The Mathematics of Evolution




Copyright © Malcolm McEwen 2006

All rights reserved

(to email: malcolm DOT mcewen AT gmail DOT com)   

The Author further asserts his Moral Rights in

accordance with the Copyright and Patent Act 1988

The Devine numbers

What started this journey for me was the drawing of a diagram: three circles around a central core. It was a simple diagram and when I first drew this diagram I was writing a book on the mechanisms of Earth, ‘The Gardens of Gaia’ and could not have had mysticism and religion further from my thoughts. For my intention had been to build a model in which I could arrange all the important components of a system within functional rather than taxonomical groups. I had wanted to build this model so that it both represented the system accurately and simply; so that non-scientist could appreciate how the components collaborate to produce the whole. Having identified that the system could be encapsulated or built around a single concept; one that all the components were dependent upon and could be regarded as being the primary objective of the system, and given my professional interests, it was logical for me to build this first model around the concept of soil fertility; for despite the rather comical connotations and simplicity of the phrase ‘the answer lies in the soil’ it is never the less, a truism. Everything on the terrestrial side of this planet is dependent on a healthy soil, not least our species. We may live in a technological age of atom bombs, space-craft and super-computers but every society in our world is still dependent on agriculture for 80% of its resources. In simple terms if there is no soil then there is no food and no life.

Having identified that the concept of soil fertility was the central concept on which the terrestrial system was dependent I then arranged the first three functional groups around it. These first three groups were encapsulated in the idea that the system was composed of a chemical process, a mechanical (physical) process and a biological product. Within each of these groups existed more functional components and so in that first model I also drew within each circle three more circles to represent this; and the realization that this diagram was recursive, that it repeated and grew in all directions, dawned. What one might call a ‘eureka moment’ occurred but this term cannot communicate the true impact of that realisation more inadequately. For this was not the mere realisation of displacement but a quantum shift in understanding; a shift that led to the opening of the crown Chakra and the connection with the Devine knowledge system known as the Akashic records. A process that radically changed who I was and the direction my life was to take. It’s fair to say that whilst I experienced a profound and life changing moment of understanding I was similarly imprisoned by the inability to communicate it. Ten days later I had abandoned everything and caught a one-way flight to India; my intention had been to immerse myself into trying to put this understanding into words, to communicate it, to share it; nothing else mattered.

After traversing India for two months I finally stopped at Pushkar and began to immerse myself fully into the work. It is perhaps a fair criticism that I wasted two whole months but in my defence I had needed to ‘recover’ from the cognitive equivalent of an Earth quake, one that had it occurred on the planet would have been in the order of 50 on the Richter scale; in other words it would have flattened every building in every city across the globe.  It was here at Pushkar though that I began to experience the lights completely and as I watched them stream and twist, morph and rotate I accepted them as being teachers. It was through the lessons of the lights that I realized that the model followed an evolutionary sequence or pattern in its growth. That what started out as one became two and when these two came together they created a third, but in doing so they became one again. Hence a system could be encapsulated as three elements, the components, inside a fourth, the whole. Subsequent growth of a system was not outward but inward, for as well as being recursive the growth was also achieved through increasing complexity. To a degree I had realized this whilst still in Cardiff and having done so realized that this pattern was a means of explaining the old adage “that the whole is greater than the sum of the parts”. The parts in my early model had been reduced to three components that I had identified as two processes and a resulting product. These three components were encapsulated within the fourth circle, the whole.

Although I had realized that within each of these three components was a copy of the whole, another three circles, I had not gone so far as to count them all, but once in Pushkar I did and it took the development of this model a step further. That first expanded model contained 13 circles, it had grown from four, which in turn had grown from one. I called this expanded model the Pushkar model; it is a title that, given the importance of Pushkar in this whole story, I am determined to keep. It would however be over a year before a numbers search on the Internet would reveal to me that this evolution actually followed a strict mathematical sequence, a sequence I now call the evolutionary sequence; that sequence being (1), 1:1, 4, 13, 43.


