# Maths

This page is dedicated to Mariusz Pianka. : Last Update completed on May 20, 2018
May 20, 2018 : Additional content added to Section 4 and a new Section 10
July 25, 2017 : Added details on the volume of two cones
May 08, 2017 : Equal area’s for inert gas
April 10, 2017 : addition of pendulum formula
January 24, 2017 : Addition of Introduction and cube/sphere volumes
January 16, 2017 : Introducing some Newtonian operations

Manipulation of mathematical formulae is not science.
Mathematical models are tools which must fit the observations not the other way around

### Introduction :

One of the most important lessons offer by WRC is ‘Nothing is what it seems’. MSS is by its very nature reductionist and seeks definitive solutions to all its questions. Mathematics is a language which has been developed to describe our observations in minute and clinical detail. WRC teaches that we rely too much on our sensing and hardly at all on our Knowing. Nature ways suggest a materialistic underbelly, yet when examined in details the lines blur. WRC wants you embrace and understand this blurring for what it really is. We observe the horizon every day. It appears to be about 15 miles away, yet, if you travel the 15 miles you will never reach it!
Using a spirit level when building a house will work well, but this technique cannot be applied to building an suspension bridge. Where does one system break down and the other begin. Do you agree that applying our ‘spirit level’ techniques to the great expanse of the cosmos is trustworthy?

By setting mathematical constants as facts severely interferes with our ability to grasp the inner Knowing that the axiom ‘As above, so below’ is indeed true of Nature’s ways. To sit on the fence is the perfect technique to employ. In this way one can ‘see’ and appreciate that all expression is two, neither one nor the other, yet simultaneously both!
Think of mathematical techniques as helpful but only in a very localised realm.
Imagine being able to converse in Welsh. While this is fantastic if you are located in Wales, but your abilities are of little use when you move to a new country !
Always treat mathematical conclusions that indicate something is definitely this or that with great caution and always keep in the back of your mind the teaching of WR ‘nothing is what it seems’.

Section 1

Fig : 1a The principles of Occam’s Razor apply

Nature is simple. The mathematics to describe how Nature operates is also simple, although the effects she creates may be very complicated. This is a two-way (motion) universe. Main stream science (MSS) has a very myopic perspective and asserts that Nature is only one-way. They describe this one-way motion as entropy, while implies that the universe will die due to expansion. WR would indeed agree that death is the condition unable to hold or contain heat, but he also teaches that there is an uphill motion which MSS ignores.

Fig : 1 indicates just how simple the mathematics is to describe a two-way universe of motion. Effects are always produced as a pair.
Those pairs oppose one another and as such operate in opposite directions.
To say centrifugal motion is the inverse of centripetal motion is to say that, centrifugal motion runs 180° to centripetal motion.

Another important insight to realise is that, within our perceived physical reality, neither centrifugal nor centripetal motion can attain 100% expression. Our physical reality MUST be constructed from pairs of opposites. A condition which expresses 100% dominance will thus negate its own existence because its opposite is not part of the construct.
If we therefore set a limit of 95% vs 5% expression we can begin to appreciate why the entropy model alone is misleading.

Fig : 2At this 95% level of expansion, MSS does not take into account the desire of the massively compressed 5% desire to expand and cool.
When this 5% begins to expand it with cause the 95% condition to CONTRACT.
The universe is breathing. This is a two-way cycle. The entropy model only applies to half the cycle.

Section 2

Fig : 2a

Fig : 2b

Fig : 2 indicates the extreme limiting conditions of our perceived reality. The reason a cube is used to describe the limiting condition is because the edges/faces of the 3D cube are flat and straight. This means that they are not polarised. Every other location within this 3D cube is curved apart from the very (0,0,0) center point which too is occupied by Mind.
All curvature is polarised as indicated in fig : 2b.

Pay close attention to the description of the cube and that of the sphere ! This will indicate to you the true two-way motion of the universal breathing cycle.
Curvature produces a pair of effects. Centrifugal motion running from the central hub out to the rim boundary will expand (1/n) but, in the reverse direction the same curvature is responsible for a compressing centripetal motion (n). As indicated in fig : 1 these two opposite direction work together to alter their dominance while never exceeding 1.

Section 3

## The Law of the Lever

Fig : 3a

The following image describes the lever mechanism for all wave motion.

A = direction of centripetal compression
La = length of lever (a)
B = direction of centrifugal expansion
Lb = length of lever (b)
F = central hub fulcrum
f1, f2, f3, f4 = location of the locked potential planes

Once again, Nature uses simple mathematical principles to create her images. A mechanical advantage  is equal to the ratio of the output force, to the input force.
When A [La] = B [Lb] then the mechanical advantage maybe described as neutral, equal to 1. This in fact describes the condition of the inert gas. The motion about the central fulcrum is balanced and undivided. All expressions of matter other than inert gases must divide this balanced condition so that matter can express itself. That division is achieved by shifting the central fulcrum with respect to [La] and [Lb].
Once the central fulcrum [F] is shifted, the lengths of lever [La] differs from the length [Lb]. This is what DIVISION means.
This topic is discussed further on the Wave page.

