs of state. Every branch of science expressed its theories and observations in terms of that same small group of numbers which are investigated in this book. One numerical code has fashioned the whole of ancient mathematics, music, astronomy, chronology, metrology, and every variety of craft. It has left its mark on every relic and tradition of ancient cultures. There is nothing artificial about it, for the conclusion to these researches is that the various orders of natural phenomena do indeed conform to certain similar patterns of number, which also provide the framework of number itself. This allows the eventual reconstitution of that scientific standard which supported the fabric of ancient societies over periods of time that, by modern reckoning, seem remarkably long. *

*The author is frankly partial to the traditional order of philosophy associated in the West with Plato but also expressed in every different culture. It is called idealistic because it is concerned with causes rather than effects and with ideal forms rather than appearances. It is also called perennial, meaning that it grows naturally in the human mind and blossoms at certain seasons. The reason for its constant, universal recurrence is that it is mathematically based. Thus it provides a most realistic view of the world, balanced and made fully human by its transcendental aspect, the traditional doctrine of the soul’s immortality. *

*The number series that is demonstrated throughout this book not only was the source of all traditional arts and sciences but also gave birth to the system of philosophy adopted by Plato. That philosophy occurs of its own accord in the mind of whoever studies these numbers, their relationships, and their applications in different branches of nature. Through such studies the Pythagorean dictum All Is Number comes to life, and thus is opened a new outlook on the world in general. This new outlook, which is not in fact new but traditional, has certain consequences, discussed in the final chapter. It opens possibilities for the future, when the lack of a common, humanistic, scientific standard in affairs has become even more glaring than it is now, and necessity compels the search for some universal guiding principle. *

*To that future this book is dedicated. Its contents may seem in part dense and obscure. That is mainly due to the author’s lack of ability to do justice to this worthiest of all subjects. But it is due also to the modern eclipse of the traditional worldview that gives significance to these studies. The science here unfolded is of no obvious relevance to the modern world, and the type of philosophy that goes with it has been supplanted by other, temporary orthodoxies. To give sense and context to the following studies in the ancient canon of number, the traditional sciences relating to it are briefly described in separate chapters, with reference to the grand alchemical science to which they all contributed and the cosmological outlook that engendered them. This last is the most important, for the purpose and methods of the old sciences are apparent only in the light of traditional cosmology. That light is still hidden below the horizon of modern consciousness, but it can never be extinguished. And when next it arises, demanding the forms of science appropriate to it, the subjects raised in this book will be once again of paramount importance. *

*This book is the outcome of its author’s quest, pursued over many years, for the legendary key to universal knowledge alluded to in esoteric traditions and early texts. Its point of departure was Plato’s statement in the Laws that the Egyptian priests possessed a canon of lawful proportions and harmonies, by means of which their civilized standards had been preserved uncorrupted for literally thousands of years. The discovery and maintenance of true cultural standards was the main theme of Plato’s own writings. His scheme for a well-governed city, described in his Laws, was based on a certain numerical formula, often referred to but specified by only one of its components, the number 5,040. From this and his other mathematical allusions, the inference is that Plato himself had studied the laws of harmony he attributed to the Egyptians. In pure mathematical form, those laws were made the cornerstone of his proposed reforms in education and politics. The following chapters on Platonic number show how the laws of harmony were expressed numerically, as the dimensions of a city, a scale of music, or intervals in astronomy. In all his cosmological demonstrations, Plato used the same set of numbers and similar geometrical diagrams, applying them to such apparently different things as music and the order of the planets, and thus illustrating his belief that number is the “natural bond” that holds together the entire universe. *

