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The Mathematics Of The World Grid

Posted on January 17, 2016 at 1:00 PM

The Mathematics Of The World Grid

by Bruce Cathie


DEFINITIONS OF TERMS


 

Harmony and harmonic etc. as defined by the Britannica World Standard Dictionary:

HARMONY: A state of order, agreement, or completeness in the relations of things, or of parts of a whole to each other.

HARMONIC: Producing, characterized by, or pertaining to, harmony,

(a). Music: Pertaining to a tone whose rate of vibration is an exact multiple of a given primary tone.

(b). Mathematical: Derived from, or originally suggested by, the numerical relations between the vibrations of the musical harmonies, or overtones, of the same fundamental tone: Harmonic functions.

(c). Physics: Any component of a periodic quantity, which is an integral multiple of the fundamental frequency.


In this book I discuss the fundamental harmonies of the vibrational frequencies which form the building-blocks of our immediate universe; and those of the theoretical anti-universe which modern scientists have postulated as existing in mirror-like image of our own. I theorize that the whole of physical reality which is tangible to us is formed from the basic geometric harmonies, or harmonics, of the angular velocities, or wave-forms, of light. From these basic harmonies, or resonating wave-forms, myriad other waves are created which blend in sympathetic resonance, one with the other, thus forming the physical structures.

 

Einstein stated that the geometric structure of space-time determines the physical processes. I theorize that space and time manifest from the geometric harmonies of the wave-motions of light. The fundamental harmonic of light, in free space, in geometric terms being an angular velocity of 144,000 minutes of arc per grid second, there being 97,200 grid seconds to one revolution of the earth.

 

When physical matter is manifested in the universe the wave-forms of light from which it is formed are slowed down fractionally in order to release the energy required for the formation process. This is demonstrated by the unified harmonic equations in Chapter One. It was found that to calculate the values of harmonic wave-forms that have sympathetic resonance it was possible to disregard zeros to the right, or left, of whole numbers and extract the values direct from the mathematical tables.

 

My interest in the increasing UFO activity in the New Zealand area led me to the discovery that the surface of the world was crisscrossed with an intricate network of energy grid lines. I began my research in 1965. The information in this chapter regarding the structure and mathematical values built into the system will consist of material condensed from my first three books plus the findings derived from my recent research up to early 1982.

 

In a general way I was convinced that UFOs were actively engaged in a survey of the earth for some definite reason. I felt that their visits, were not haphazard; they were not just on casual sightseeing tours. Quite a number of investigators around the world had come to the conclusion that the sightings were beginning to form a pattern. At this period, however, this pattern was so complex as to defy any definition, or solution. By the correlation of sightings small sections of track had been identified, and some saucers had been seen moving along these set paths. Some of these had hovered over certain spots at set intervals. But these bits and pieces of track-lines were so scattered around the surface of our planet that it was quite impossible to fit them together into any semblance or order.

 

I was certain that if an overall pattern could be found and plotted, it might be possible to establish the reason behind U FO activity. 1 considered that the pattern would be geometric if these things were intelligently controlled, and that if somehow I could find the key to one section then I might solve the rest by duplication and inference.

 

I had sighted a number of unidentified objects in the sky over a period of several years, and by correlating two of these with other data 1 was eventually able to construct a grid system which covered the whole world.

 

One of the sightings was in 1956. 1 was a DC3 co-pilot crewing a flight from Auckland to Paraparaumu. It was about 6pm, conditions were calm, and there was unlimited visibility. We were just south of Waverley at 7000 feet when I saw this object at an extremely high altitude in the east. 1 drew the captain's attention to it and together we watched it travel in a curved trajectory from east to west across our track until it disappeared in a flash of light at about 10,000 feet in the area of D'Urville Island. It appeared to travel across New Zealand in the vicinity, or slightly to the north, of Cook Strait. and it was so large that two streaks, similar to vapor trails, were seen to extend from either side of its pale green disc.