Fig : 3b

When the principles of levers are applied to WRC/thermodynamics, then the basic working of the entire two-way motion of the universe is revealed.

The reason pi is an irrational number is because the rim of a circle has effectively two faces, an inner and an outer arc. The area between these face being the thickness of the rim itself.

In the straight line the dimensions of face (A) are identical to those of face (B). However, when that line/wire is curved face (A’) is longer then in the inner arc of face(B’) and from a mathematical point of view this makes it impossible to define one single value for the radius !

Q. When Nature creates her complex shapes and structure which value of pi does she use ?
Q. Should mathematical philosophy and equations/formulae really precede observations ?

I get a cold shiver when I hear a ‘show me the math’ type argument !

Section 4

Fig : 4a

Fig : 4b

One afternoon, Newton decided to take a break from his usual day job and invent calculus, a new branch of mathematics. This new development is concerned with rates of change but, unlike his other invention (G) this one is really useful. using this technique, one can make accurate predictions about future events, but also because it implies resultant forces are vectors and this has a direct impact on how images are formed within the cubic wave field.

The calculation of rates of change are based on the Pythagorean (3456) right-angled triangle.
Pythagoras showed that for the right-angled triangle a² + b² = c².
3² +4² = 5² and the area of the enclosed triangle is 6.
It just so happens that the note F is located at 345.6 Hz when tuned to 432 Hz !
Rate of change are defined as changes in disturbance (x) with time. We can say that the force of the disturbance to Stillness F = ?x/?t, F is the physical reflection of Mind Thinking. Mind Thinks directly into the physical universe. This is why matter and motion seem to appear out of THE void. The void is Mind. When we feel a force we have a direct connection to Source itself.

We will define the force necessary to overcome the inertia of Stillness as F = d(mv)/dt where motion is defined as mass x velocity. This can be manipulated to yield F= ma.
A 3D spherical universe implies vectors as WR also describes and as the cubic wave field indicates, the diagonal vector is the result of those 3 (xyz) forces.

Fx = d(mv)/dt for the x-axis, Fy = d(mv)/dt for the y-axis, Fz = d(mv)/dt for the z-axis. These vectors are the shafts about which motion will spiral. A Thinking Mind will thus introduce a force to each of the 3 axes, but, not always equally. This will impart a circular, rotational motion discussed on the Cube/Sphere page.

Motion within a loop of force may be described by the function for angular momentum (L). Consider the lengths x and y as levers working against one another and the resultant torque force will trace out the circumference of the circle. This equation would describe 2D cone base.
The rate of change of angular momentum is the torque force (T).
T = dL/dt

We know the triangle is the most rigid geometric form. It acts as the underlying unit of a geodesic dome for instance. Each straight edge of the triangle will effectively stabilise its opposite angle. This is a very desired geometry because Nature is forever attempting to express herself through motion but doing so by holding on to as much stability or Stillness as possible. The Stillness of Source is the only true reality. If Nature must express herself she will mimic Stillness at every opportunity.
She will always attempt to achieve the most with the least effort. The triangle is an example of this effort by enclosing the greatest area with the least number of sides/angles.
Now, if we use this geometry to enclose a volume then 3 triangles surrounding one corner will default to a tetrahedral
structure (3 x 120°). Two interpenetrating tetrahedra will yield one form of cubic structure.

When 4 triangles surround one corner and octahedron (cube) will result (4 x 90°).

When 5 triangles surround a single corner then the icosahedron will become evident (5 x 72°).

These are the fundamental geometries of our perceived 3D reality. There are limit conditions, less than 3 angles/sides is not possible to go while 6 triangles about a single corner will result in a flat geometry ( 6 x 60°) extending to infinity.

Section 5

50 : 50 Potential split

There is one little surprise in the cube/sphere geometry, and that relates to the 50 : 50 volumes.
If you inflate a sphere inside a cube the sphere will almost be as large as the cube when the volumes are equal. This is the starting condition for compression of the inert gas to the apex of the octave wave.

Notice the 4/3 constant for the sphere. This indicates the musical interval (4/3) of a perfect 4th is very important to bring spherical form into the physical universe !

Section 6

## The Pendulum

This device as a means of holding sacred secrets first came to my attention in a book, Civilisation One by Chris Knight and Alan Butler. Part of the book is presented here.

However, although I have suspected a connection between a sacred measure to the motion of pendulum, I have a sense the ancient peoples used much lower frequencies namely their own at rest heart beat to then extract from that pendulum  a straight line perpendicular length and a curved travelling path dimension. I propose this is even why Tesla decided on 60 hz for his ac systems.

A simple pendulum can be described by T = 2π√l/g while the motion of a conical pendulum is described by T = 2π√lcosθ/g. Therefore a sacred oscillation is directly related to the pendulum’s cord length (l).