*One of the conclusions from this study is that Plato’s symbolic arithmetic was not a contemporary discovery but a heritage from the distant past. The ground plan of his imaginary City (figure 47) consists of the same combined shapes and numbers as the Stonehenge plan (figure 6) laid down some 1,500 years earlier. Their common units of measure were derived from the same archetype, the numerical image of the cosmos. In chapter 3, the ancient units are analyzed and given their exact values, from which it appears that their lengths represent subdivisions of certain basic standards. The standards referred to are not in the first instance physical: they are indeed reflected in the actual dimensions of the earth and the solar system, but in essence they are purely numerical. And the numbers that express ancient units of length are the same as those that denote the scales of traditional music. The forms of music and measure known to Plato were defined and codified thousands of years before his time. Their common source was the canon of number, which Plato either learned wholly from certain teachers or partly reconstructed. His own concern as a would-be reformer and cultural revivalist was to renew the influence of the canon and make it once more effective as an instrument for universal harmony and stability. *

*It was probably through the Mystery schools, the select institutions of scholarship and mystical inquiry in classical and early Christian times, that the esoteric tradition which Plato drew on was passed down to the founders of Christianity. They were the cause of its last flourishing, soon to be blighted. St. John’s New Jerusalem, a visionary form of Plato’s ideal City and numerically identical to it, was a token of the “new heaven and new earth” that the prophet foresaw as the issue of renaissance through Christianity and the restoration of the true cosmic standard. Early Christian traditions are particularly useful through indicating the relative meanings and importance attributed to those numbers that occur in earlier sacred contexts. Thus, for instance, we learn of the supreme significance to Christian mystics of the number 3,168, which was also the paramount number in the ancient canon. Those Christian sects who practiced the numerical theology claimed that, through assimilating the pagan science, Christianity had become the legitimate heir to the ancient religious tradition. *

*The significance of this present subject can be summed up in many different ways. To artists, architects, and musicians, the study of number and proportion has been of traditional interest, and when the current vogue for novelty and individualism has run its course, it will become so again. With scientists of all disciplines, the case is similar. Bereft of guidance by any common philosophy, their researches and products are determined by the whims of commerce, militarism, national pride, and similar vanities; and the world of scholarship is likewise dominated by faddish intellectualism. Thus are created weird, aberrant thought-forms and monstrous manifestations. At such periods of philosophical anarchy, says Plato in the Republic, when there is no common means of distinguishing between beneficial and destructive products, popular demand arises for a standard of judgment. This is usually answered by some tyrant with his own prescription for standards. The demand, of course, is for an objective standard, one that is rooted in nature and reflects no particular theory or ideology. With this consideration begins the quest for the venerable cosmic standard or unified world image that is numerically structured to represent, in essence, the entire universe.’ *

### Introduction

##### My story begins on September 1^{st} 2010, a day I never forget.

##### After a sabbatical following a long contract with a leading hedge fund, I was back to my desk and considering the best way forward for my career. I had been sat down for just 15 minutes when I happened across a quote attributed to Nikola Tesla that changed my life:

##### ‘If you only knew the power of the 3 6 and 9 you would have the power of the Universe at your disposal.’

##### I sat there perplexed as I took the quote in. It didn’t make any sense. I knew a little about Tesla, enough to know he was thought an exceptional genius, one of the greatest to walk the Earth in modern times.

##### I googled the quote and for 3 weeks solid, 18 hours a day I became transfixed by this enigma eventually finding my way to a rather obscure and esoteric, fringe, branch of mathematics named Vortex Based Mathematics (VBM) founded by Marko Rodin and brought forward by Randy Powell who has been a particular rock of support throughout. This ‘stuff’ is certainly well outside mainstream academia and yet I knew they were on to something very deep and very important.

##### Very briefly, VBM can be defined as the study of resonance and ratio that attempts to identify the natural flow of energy.

##### As is likely with most readers – I have no scientific background whatsoever, and being totally ignorant about how electricity and magnetism work, I found it hard to take in what they were talking about. However, what I really zeroed in and what really caught my attention was the use of Modular Arithmetic, also known as clock arithmetic or as I prefer, the arithmetic of remainders. Of particular interest was Mod 9 which is central to VBM and of course the only Modular base to include the only numbers we have.