The Pushkar Model and the Evolutionary Sequence

 The Pushkar model as mentioned above was first drawn in February 2005 in the holy city of Pushkar. It was a diagram composed of three circles in each of which was three more and these twelve were contained inside one large circle; the whole, giving a total of thirteen circles as in the diagram below. At the time I drew this diagram I was still applying the model to agricultural systems and in an effort to make it more useable I expanded the model to show the relative relationships of the components to Man. However I was prompted to do so; prompted by an event that in retrospect was likely misinterpreted by me. The event that prompted me to expand the model was a manifestation; an astronomical event that occurred in the night sky above Pushkar. This event occurred when one night I awoke with a strong desire to go out into the desert. Once there I noticed a bright star, one I learned the following day was Jupiter and beneath it was a second bright star, Sirius. I further learned from a web search that the moon would ‘leap’ between these two and so over the next few days I kept a careful eye on these bodies making several drawings of the events. One drawing in particular was to be both a strong influence on me at the time and subsequently on my return.

It was at Pushkar, in an effort to interpret the meaning, that I applied those drawings to the model and came up with the expanded diagram below. At the time I had no knowledge of the Ten Sefriot let alone that it was a map of God in the image of Man.

This model, and the sequence it evolves by, is surprisingly simple. It follows a simple mathematical formula with each number in the sequence being three times the previous plus the one before; thus 4 = (3 x 1) + 1, 13 = (3 x 4) + 1, 43 = (3 x 13) + 4. Although at the time I never took the model to the fifth step, to 43, nor did I identify it as a sequence until many months later, and then only by chance. For it was whilst doing an Internet search that I came across a site dedicated to integer sequences and through that site I learned that this mathematical sequence had already been identified.





The Pushkar model. Note its central core surrounded by three circles; the essence of the Sri Chakra of Sharda.

The interpretation of the manifestation as applied to the Pushkar model. Note the ten main circles and its strong similarity with the Ten Sefriot



The manifestation

The original drawing


The sequence submitted by Frans Faase (1997) was defined by the equation: a(n) = 3*a(n-1) + a(n-2) and has the ref A003688 (integer sequence reference site). Had I have realized this sooner then I would have likely identified the meaning of the 43 triangles that surround the Sri Chakra at Sharda.

Similarly in the first draft of this chapter I debated whether to including details of another numbers aspect that I didn’t fully understand but was emphasized repeatedly by the lights. This second bit of numerological wisdom was not a sequence but an actual numbers base. Bases being systems of counting that involve two or more characters; thus binary, the simplest counting system uses two symbols (0 & 1) whilst the more familiar base ten uses the numbers 1,2,3,4,5,6,7,8,9 & 0. There are other counting systems and bases, such as base 12 and base 60 which have been used in the past. We still have the remnants of these systems in our measure of time and not so long ago in monetary and length systems for both the pre-decimal coinage of the UK and the imperial system of measure are essentially base 12 systems. However all I knew was that there was a base three numbers system that was important. During my journey and encounter with the lights these three values were repeatedly communicated and whilst they were not totally unfamiliar to me I had only ever known them in the context of tools for showing relative values; for making simple representations of concepts and ratio’s and then I had only ever used two of them not three.

In computing the simplest base, base 2 or binary is commonly used in program language and it is the position of this base as the primary building block that gives rise to the growth of computer powers in multiplications of 2 (i.e. 8, 16, 32, 64, 128, 256, etc).  However binary is a very simple language which determines that a thing is either true (1) or false (0) and as we know in the universe we inhabit very few things obey this simple logic, for there is often a third state, neither true nor false. This obvious flaw would seem to be corrected by progressing from a binary to a higher base and introducing a condition for neither. The natural progression from base 2 would therefore seem be to base 3 (0,1,2).