The motion of the pendulum is assigned to a Thinking Mind. How this forward/backward motion (2D) manifests within the physical 3D is the function of the cubic wave field and the motion therein.
It is my present understanding that counting beats > 100 was difficult for the ancient peoples, in fact I don’t think they even used a base 10 system.
Using a base 6 system allows one to count 1 to 5 on the left hand then 1 on the right to total 6, left hand back to zero.
The system is repeated. If you follow, then holding 3 fingers (3 units) on the left with 3 fingers (3 x 6 units) on the right = 21 and
all 10 fingers = 35.
I am suggesting that a sacred measure for a coil or device would be,

• measure (drum) the heart beat at rest. 60 beats a minute
• make a pendulum to match this rhythm

The perpendicular length of this pendulum is your sacred dimension for device design.
Now, we have two choices. a pendulum made with a string and one made with a fixed rod. In order to have these two devices beat in phase then the rod must be made longer than the string equivalent.
The coupling factor is L (rod) = 2/3 L (string). Note, the musical interval (Perfect 5th) again.
If we now consider that male expressions manifest as a result of oscillating with fixed rods and female expression manifest as a result of strings, then it may explain why men are taller (2/3) than women ?

Fig : 6a

Remember, Nature’s pendula do NOT swing backwards and forwards in the same way a simple pendulum does !

WR teaches that Nature never reverses, motion is continuous. So, motion within the wavefield rather than oscillating backwards/forwards, Nature behaves a little like paddling a canoe. Because point x and x’ are the same point, imagine the pendulum bob exiting at  apex x, but reappearing at apex x’. Section 4 will return the motion to the starting point ready for the next cycle !

Section 7

Fig : 7a

Fig : 7b

When we consider the inert gas condition in terms of area then, when area A = area B, radius B < radius A.
This conflicts with Fig : 4 above but it may still be valid in order that the inert gas is perceivable within the universe.
When area A = area B then, area B is about 71% that of area A.
As the generative half of the cycle proceeds, area B reduces but area A increases. This is why WR teaches that cold generates.
When extension into the 3D physical universe is achieved two equal but opposed forms are now possible and indeed very likely. When full extension is achieved the volume of the positive male sphere is equal to the volume of the positive female annular ring.

Section 8

Fig : 8a

Two wrong’s may not make a right but, two cones make a sphere !
It is an interesting fact that when there is a common radius between the cone/sphere the volume of two cones is identical to the volume of a sphere. Considering WR assertion that opposed forces are described in terms of a conical potential distribution, when opposed balanced sex mates unite a sphere is the expression of balance.

Section 9

Fig : 9a

Man has developed his mathematical language to accurately describe his world. When all the correct parameter are considered and the mathematical model is constructed with sound comprehension then man can indeed create a robust tool to express his observations. But, one needs also to be cognizant of how simple terms can be passed off without a thought as too the implications. Take the simple case of multiplication and division.

WE can easily consider multiplication as the only way to increase in number/volume. 2 x 2 = 4 or 2 x 2 x 2 = 8. Nature though does not increase by simple multiplication. She multiplies through division !!
On the face of it if we limit our thinking of division to 8/2 = 4, then we miss a trick.

Nature takes 1 and divides it in half not to arrive at 1/2 but to yield 2. Two divides to become 4, 4 becomes 8, there is exponential growth through DIVISION !

Section 10

 Ocatve Keynote C Note C# Note D Note D# Note E Note F Note F# Note G Note G# Note A Note Bb Note B Note C 9 256 271.2 287.4 304.4 322.5 341.7 362.0 383.6 406.4 430.5 456.1 483.3 512 (1) 8 128 135.6 143.7 152.2 161.3 170.9 180.9 191.8 203.2 215.3 228.0 241.6 256 7 64 67.8 71.8 76.1 80.6 85.4 90.5 95.9 101.6 107.6 114.0 120.8 128 6 32 33.9 35.9 38.1 40.3 42.7 45.3 47.9 50.8 53.8 57.0 60.4 64 5 16 16.95 17.96 19.03 21.34 24.03 22.62 23.97 25.4 26.9 28.5 30.2 32 4 8 8.4752 8.98 9.5136 1.2599 10.079 11.312 11.986 12.699 13.454 14.254 15.101 16 3 4 4.2376 4.49 4.7568 5.0396 5.3392 5.656 5.9932 6.3496 6.7268 7.1272 7.5508 8 2 2 2.1188 2.245 2.3784 2.5198 2.6696 2.828 2.9966 3.1748 3.3634 3.5636 3.7754 4 1 1 1.0594 1.1225 1.1892 1.2599 1.3348 1.414 1.4983 1.5874 1.6817 1.7818 1.8877 2

Fig : 10a

This table should be viewed in conjunction with WR’s harp arrangement of the periodic table. The inert gases (9) lie nested one inside the other like Russian dolls.
Depending on the desire to express the appropriate octave will unfold. For instance, if the desire of Mind to express is equivalent 16 then the 5th octave will manifest, with the expressed range lying between 16 – 32.

The lower octaves tend to express simpler 8 note octaves or elemental expressions whereas the higher octaves tend to utilise the full octave range include more in-between tones.

The idea here is to indicate some measurable degree of difference between one elemental expression and another which will become necessary when tuning coils and circuits during the transmutation processes.