##### It was this that has led me to more of an understanding of what Tesla may have meant by that quotation above, and this research is dedicated to that end.

##### His quote unequivocally infers that Numbers are real in some causal way and it is in understanding the archetypal properties or ‘personality’ of each Number 0 to 9 that we can know, not guess at, how everything works, everywhere in the Universe.

##### It becomes clear that Mod 9 can and must be used to extract useful information from data available to us that would not otherwise be readily identifiable and that it reveals clearly the causal explanation for the effects we see and measure.

##### Included here as evidence for my assertions, I start by showing some of the basic VBM work pioneered by Marko Rodin and progressed by Randy Powell and others which covers Cellular Mitosis and the Fibonacci Sequence. This will then lead on to my original applications of Mod 9 to other Integer Sequences, to the problem of Prime Numbers, to Music and on and on. It is quite a journey.

#### Vortex Based Maths – Mod 9

**Modular Arithmetic is the Arithmetic of Remainders**

##### To Illustrate Modular Arithmetic very simply, let us take the number 12 as an example:

**In Mod 9, 12 is 3 because 9 goes into 12 once, leaving a remainder of 3, so we write 12 = 3 Mod 9.**

**35 is 8 Mod 9 as 9 goes into 35 three times, leaving a remainder of 8.**

##### Please note that when working in other Moduli the answer would be achieved in the same way. For example. Take the number 35 again, but this time in Mod 8 – 8 goes into 35, 4 times and leaves a remainder of 3 so we would write 35 = 3 Mod 8.

##### For the purposes of my research I am only interested in Mod 9 because of its exclusive properties.

**Number Pairs**

##### Above I have used a Circle as a Control for the 9 Natural Numbers of our Decimal System and then use the Multiplication Tables for each number.

##### When we get a result, for example, 4 x 4, it gives the natural result 16, Mod 9 is applied to the result to get the answer. So, in this case 4 x 4 = 16 = 7 Mod 9 because 9 goes into 16 leaving a remainder of 7.

**The Remainder is what we are interested in.**

##### To create the geometries you see above, we simply go from result to result for each number’s multiplication table and join the lines up.

##### Above we can clearly see the Geometric Qualities exhibited by each of the first 8 numbers when we apply Mod 9.

**For those who are new to Modular Arithmetic and were wondering what happened to the 9 and 0?**

**For those who are new to Modular Arithmetic and were wondering what happened to the 9 and 0?**

**Well, whatever Modular base you work in will necessarily result back to itself or zero.**

**Well, whatever Modular base you work in will necessarily result back to itself or zero.**

**In Mod 9 9 is Paired with 0**

##### For example, 1 x 9=9 or 0 as there is no remainder, 2 x 9 = 18 = 9 3 x 9 = 27 = 9 4 x 9 = 36 = 9 etc.

##### To clarify absolutely how we get to the above geometries, let’s start with the 1 times table: 1 x 1 = 1, 2 x 1 = 2, 3 x 1 = 3 etc.

##### You can see that the one times table creates a geometric shape called a nonagon and you can see that the direction of the flow is clockwise.

##### Now the 2 times table goes 2, 4, 6, 8, 10 is 1 (Mod 9), 12 is 3 (Mod 9), 14 is 5(Mod 9) etc.

##### Here we have a different geometry creating an internal enneagon created, again, flowing in a clockwise direction.

**The 4 times table goes 4, 8, 12 is 3 (Mod 9), 16 is 7, 20 is 2 (Mod 9) etc. It produces a 9 pointed star, again flowing in a clockwise direction.**

**The 3 times table goes 3, 6, 9, 12 is 3 (Mod 9) 15 is 6 (Mod 9), 18 is 9 (Mod 9) and so on, creating the triangle, again the flow is clockwise.**

##### The 8 times table goes 8, 16 is 7 (Mod 9) 24 is 6 (Mod 9), 32 is 5 (Mod 9), 40 is 4 (Mod 9) etc – notice the 8 shares the same geometry as the 1, except it is flowing anticlockwise.