However with all bases (base 2 to 60 and beyond) there is an inherent flaw, they are unidirectional and there is no way to identify from the numbers themselves the direction (negative/positive) that the progression is in without the use of additional notation (+/-). Since we generally encounter only positive numbers then for the most part this is not a particularly important flaw. In fact the Romans managed to build an empire using a numbers system that was not a base system and completely omitted the concept of both negativity and zero.  Whilst this still permits one to do commerce when it comes to logic the negative direction is however as important as the positive and therefore a system that does not incorporate a mechanism for identifying the direction of progression reveals only half of the total range of outcomes. Since numbers systems are theoretically infinite then half of infinity is as large as all of infinity, however we never work with infinite numbers only with finite subsets and so half in most cases is just that…half. 

Then by chance I happened across another web site, one that mentioned a method of counting called balanced ternary. It was a unique base or numbers system, for unlike all other bases, which are unidirectional; it did not differentiate between positive and negative values.

The system as with the previous integer sequence had been long known. It had been first devised in the west by Augustin Cauchy (1840) and during the 20th Century it saw several re-inventions, most notably be Russian Scientist who used it in the early days of computing as a logic system but it’s actual origins are much older for there is some evidence that it was already implicit in the Hindu Vedas; thus making it older than any other current numbers system and perhaps the oldest base of them all. In his book ‘The Art of Computer Programming’, Donald E. Knuth described Balanced Ternary as "Perhaps the prettiest number system of all" but it is more than pretty, it is Devine.  

The last and perhaps most incredible sequence of the three is the interactive sequence and it is the means by which a system communicates. It is, as with the other two mathematical concepts introduced here, from another highly specialised branch of modern mathematics; that branch being artificial neuron nets, but these nets are not artificial, nor are they modern, for you are already familiar with one of them; one that has a net weight of approximately 3.5lbs and occupies a space the size of a small melon. That natural neural net is your brain and it’s a pattern-storing organ.

 For what you see, feel, smell or to be more encompassing, perceive of the world around you is not what is actually there; it is how your brain interprets and recreates the information that your senses relay to it. One does not see the world but instead recreates it in the mind based on the information it receives. The brain does this through pattern creation and recognition, and it uses a mathematical sequence based on the powers of 3. This, the interactive sequence, is the means by which different sub-sets or components within a system communicate. It is a system of pattern recognition that is based on topological pathways and it is the means by which the human brain, currently the most advanced sub-system within the universe, stores information, as patterns; a means by which the Super-Mind similarly stores information, only on a much grander scale.

As sequences go this one is the ‘daddy of them all’ for it generates huge numbers; ones that are barely comprehensible and as with both the previous I was made aware of this sequence by the Lights at Pushkar but just as my lack of familiarity with the previous two branches of mathematics made it difficult to understand so I was equally confused by this sequence.  It was though the realisation of this sequence and an initial calculation whilst deciphering the puzzles a year later that resulted in my ‘discovery’ of the previous two. So big are the numbers generated by the interactive sequence that entering them into a search engine yields useful leads. Whereas small numbers, such as those generated by the evolutionary sequence, are so numerous in web pages one is rarely taken to any sites that aids in understanding them. That original number was 7,625,597,484,987; it is a number that is generated by the interactions of a system that contains 43 primary components or neurons. It’s a big number but when compared with a system that has billions of neurons, such as the human brain the numbers generated become incomprehensible. When then compared to the Super-Mind the number of interactions approaches infinity. The equation for this sequence is, despite the huge numbers it generates, ironically rather short being

3^(3^n), it was submitted to the integer sequence site by Henry Bottomley and caries the reference A055777.   

In this chapter I have so far introduced the concept of three mathematical process, ones ‘revealed’ to me by the Lights at Pushkar but not understood. These concepts are all related, being based around sets of three, but what really brings these three numbers systems together though is another mathematical branch, one bought to my attention by an acquaintance who I showed some of my diagrams too and who recognised them as having similarity to an area that interested him; that area being topology.