 

When about halfway across the Strait a small object detached itself from the parent body and dropped vertically until it disappeared. It looked almost as if the main disc was at such a high temperature that a globule had dripped from it. I thought about this later and decided that if that were so, the small object would also have a curved trajectory in the direction of the parent body. But this was not so; it detached and dropped vertically down at great speed. There could be only one answer for this action; the small body must have been controlled.

 

Calculations at a later date proved this UFO to have been between 1500— 2000 feet in diameter. A report in a Nelson newspaper on the following day described an explosion at a high altitude to the north of the city. The shock-wave broke windows in some local glasshouses.

 

The other sighting occurred on 12 March 1965. This was the be stand most interesting of them all, and from then my investigations were pressed on with all speed until they culminated in my present findings.

 

I had always expected to see UFOs in the sky, and that was where my attention was usually focused. When 1 was flying I was alert and ready to analyze any object sighted from the aircraft. I never expected to find a saucer landing at my feet and so far this has never happened. This sighting however, was different from all the others because I observed it lying under thirty feet of water.

 

I was scheduled to carry out a positioning flight from Whenuapai, Auckland's main airport at the time, to Kaitaia. Departure was at 1 am and as no passengers were involved and the weather was perfect, I decided to fly visually to Kaitaia along the west coast. An officer from the operations department was on board and this was a good opportunity to show him some of the rugged country to the north. (I must stress that air-traffic regulations were strictly observed during the flight).

 

On leaving Whenuapai I climbed to clear the area and when approaching the southern end of the Kaipara Harbor, just north of Helensville, I dropped to a lower altitude to have a better look at anything in the flight path. The tide in the harbor was well out, and the water over the mudflats and estuaries was quite shallow.

 

I suppose we were about a third of the way across the harbor when I spotted what I took to be a stranded grey-white whale. I veered slightly to port, to fly more directly over the object and to obtain a better look.

 

I suppose a pilot develops the habit of keeping his emotions to himself. As far as I can remember I gave no indication of surprise, and I said nothing as I looked down. My "whale" was definitely a metal fish. I could see it very clearly, and I quote from the notes I made later.

The object was perfectly streamlined and symmetrical in shape.

It had no external control surfaces or protrusions.

It appeared metallic, and there was a suggestion of a hatch on top, streamlined in shape. It was not quite halfway along the body as measured from the nose.

It was resting on the bottom of the estuary and headed towards the south, as suggested from the streamlined shape.

The shape was not that of a normal submarine and there was no superstructure.

I estimated the length as 100 feet, with a diameter of 15 feet at the widest part.

The object rested in no more than 30 feet of clear water. The bottom of the harbor was visible and the craft was sharply defined.

Inquiries made from the navy confirmed that it would not have been possible for a normal submarine to be in this particular position, due to the configuration of the harbor and coastline.

 

An American scientist checked this spot on the harbor with a depth-sounder in September 1969. He informed me afterwards that a hole had been detected in the harbor bed approximately one eighth of a mile wide and over 100 feet deep, which 1 consider would indicate some activity had been carried out in this position some five years previously. 1 published the scientist's report in my second book.

 

I had a further key to the puzzle in April 1965. My wife saw an advertisement in the local paper seeking members for a UFO organization called New Zealand Scientific and Space Research. I contacted this organization and found that a vast amount of information had been very efficiently compiled. Material had been collected from twenty-five different countries over a period of twelve years. 1 was invited to study the information at leisure.

 

Amongst this mass of data I discovered the reports of a UFO that had been seen from several different localities in both islands of New Zealand on March 26 1965. People in Napier, New Plymouth, Palmerston North, Wanganui,Feilding and Otaki Forks in the North Island; Nelson Coast Road, Blenheim and Westport (Cape Foulwind) in the South Island, had all reported sightings.