##### Similarly for the 7, 5 and 6 which produce the same geometry as the 2, 4 and 3 respectively.

##### We can see clearly that the **Numbers are Paired Geometrically **and have a Positive / Negative, Clockwise / Anti-clockwise, Relationship.

**Numbers are Paired Geometrically**

**1 and 8 2 and 7 4 and 5 3 and 6 0 and 9**

##### Mod 9 is the only modular base system that displays this kind of symmetry where all the numbers 0 to 9 are paired off geometrically to form 5 pairs.

**Two Distinct ‘Circuits’**

##### You can see from the visual that there are 2 distinct ‘circuits’ at work here by noticing that the geometries of the numbers 1 2 4 5 7 and 8 all touch each of the 9 numbers around the circle, whereas the 3 6 and 9 keep to themselves.

##### Seeing Numbers Pictorially had a very profound effect on me.

##### I resonated so strongly with it, it was like it was calling out to me!

**Cellular Mitosis Sequence**

##### Essential To Life – How Our Cells Divide And Replicate.

##### Cellular mitosis is essentially the process of cell division that allows humans to grow and for cells to repair themselves.

##### It gives the following sequence: **1,2,4,8,16,32,64,128,256,512,etc** – i.e. the cells simply double and double and double.

##### When we apply Mod 9 to this sequence, again using the circle as our control, we see a repeating sequence emerge.

**1 2 4 8 7 5**

##### The VBM guys refer to this as the ‘Doubling Circuit’. They are calling the point at which the line 4 8 crosses the line 1 5, the Vortex, or Zero point.

#### Family Number Groups

##### As I apply Mod 9 in different scenarios moving forward through this work, it is important to indicate that in addition to working in pairs, these numbers also appear to work in 3 definite groups in VBM, the numbers each simply separated by 3 giving 1 4 7 2 5 8 and 3 6 9, called Family Number Groups.

**3 Family Number Groups**

**1 4 7 2 5 8 3 6 9**

**The 1 4 7 and 2 5 8 Family Number Groups are proposed as representing the Electric.**

**The 3 6 9 Family Number Group is proposed as representing the Magnetic.**

#### Family Number Group Interaction – The Engine Room

##### This integration of the electric family number group numbers 1 4 7 and 2 5 8 produces matter through the precise numerical and mathematical coalescence to produce items such as apples, trees, Man.

##### What I want to show here is the Family Number Groups interacting with each other to produce what is effectively the engine room of the decimal system of numbers.

##### Here we can see exactly how Electricity, as defined by the Prime Number dominated 1 4 7 and 2 5 8 Family Number Groups, is connected to and perhaps produces Magnetism 3 6 9.

##### 147 v 258 Additive

Pythagorean Musical Tuning A = 432 174 + 258 = 432 147 + 285 = 432

##### Void Frequency Found in Music 147 + 582 = 729 471 + 258 = 729

##### Looking a the yellow highlighted numbers that run the diagonals we see

##### 999 = 27 x 37 1110 = 30 x 37 1221 = 33 x 37

##### Above I have combined the other family number group 3 6 9 with each of the Electric Family Number Groups 1 4 7 and 2 5 8

##### The interaction between the 1 4 7 and 3 6 9 produces only 3’s

##### The interaction between the 2 5 8 and 3 6 9 only produces 6’s

##### 21 so evident in both with the 1110 breaking down to 11 + 10 = 21 and the 1221 palindrome on the diagonal, using the mirror 12 and 21. This becomes even more important when one has an appreciation of the Partition Theory paper as this is where everything ‘happens’ in the Partition Table.