Topology as with the previous mathematical concepts is a little obscure, but it is a branch of mathematics that has in recent years been the subject of considerable interest, for topology, or knots theory, is the study of dimensionless geometry. At first sight this term seems to be a contradiction for geometry is about shapes and shapes have dimension but topology deals with the way things connect, hence it can be used to connect these three numbers systems. An example of the geometry of topology is the mobius strip, introduced in the earlier quantum section of chapter one, and a practical use of topology is in the setting up of computer networks. In such a situation it doesn’t matter where the computers are in relation to each other, what matters is the way in which they are connected. This is what makes topology interesting, it is not bound by spatial concepts so one can use it to describe relationships and behaviour at both the quantum and the macro scale. Similarly it is not a purely theoretical branch; it has practical application, and can be used to join theoretical and practical models together. In the case of the ‘Devine’ numbers it serves the purpose of bringing the Evolutionary and Interactive Sequences and the Balanced Ternary numbers base together. 

What Topology does is allow for the description of systems and shapes by the way they connect. Practical uses for topology include the setting up of networks and in the drawing of maps. One such example of a topological map is the London underground maps, which straightens each line and show the stations as equally spaced, despite the fact that the lines are not straight or the above stations bear any such geographical relationship.

In the majority of applications a system forms one topological map however with increasing complexity the system can evolve so that sub systems are created. Continuing with the underground example this is demonstrated well by the differences between the Lisbon underground, which has only two lines and the largest underground, The London tube. The former forms only one topological map; there is only one way to traverse the Lisbon underground, however the complexity of the London underground means that one can traverse via many routes so that one can move between two stations using different lines and in some cases use in excess of five ways to traverse between two points. In the language of the topologist these sub-systems are termed hyper-spatial systems for they do not exist independently but as a consequence of the arrangement of the greater system. But perhaps the greatest example of a topological system is the Universe itself.

This occurs very early on in the study of the universe and is demonstrated at the quantum level, where it is possible to calculate the position and volume and hence size of the nucleus but not however the component quarks. The position and dimensions of a neutron or a proton are generated as a hyper-spatial consequence of the three quarks, thus the nucleus exists as a consequence of the system, it is the fourth and only component that exists in the three spatial planes, hence it is the only measurable component but it is similarly a hyper-spatial component for it exists as a consequence and not independently of the other three. Whilst evolution and hence the order of Importance of the Devine numbers begins with Balanced Ternary, then the Evolutionary or System Sequence and Finally the Interactive or Communicative Sequence exploring these further, and in particular their relationship is best achieved by beginning with the Evolutionary or System Sequence. 


The Evolutionary or System Sequence

In the evolutionary sequence the first number or 1st Step is 1; the state of Absolute Oneness that this book begins from, it can be represented mathematically by zero or 1, scientifically by the Singularity; and philosophically by God. The 2nd Step, 1:1, whilst important mathematically is however not a true level of system but a state of opposition; it is though a necessary condition without which the Singularity cannot progress through the other levels of system evolution. This second level can be represented by the emergence of Time and Space or the mathematical notations of (+) and (-) but in truth their opposition is as a consequence of being the sole elements. Thus as long as they are identical they remain undifferentiated; as the Singularity; but the moment that they differentiate then, in the absence of any other reference point, they immediately become opposites; even if this differentiation is miniscule it is, in relative terms, considerable. Therefore this second step of differentiation can only result in the creation of opposites and not a system, hence the use of the notation 1:1.

The third level of system evolution, the 4th Step, is the first true system to evolve. The emergence of the four fundamental forces of Gravity, Strong and Weak Nuclear and the Electromagnetic forces are one possible example of the 4th Step but from our perspective it is the formation of atomic nuclei that best typifies the development of a complete system following the differentiation of the Singularity. This duality in the representation of the 4th Step is well demonstrated by the Sri Chakra, which contains the four gates (interpreted as the fundamental forces) as well as three circles surrounding a central core. It is similarly represented, although not as accurately, by the upper trinity of the Ten Sefriot and whilst it is perhaps confusing to talk of trinities when the system contains four components, the fourth is not a distinct element but a consequence of the other three; it is the first hyper-spatial component. These first three progressions; 1, 1:1 & 4 can be represented diagrammatically as below:



Step 1: The Singularity

This Step can only be represented by a single disc but may be either white or black

Step 1:1 The Division.