 

It was decided that I try to plot the track of this UFO. From the considerable amount of information available I found that the maximum variation in the times of sightings from all areas was 15 minutes. Most reports gave the time as 9.45pm. This proved that the object must have been very large and at a high altitude during the greater part of its trajectory.

 

There was nothing of any great significance or originality in these accounts, and they followed the pattern of many other sightings. However from the mass of detail supplied by so many different people over so wide an area, it was possible to plot the track of the object with reasonable accuracy. 1 started work on a Mercator's plotting chart, and after several hours of checking one report against the other, and calculating possible elevations and trajectories, 1 felt I had refined the plot sufficiently to draw in the final track of the object, or objects. The result is shown on map I.

 

The track began about seventy nautical miles north of New Plymouth, passed just over to the west of Mt Egmont, and finished at D'Urville Island. When first seen the altitude would have been about 30,000 feet curving down on a flight path to somewhere around 10,000 feet when it disappeared.

 

Some time after those sightings on 26 March 1965 I had another look at the plot 1 have made. I could find no flaws in my thinking, but I needed more information. As I was to discover many times later, the clues were quite obvious, but 1 was not then sufficiently expert in realizing their significance. In point of fact this first trackline was to be the starting point of a whole string of discoveries of which I have yet to f i n d an end.

 

I pored over that plot for a long time before it suddenly occurred to me that the track appeared to be in line with the position where 1 had sighted the unidentified submarine object, or USO, on 12 March 1965. On extending the line back 1 found it was in line with the sightings of 26 March. 1 was positive there had to be a connection — but to prove it was a different matter.

 

I checked my report files again and found that on 2 March some fishermen just north of the coast of New Plymouth had seen a large object plunge into the sea and disappear. They thought it was an aircraft and reported the incident to the appropriate authorities, but no aircraft or personnel were missing. I checked this position on the map and found that it also fitted the established trackline. Was this connected with the USO of 12 March, and could the two sightings be of the same object, sighted twice in ten days? Could it be working slowly up this track carrying out some project on the sea bed? 1 tucked this thought away for future reference and carried on with the search.

It was some days later that I remembered the UFO I had seen in 1956. This object was similar and, most significant of all, both objects had apparently traveled at 90° to each other, and finished in the same grand all-illuminating flash in the area of D'Urville Island.

 

If these objects were not controlled, how could anyone explain such coincidences? No two meteors or other natural phenomena could coincidentally carry out similar maneuvers, travel at 90° to each other, and both decide to end their existence at the same point in space, within nine years of each other. Also, in both cases, objects had been seen to emerge from the parent bodies. Was this irrefutable evidence that they were intelligently controlled vehicles?

 

I plotted the track of the 1956 U FO on the map at 90° to the north-southline. I realized that 1 had no definite proof that they were at exactly 90° to each other or that the 1956 track was not a few miles north or south of this position — still, I had to start from somewhere, and I would assume this to be correct unless and until other evidence proved me wrong.

 

Two track lines at 90° meant little on their own. If 1 found several at 90°, 1 might have something — a grid perhaps? These two lines hinted at this, and I believed that if 1 could solve the system of measurement, then 1 had two ready made baselines to work from.

 

Once again I went to the UFO files and found that a Frenchman by the name of Aime Michel had been studying UFOs for a number of years and had found small sections of tracklines in various areas of Europe. Saucers had been seen hovering at various points along these tracklines, and Mr. Michel had observed that the average distance between these points was 54.43 kilometers. By itself this was only a small grain of information but, like a starting gun, it set me off again.

 

Using the Kaipara Harbor as a starting point, I marked off the 54.43 kilometer intervals along the trackline I had found. I was disappointed when I was unsuccessful in obtaining an even distribution of positions to the D'Urville Island disappearing point. I checked and re-checked, but nothing worked out. 1 slept on the problem, and at some time during the night inspiration turned up the wick; once more the light grew bright.

 

I remembered that a great number of sightings had occurred around the Blenheim area. Even before the advent of ordinary aircraft in New Zealand, this area had been visited by UFOs. I had read about them in old copies of the local papers, and many recent sightings suggested again that this area had something special about it.

