The Children of Shunya and the Vedic tradition of the Markova Rodin Vortex Mathematics.
Markova is a humble man. He is not hyperbolising his discovery for vain glory. Even with all this hype it is still not thoroughly understood or investigated until Randy Powell tackles the topic.
The vortex mathematics is sometimes belittled as casting out 9s sometimes derided as module 9 arithmetic and sometimes ghettoised as clock arithmetic on the 9 numerals.
Vortex mathematics is in fact a ring theoretic structure on a group of 9 labels. The ring is in fact a field and it has an associated closed geometry or rather spaciometrical form. However, because it is fractal this spaciometrical picks out a particular form which is evident at all scales in space. This form is the torus, and the topological analysis of the torus by this ring structure is truly breath taking.
Associated with this topological analysis are certain engineering and biological and zoological principles which are impact full and revolutionary for human experiential development, but it is not the ultimate knowledge. In a fractal continuum there is no ultimate knowledge, but it is the ideal form of dynamic equilibrium in a way that the sphere cannot be.
We experience dynamic equilibrium, typified by the torus, static equilibrium, typified by the sphere and explosive disequilibrium for which the spiral form is the typical example. The quantisation of these foms means that as we respond to the rhythms of them we notice patterns, and the topology drives certain patterns into our consciousness. The so called number patterns are our apprehension of the relations between these quantities of magnitude as they sit on these topological spaces in dynamic states of equilibrium. The numbers are nothing but labels for relationships in space of conjugated regions of magnitude, quantities of magnitude in and of space, and thus dynamic and oriented. How we explore and utilise these relationships is dependnt on our mythologies and empirical findings. This is how and why we create our technologies.
In Spaciometry there are2 aspects to the notion of contra: contra rotation and contra orientation. Of the 2 contra orientation is the most special . It occurs only on a good line. A good line is a special line defined by the intersection points of 2 arbitrary points used as the centre for spheres. The intersection points are called dual only if the Merton used for the spherical radii is identical for the two spherical centres. For all identical matrons all dual points relative to these 2 arbitrary points which have a fixed relationship between them, form a structure called a plain surface. If the relative motion of the 2 points is itself spherical then the dual points form a solid spaciometrical sphere with a centre on the fixed good line between them at precisely half the matron.
This reveals that within the image of the sacred geometry there is a profound embodiment of the notion of relativity.mfor, whoever takes a fixed position at one of the intersections in a dynamic form will see the others circling in syn circularity because of the fixed Medtronic relationship. . In fact the fixed relationship extends to any constraint on motion, so that for any law of constraints, the motion is similar or congruent for all points to which the constraints apply regardless of which point one adopts as a fixed position. This is a general law that applies to all fixed constraints, however for dynamics in which the constraints are not fixed, but nevertheless follow a rule that is periodic or harmonic, then the motions follow the sme sequences of behaviour regardless of the relative position of the observer in the system.
Where ther is no fixed or periodic relation there is no similarity beyond all being trochoids in various stochastic courses of activity.
So returning to the circular plan of dual points we enforce one more constraint on 2 arbitrary dual points in the plain: they must pick out only those dual points in this plane whose Merton is identical for the 2 points this set of doubly dual points is called a good line. Along this line alone can I define a contra orientation, for the moment I deviate from these points I am no longer on the orientation of this line, and only pick up the orientation when I have tuned a full half circle precisely. In this case I am facing in the contra orientation. For this reason the good line is called straight, for it is strictly only oriented along its dual points, and these points are doubly dual!
Contra rotation on the other hand is not restricted in the plain, but it is restricted by rotation of the plains around the diameter of the rotation, for any fixed point arbitrarily chosen if I choose an orientation along a straight line then I can define a rotation as being anti clockwise if the line passes through the centr of a circle which I can draw with my left arn, left hand starting on my right.msimilarly clockwise is drawn by my right arm, right and starting on my left..
Only when my line of orientation passes through the diameter of the circle
Does this definition require adjustment. However, the circlular rotation switches relative to my position as it moves from being in line with my orientation. For this reason the definition of contra rotations is made local. I always position myself so I can see the circle , and in addition I attach an orientation to the itcle called a face. This orientation can be anything from an actual face, to a pointer that sticks ot from the circle centre in a constant fixed relsionhip.
In the vortex group module 9 there are 3 contra cyclic rings. These sure not aligned by axis but by the clock face. The resulting Spaciometry fits a torus and a sphere, but because of the non alignment of these contra rings, the torus is the best fit for the vortex group module 9.
In order to actually map this group into 3d space, the developers have introduce negative labels. This makes the vortex group as engineered actually the vortex 18 group!
I actually forgot how to convert a ring or group structure into a 3d fractal generator equation! This is because I have no more experience of doing these things than the casual reader , what I write I write by inspiration intuition and insight at the time, and then I forget it.,this is helpful, because I always come at an issue on new legs, solve it again , sometimes reinventing the wheel but other times gaining greater insight and more flexibility.
The children of Shunya come to my aid and the routes to a solution reveal more about the house of the children of Shunya as the roots of unity and the factors of one.
Hamilton had a jolt of electricity and it was what he called the calculation axis. This axis I used to develop the Newtonian triples, or Hamiltons triples if you will. This axis I used to correct the quaternionm8 group and to reveal Hamilton's mistake. This axis I realised as the polar axis in spherical geometry and the labels I,j,k as the great circular plains in the globe.
Thus it seemed to me that these so called algebraic extensive forms were an encoding of spherical geometry..mbut what was not clear until now was how the rotation from great circle to great circle was effected.
The children of Shunya move together in lockstep, so when I use them in the great circle planes they move as one, it is my notation that moves my attention from one plane to the other, just conjugating the movement around the circular planes. This conjugation moves my attention around the spherical reference frame In a swath that looks like a torus edge on.
I am still in early days but I may be on the track of the intimate connection between the torus and dynamic rotational stability.