Conjoining the above ‘two’ conditions of the Singularity can represent this Step. It ultimately results in these two conditions becoming separated to produce two distinct co-existing but opposite conditions.



Step 4: First true system

At Step four the two come back together to create a third and in doing so become a system. This system is the fourth component and is represented by the central dot in the right diagram

It can be difficult to see why three is a system and two is not however if one visualises the gold triangle as a path on which one moves along, always in the same direction, never retracing a step, one ends up back where one begun. Without the third point the same action with only two points requires reversing the direction; one moves from white to black to white thus retracing the route; reversing the direction and we end up not with an evolving universe but one that oscillates between two states. This is why three is a system and two is not.  


The fourth level of system evolution, the 13th Step likely occurred with the unbinding of light some 12.9 billion years ago and whilst it may be possible to actually identify when this occurred and what units were involved it is unlikely to actually provide us with any useful information. It is though not possible to equate this with any current scientific view of the universe during this time, not because it doesn’t fit one but because we simply do not have one or at least a coherent one. Science has only concentrated on the extremes, the beginning, the first three minutes of the universe and the most recent, the last million years. The 12.9 billion years that make up the majority of the universes’ existence has received relatively little attention in comparison to the first three minutes and the last million years.  However this absence of a scientific comparison does not prevent us from representing this Step diagrammatically.


The 13th Step showing it both as a diagrammatic representation constructed from the 4th Step and as the Original Pushkar Model that can be used to model and understand practical situations. Note that at the 13th Step the model has four hyper-spatial dimensions; one in each component and the one generated by the three components working together. 


At the 13th Step we can actually use one diagram to represent the evolutionary sequence as a series of steps from a singularity to a system of 13 components; a star or spiral (serpent).


13 components: 2 equilateral triangles inside the next step, 43

Step 1- The Singularity at the centre

Step1:1 – Division into the first state

Step 4 – Union, thus creating the first true system

Step 13 – The ‘Star’ as 13 components

The Star ‘connected’ and working as a single system

The growth of the star as a Spiral or ‘Serpent’

The Serpent & Star co-existing.


As the above diagrams demonstrate at the 13th Step the system can be represented as two equilateral triangles overlapped to form a six-pointed star or as a growth spiralling out in a way that mimics a serpent. Both these diagrammatic representations include all the components in a system at 13 and so can co-exist; at the next point in the sequence, the 43rd Step the situation however changes. To understand the 43rd Step though one needs to first discuss the other mathematical concepts and their relationship with the Evolutionary or System Sequence. 


Balanced Ternary: The Mathematics of the Devine

With all of these sequences the number three is of utmost importance, Guderief called it the Law of Three and in his writings he persistently emphasised the importance of three. I could not agree more, however the Law of Three is actually Four. Perhaps this is why it has for so long been so difficult to properly understand, for the ‘hidden’ Law of Three is that when ever three come together they become ‘whole’ and that whole is the fourth, component: this I would aver is the Law of Three. This is even true for this next mathematical concept for whilst Balanced Ternary, as with ordinary ternary systems is composed of digits that are coefficients of powers of 3, they are however not coming from the set {0, 1, 2}, but from the digits  –1, 0 and +1. Unlike other ternary systems where the numbers are arrange linearly the numbers in balanced ternary are arranged symmetrically about the zero. Everything therefore appears to spring, or grow out from zero in a symmetrical pattern.  If one plots these numbers what one produces is not a straight line, as with normal bases, but a rotational system where the rotations decrease in size as the numbers grow. In other words it has a recursive rather than a progressive nature. The simplest representation of balanced ternary is the diagram below.