##### 37 is the 12th Prime Number and 73 is the 21st Prime Number.

##### Self Similar Family Number Groups – Additive

##### Here we see the effect of the additive interaction between the self similar Family Number Groups

##### Note the Yellow highlighted diagonals as multiples of 37 again

##### 888 = 24 x 37 1110 = 30 x 37 1332 = 36 x 37

##### Multiplicative

##### Multiplicative Interaction between the family number groups also produces nothing but 9.

##### Perfect equilibrium.

##### Self Similar Multiplication

**Family Number Groups**

**Combinations**

##### Here I looked at the group of 3 digit numbers that make up each Family Number Group to see

**3 6 9**

##### 369 + 396 + 963 + 936 + 639 + 693 = 3996 = 108 x 37

##### And 369 = (10 x 37) – 1 = 369

**2 5 8**

##### 258 +285 + 528 + 582 + 825 + 852 = 3330 = 90 x 37

##### And 258 = (7 x 37) – 1 = 258

**1 4 7**

##### 147 + 174 + 741 + 714 + 471 + 417 = 2664 = 72 x 37

##### And 147 = (4 x 37) – 1 = 147

##### Interestingly this is the distribution of Hydrogen atoms in the Side Chains for Adenine and Thymine led codons found in DNA…. It is supportive of my assertion that the system of Numbers 0-9 is perfectly congruent and at the root of All.

__Vortex Based Mathematics & The Torus__

__Vortex Based Mathematics & The Torus__

__The Torus & Arthur M Young – The Reflexive Universe__

__The Torus & Arthur M Young – The Reflexive Universe__

##### In his beautiful book, The Reflexive Universe, Arthur Young describes his theory of the evolution of the universe.

##### This book is a must read for anyone delving into the how the numerical machine works and how my Integer Partition Theory might not seem so outlandish after all.

##### Young’s theory is dependent on the idea of a theory of structure, process and purpose to the universe. He had become interested in ancient myths, in particular the myths describing how the universe came into existence. Many described the process occurring in 7 stages inspiring him to adhere to there being 7 stages of his process.

##### With the number 7 in mind, a friend of his reminded him of the unique topology of a torus *‘such that a map drawn on its surface requires seven colours in order for all bordering countries to be distinguished by differences in colour. Now on the ordinary surface, that of a plane or a sphere, such a map requires no more than 4 colours. Since colours are distinctions, it occurred to me that, just as a sphere may be thought of as analogous to structure, so the torus may be analogous to process. If so, its seven colours would correspond to the 7 stages which might be expected in process’*

##### He goes on to write –

*‘Now the torus shape, which is also that of a vortex, occurs widely in natural phenomena: it is the shape of a magnetic field, of a tornado, and of eddies in water. And especially interesting is the fact that it is the only manner by which self-sustained motion can exist in a given medium. It is a unique manifestation of air in air (a tornado) or of water in water (an eddy or whirlpool). Of course, we can have waves on the surface of water, but that is at the boundary between two elements. The vortex is consubstantial with its matrix; they are the same material.*

##### In the appendix Young goes further on the number 7 and the torus –

*Even more impressive are the mathematical credentials of the torus. Mathematics recognises topology, the science of surfaces, as dealing with more profound relationships than does geometry. Geometry deals with measure and angles of figures on a surface, but topology deals with different classes of surface such as the Moebius strip or the torus. This should be important because the abstractions of mathematics have often proved to apply to real situations; the imaginary numbers are invaluable in equations which deal with waves or oscillation; the curved space of Riemann gave Einstein the basis for relativity. Toroidal space-time could be next.’*

* ‘The intelligent reader is likely to regard with suspicion a theory which bases itself on the number seven. Why? Is it because any reference to seven conjures up the prescientific?- Legend, myth, fairy tales, and even superstitions are encumbered with sevens for no apparent reason and, by giving this number a mystique that the modern mind cannot accept, have given it a bad reputation.’*

##### When Young realised that topology could supply formal reasons for a sevenfold ordering he was* ‘prodded into a re-thinking of the concepts embedded in relativity whose theories of curved space-time had provided the foundations for modern speculation on the nature of the universe.’*