The Mathematics Of The World
by Bruce Cathie
DEFINITIONS OF TERMS
Harmony and harmonic etc. as defined by the Britannica World
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,
(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
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
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
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
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
most interesting of them all, and from then my investigations were
pressed on with all speed until they culminated in my present
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
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
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
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
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
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
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.
It appeared that 1 had found a section of geometric grid pattern in
the New Zealand area. I now had to form some theory of construction
for the whole world. I could then possibly fit the New Zealand
section into it.
By drawing a series of patterns on a small plastic ball I finally
found a system which could be used as a starting point for a global
investigation. (The basic pattern is shown in diagram 1).
I was sure I was on the right track, but now I had to super-impose
this pattern on the world globe. It was essential that I find a
point position somewhere on the earth upon which to orientate the
geometrical pattern. I finally came up with an item of news that
gave me a very important clue on how to proceed.
On 29 August 1964 the American survey ship Eltanin was carrying out
a sweep of the sea-bed off the coast of South America. A series of
submarine photographs was being taken of the area by means of a
camera attached to a long cable. A surprise was in store when these
photographs were developed. On one of the points, in marvelous
detail, was an aerial-type object sticking up from an otherwise
This object appeared to be metallic and perfectly symmetrical in
construction. The array consisted of six main crossbars with small
knob-like ends and a small crossbar at the top. Each cross looked to
be set at angles of 15° to the others, and the whole system stood
about 2 feet in height. The position where this object was found was
given as latitude 59°08' south, longitude 105° west.
As this bit of ironmongery was
situated at a depth of 13,500 feet
below the surface, I was certain that no human engineers had placed
Scientists may be able to descend to those depths in specially
constructed bathyspheres, but I don't think they could work as
deeply as that on a precision engineering problem. In view of my
earlier sightings in the Kaipara Harbor, I was willing to accept
that the aerial-type object had been placed there by an un-identified
submarine object, or USO.
Since this photo was taken there has been a determined attempt by
the scientific world to label this object as nothing more than a
plant of some sort. A journalist friend and I managed to visit the
Eltanin during one of its few visits to New Zealand and when we
discussed this object with some of the scientists on board, the
comment was that it was classed as an artifact. This was before the
great hush-up but, regardless of that, I believe that the
mathematical proofs will show without doubt that the object is
artificial, and most probably an aerial of some sort.
An "OOPART". Photographed on the sea-bed at a depth of 2,500
fathoms,1,000 miles west of Cape Horn, by US survey ship Eltanin,
whose officers are close-lipped about it. "It's a marine organism,"
maintained an Eltanin officer in Auckland in 1968. Pressed further,
he admitted: "But it still looks like an artifact to me!"
The form of this aerial-like structure also fitted in with the
general pattern of the grid as I had envisaged it on the plastic
ball. The six main crossbars denoted the radiating points of six or
twelve great circles which form the main structure of the grid.
I centered the grid on the position of the object found by the
Eltan'm, and the 180° reciprocal of this in Russian Siberia, lining
the whole thing up with the section I had found in New Zealand. I
found the system to be lined up very closely with the magnetic field
of the earth. The equator of the grid followed very closely the line
of zero dip around the world. (That is, the positions on the earth's
surface where a magnetic compass needle has only a horizontal and no
In my first two books 1 discussed the methods 1 used to line up the
system and calculate the first estimates of the grid pole positions,
and the mayor focal points of the grid similar to the Eltanin
The reciprocal position of the Eltanin "aerial" is at latitude 59°
08' north, longitude 75° east, in Siberia. I calculated the length of
the diagonal of what I call, for simplicity, the "polar grid square"
and found it to be 5091.168825 minutes of arc long. I plotted a
track from the Siberian position through the north geographic pole
and measured off this distance to locate another corner "aerial" of
the polar square. (Square is not technically the right word to use
as the four sides are formed by sections of small circles which are
in different planes to each other. When the "polar square" areas are
transferred from the surface of the earth sphere on to a flat plane
such as a map. then a perfect square is formed with sides 3600
minutes long and diagonals of 5091.168825 minutes of arc).