Insert linear representation of normal ternary




The notations –, 0 and + or the more common 1, 0 1 are themselves actually poor choices in representing balanced ternary in terms that are relevant to the importance of this base in describing the mechanism by which the universe grows for they encourage visualization of a positive and negative existence in which positive is seen as large or good and negative as small or bad. Instead it is better to visualize these numbers as rotational directions; to use the notation of right (R) left (L) or straight (S) and to visualize the difference between the numbers as being alternate rotations (R and L) for true and false and no rotation (S) for unknown. In this way there is no implied size or qualitative aspect.  This base system is what underlies the entire universe; it is like a skeleton upon which everything else is built. I regard it as the mathematics of the Devine for everything that exists does so because of this numbers system.

The Math’s of this base is interesting and as demonstrated by the above diagram it is based around equilateral and tetrahedral shapes. If the numbers are expanded and plotted then one creates a balanced ternary tree that has three branches and on each branch the numbers grow in concentric circles. The circles become complete in groups of three but equally form groups that follow the earlier evolutionary sequence. Below is a diagram of a complete tree and the steps in the evolution sequence of one branch to 13.


Balanced ternary tree showing the growth of three branches from the central zero

Balanced ternary tree using the notation of left (L), right (R), and Zero (0) instead of the usual -, + & 0.   

Evolutionary sequence (circles) imposed over the first four numbers of a balanced ternary tree.

Evolutionary sequence (circles) imposed over the first thirteen numbers of a balanced ternary tree.


As the above demonstrates the balanced ternary notation actually underlies the earlier evolutionary or system sequence. What becomes interesting is what happens when the tree is expanded to the next step in the evolutionary sequence, 43. At this point the mathematical field of topology really comes into play. For at 43, the next step in the evolutionary sequence, something special happens in the balanced ternary notation, it creates a new and very much larger hyper-spatial system.

In the evolutionary sequence 43 is achieved by tripling the previous Step (Step 13) and adding the Step before that (Step 4). In both the earlier Steps of the evolutionary sequence this addition of the earlier system has always been one but now it is four and at this next level something significant happens: for on the existing branches of the balanced ternary tree the system becomes complete not at 43, as indicated by the evolutionary sequence, but at 40. However in doing so it creates three hyper-spatial dimensions between the other 40 components. It duplicates the first system of four inside the greater system as demonstrated in the diagrams below.


Balanced ternary tree at 40 showing the earlier system of four as a green hexagon

Manifestation of three hyper spatial systems within the model and about the centre of the entire system

The completed system at the 43rd step showing the duplication of the earlier system of four duplicated in the centre.

Diagram of the hyper spatial dimensions (green) that evolve in a topological representation of a balanced ternary tree.


What the above is beginning to demonstrate is that operating within the universe are two mechanisms of evolution; the first is a logical numbers system called balance ternary and overlain this is a second, the evolutionary sequence of systems. These systems whilst appearing to exist in a spatial context actually operate in a topological one. However this is not so apparent from the static diagrams above. As mentioned the traditional notation for balanced ternary uses -, +, & 0 and this does not permit the visualisation of the movement in the system. For this is a ‘living’ numbers system, the branches are in fact rotating, and visualization of this is best done by assuming the notation of left, right or no rotation, although there are actually three rotational directions and these are relevant to the generation of 3-dimensional space however it is easier to follow this explanation by overlooking this aspect for now. The rotational aspect of the system was personally realised back in those early moments of that cognitive quake; long before the sequences or balanced ternary were known or understood. Hence at the time it was impossible for me to communicate what I was seeing although I was able to draw it. And what I drew was a rotational system. Now if that original drawing is combined with the concept of a balanced ternary tree what one gets is a rotational system, a system that produces complimentary rotations, hyper-spatial rotations or dimensions as below.


The original diagram as seen but not understood in mathematical terms.

The balanced ternary model of the evolutionary sequence (4) now as rotations and not as numbers.