 

So I dragged out my map and extended the trackline until it cut a 90° coordinate from the town of Blenheim. The distance from this point to the Kaipara position I found to be exactly 300 nautical miles, and one nautical mile is equal to one minute of arc on the earth's surface. Could it be that the rough interval of 54.43 kilometers discovered by Michel was, in fact, an interval of 30 nautical miles when corrected? If so then this interval could be evenly spaced along my trackline ten times. Was this the system of measurement used by the U FO's? There was no proof, of course, but it seemed a reasonable assumption. A minute of arc is a measurement which could be applied to the whole universe.

 

University personnel and others in the academic field attacked me repeatedly over this issue. They maintained that degrees and minutes of arc were arbitrary values set up by the ancient mathematicians and that therefore my calculations were meaningless. I finally found proof of my argument in the works of Pythagoras. As my research progressed 1 discovered that the harmonic of the speed of light in free space had a value of 144. If this was divided by 2, to find the harmonic of one half cycle, or half-wave, the answer was 72. If this value was then applied to the Pythagoras right-angled 3, 4, 5 triangle and each side was extended in this ratio then the figure had sides of 216, 288 and 360 units. The harmonic proportions thus derived were equal to:

2 1 6 = 21600 = the number of minutes of arc in a circle.360 = 360 = the number of degrees in a circle.288 = (144 x 2) = 2C, where C = the speed of light harmonic.

It appeared from this that the harmonic of light had a very definite relationship with the geometry of a circle, and that the early mathematicians were fully aware of the fact. This will become clearer as you read through this book.

 

The fifth interval of 30 nautical miles from the Kaipara position coincided with the position off the coast of New Plymouth where the mysterious object had plunged into the sea. The plotted points of disappearance of the two large UFOs at D'Urville Island did not quite match up with the ninth interval, but this did not worry me unduly as I expected that a small percentage of error must be expected in my original plot. I readjusted this position to the ninth interval, and carried on the search to see how many other sightings I could fit into this pattern.

 

The results exceeded my expectations. I found that by using units of 30 minutes of arc latitude north-south, and 30 minutes of arc longitude east- west, on my Mercator's map, a grid pattern was formed into which a great number of UFO reports could be fitted. I eventually had a map with sixteen stationary and seventeen moving UFOs plotted on grid intersections and tracklines.

 

Having satisfied myself that my reasoning and plotting were not false, 1 considered that I had good proof that New Zealand, possibly other countries, and probably the whole world, were being systematically covered by some type of grid system.

 

In my first book 1 demonstrated that the main grid pattern consisted of gridlines spaced at intervals of 30 minutes of arc (latitude and longitude). In my second book I probably confused the issue a bit as I stated that the east-west grid lines were spaced at 24 minutes of arc. This was due to the spacing being measured in nautical miles, or values in minutes of latitude. The actual length of a minute of longitude varies mathematically from one nautical mile at the equator, to zero at the north and south poles.

 

The value of 30 minutes of arc in terms of longitude in the New Zealand area happened to be an average of 24 nautical miles, which can be confusing those readers who are not familiar with map scales.

Reference to the grid structure will therefore be stated from now on in minute of arc values only, for latitude and longitude, to minimize confusion.

 

I subsequently discovered that the grid lattice could be further divided. It is now evident that the grid lines in the main system are spaced at intervals of 7.5 minutes of arc north-south, and east-west. The importance of this will prove itself when compared with the rest of the calculations in this book. There are 21,600 minutes of arc in a circle, and when this is divided by 7.5 we get a value of 2880. The grid lattice therefore is tuned harmonically to twice the speed of light (288), as will be shown in other sections.

....... http://www.bibliotecapleyades.net/ciencia/antigravityworldgrid/ciencia_antigravityworldgrid04.htm#The Mathematics Of The World Grid

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