At the next level; 13 in both the balanced ternary and evolutionary sequence we see the development of a complete but still a component based system where interaction within components dominates over interaction between components

Finally at 40 in the balanced ternary notation the components begin to interact at a level where they are now dwarfed by the level of interaction occurring between them. A level that generates three hyper-spatial systems; the ‘seat of consciousness’ thus generating the 43 components of the evolutionary sequence; a complete system.


This though is not the end of the story; for at the 43rd step there is a third sequence that comes into play and this sequence is the cognitive equivalent of a sonic boom. When this sequence activates the whole becomes one; what once appeared as separate components now exist within a neural net; a super intelligence that resides not in the components but between them, in the hyper-spatial dimensions. This is consciousness and it is as a consequence of growth in the interactive sequence, the communicative aspect.


The Interactive Sequence

The interactive sequence, whilst it is generated by the simple equation 3^(3^n), is one that generates huge numbers. It could similarly be described as the communicative aspect and it comes into play and remains so as each time a Step in the Evolutionary sequence is completed. Hence at Steps 4 and 13 in the evolutionary sequence, the interactive sequence resulted in a communicative force coming into existence. At Step four this communicative force was sound, a force that is communicated directly through matter interacting with matter; at Step13 it was light, a force that communicates both as a wave and a particle and does not need direct contact to be transmitted. That first communicative force, sound whilst being a wave is a wave that requires matter in order to both be generated and to travel, for sound cannot be generated without two particles of matter colliding nor can it traverse a space that is devoid of matter; a vacuum. Similarly sound in this respect covers all forms of contact communication and not just sound as in noise but also touch, smell and taste. This is a much wider definition of sound than we are normally used to but all of these are communicative forms that only work through continuous contact, direct interaction with matter, be that touch, taste, smell or hearing. Sound though did not become unbound until the quarks organised into nuclei, matter, and began to collide. Hence sound, as a communicative force, as interaction did not come into being until the universe had reached Step 4 in its evolution. The sequence identifies that at this level there are a total of 27 pathways by which sound is communicated.

Light, the second communicative force came into existence at the unbinding of photons some 700,000 years after the emergence of sound. Unlike sound light does not require continuous contact but can traverse empty space. It is similarly a force not restricted to just visible light, for visible light accounts for less than 0.1% of the electromagnetic spectrum. Without this ability to cross a vacuum then light would not traverse space; we would not see the stars and even our own sun would not be visible. In essence we would be in a cold and dark universe in which were only aware of those aspects that we were in direct or indirect contact with. Theoretically there are an infinite number of wavelengths in the electromagnetic spectrum however this must be tempered against the scientific view that the shortest possible measure of length is the Planck length and the longest the universe itself. Therefore this infinite possibility actually has a finite number of 1043.  However each true wavelength actually straddles more than one possible position; for instance visible light covers the lengths from 400um – 700um, hence each colour approx occupies 50um or 6million Planck lengths, whilst micro-waves are measured in millimetres and radio waves are measured in 10th’s of a meter. Whilst there are a theoretical infinite number of wavelengths that number is similarly bound between the shortest and longest lengths and as each wave increase in length it appears to occupies more and more of the theoretical positions. Clearly whilst in theory there are an infinite number in practical terms there is not. The interactive sequence identifies that there are 19,683 pathways by which light is communicated. If visible light was regarded as occupying just six of these pathways then it would account for 0.03% of the total.

This next communicative force is likely to be already in existence but just as light existed but was bound for 700,000 years, so currently is this force. We can though theorize what form it will take based on any communicative forces that we know exist but are currently bound. Similarly we can look for evidence of any hidden forces that exist in the universe. However rather than refer to these aspects as communicative forces we could call them energies then two such energies, one that is bound and one that is hidden, potentially fulfil this criteria. The bound force or energy is thought, for thought is currently bound within the organisms that experience and express it. Similarly there is an energy in the universe which is extremely large and currently hidden; this energy is referred to as dark energy by the cosmologists.  There may equally be an equivalent mechanism, that like the photon that carries light, carries this energy and in physics there may already be a term for this mechanism; the tachyon, the faster than light ‘particle’. 


The Eight- Cornered Universe

 All these mathematical concepts, the underlying balanced ternary base system, the overlying evolutionary sequence and the final interactive sequence, operate in concert within a topological framework to produce all the systems from the atomic nuclei to the human condition that are found in our corner of the universe. The explanation as outlined above is correct to a point; however what has been omitted although raised in chapter two is the influence or rather the consequence of the spatial aspect, one that through the quarks in the nuclei generate our spatial condition. For this spatial aspect did not generate just one set of polar co-ordinates in those early minutes of the Universe but eight and this has subsequently resulted in the generation of eight material or cognitive realms that have been evolving in parallel with our own. The differentiation of these two terms, material and cognitive is a perspective one; for from Mans perspective these realms are material but from the Super-Mind’s they are cognitive. These spatial aspects correspond with the earlier references in chapter two to the eight realms of the Super-Mind and their likely existence can be shown if one examines the early development of the atomic nucleus and its relationship with the quarks. In the balanced ternary section above it was suggested that the standard notation of 0, - & + be replaced by L (left), R (right) and S (no rotation) to indicate that these numbers were in reality different directions of rotation. If however we look at these rotations as being first spatial and then directional then the system develops a total of eight potential combinations. This can be shown, as explored in chapter one, by assuming that each quark occupies a spatial co-ordinate, X, Y, Z, and the integer spin of the quark was similarly likened to a path on a mobius strip. Such a path has two potential directions, clockwise (left) or anticlockwise (right). Therefore for each quark there exists a possibility of two directions of spin. The atomic nucleus is composed of three quarks, each occupying a spatial co-ordinate. The interaction of these three quarks is what generates the polar co-ordinates that permit both the position and the size of the nucleus to be calculated. If each quark similarly has a choice of direction of spin then there are eight possible quark combinations in a nucleus. If those eight combinations similarly result in a nucleus that interacts exclusively, that is only other nuclei that are generated by quarks that rotate in the same direction and in the same plane, then each combination results in a distinct physical universe. Presently we call these other ‘Universes’ dark matter.




The mystics, particularly the Yogi’s of India, have long claimed that our universe has an anticlockwise (righthand) direction. If we assume that the quarks in the matter in our universe all have right hand spin then there likely exists another universe in which the matter is made up of quarks that all have left hand spin and six other universes in which one of the quarks spins in the opposite direction to the other two. If these universes don’t interact in a physical sense or emit light that the other can detect then we would be oblivious to their existence. This situation would be maintained as long as communication requires a physical aspect, as in sound or light. However whilst this was the case and has been maintained during the first four evolutionary stages at the 43rd step the unleasing of tachyons, which are faster than light and don’t require a physical aspect then  those eight universes will become ‘visible’. In all likelihood they will have the potential to be united through the generation of the three hyper-spatial systems and the unbinding of thought. What is important is to emphasize that the universe is approaching the 43rd step on a grand scale; it is about to develop a level of consciousness that extends across the entire universe, one that will connect these universes in the same way sound connected and still connects adjoining matter and light connects distant matter that exists in the same spatial dimensions. We are now though approaching the 43rd Step and these other seven ‘universes’ are about to connect with ours; we already have the evidence of their existence, the 25-30% of matter known as Dark Matter and the 70% of energy known as Dark Energy; Saul Perlmutter, leader of the Supernova Cosmology Project headquartered at Princeton University and Lawrence Berkeley National Laboratory said of this, "The universe is made mostly of dark matter and dark energy, and we don't know what either of them is."  However the potential of quarks to have direction of spin as well as momentum can account for the Dark Matter held in the seven hidden realms and the concept of a currently bound energy, a communicative force we call thought can account for Dark Energy. 


The 43rd Step