In my first two books 1 stated, in error, that the sides of the
"polar squares" were formed by sections of GREAT circles 3600
minutes of arc long, instead of SMALL circles. The great circle
distance between these points is in fact 3418.606915 minutes of arc,
which is very confusing to any investigator attempting to
reconstruct the grid. I apologize to my readers for this error, which
was caused by my lack of access to calculators during my earlier
research. In the grid pattern there are actually two small-circle
segments, and one great circle segment connecting each of these
points which form the polar squares.
Each of the segments has a
different path over the earth and some tricky calculating is
necessary to ascertain the true length. Although I used the wrong
term in my earlier publications, the actual calculations derived
from the grid system are not altered in any way, and still stand the
test of time. Over the last few years I have slightly refined the
values I demonstrated previously, derived from a mixture of
practical and theoretical studies. I have now set up what 1 see as a
completely theoretical system, discovered by working entirely by
calculator. Time will prove how close my calculations are. I have no
doubt that I, and others, will continue further to perfect the
system as more facts come to light.
Once I had established this first base line I found it quite easy to
construct the main skeleton of the grid over the whole surface of
As my work progressed 1 found that there were in fact two similar
grids, interlocked with each other. The poles of the grids were
spaced at different distances from the north geometric pole, and
this arrangement set up a series of geometric harmonics which were
directly related to the speed of light, mass, and gravity. The
interaction of the two grids created a harmonic resonance which, in
turn, formed a third resultant grid.
After ten years of work and correlating information 1 have now
theoretical positions for the three grid poles in the northern
hemisphere which are very close to my original estimate. Reciprocal
positions will give similar values for the southern hemisphere.
Grid pole (A) = Latitude 72.4266°/longitude 90° west 1054.4 minutes
of arc from the north pole.
Grid pole "B" = Latitude 78.4266°/longitude 105° west 694.4 minutes
of arc from the North Pole.
Resultant grid pole "C" = Latitude 75.6°/longitude 97.5° west 864
minutes of arc from the North Pole.
The diagonal of the "polar square" of 5091.168825 units can be
broken down into a series of values:
5091.168824 /2 = 2545.584412
2545.584412 / 7.5 = 3.39411255
3.394112552 = 11.52
11,52 / 8 = 1.44 (speed of light harmonic)
2545.5844122 = 6480000
Reciprocal of 2545.584412 = .03928371
The harmonic value of 3928371 is of extreme importance as it has a
direct relationship with the earth's magnetic field. The harmonic 648
was also shown, in my earlier books, to have many interesting
associations. In particular the harmonic table for temperature.
The many other harmonic factors, centered around the "polar square"
corner "aerial" positions, form a series of complex mathematical
associations, and this can be left for those who wish to carry out
their own research. If I can show how to construct the main "bones"
of the grid my part of the job will be complete. I have found it
impossible, so far, to plot the fine grid structure of lines 7.5
minutes apart, over the whole world, because of the complexity of
such an exercise. (A full computer program would be necessary and
I do not have the finance required for such an undertaking).
So far I have confined myself to the New Zealand area, with the
section of finely-spaced grid lines that I originally discovered.
Over the years I
have been able to plot into this map a great many interesting facts
indicate activity by various scientific groups. This has helped me
to gradually build up my own knowledge of the system.
My nosiness has not gone unnoticed — as evidenced by the constant
probing of interested parties endeavoring to find out the extent of
discoveries. I hope that in the near future the international
in this advanced research will make known to the public the vast
scientific knowledge they have acquired. Possibly this will only
happen if and
when a world government has been set up to control the scientific
which are now within our reach. Enough is known already to make most
of our energy and transport systems obsolete — which may explain why
the facts are being suppressed?
I have been able to check activity in other parts of the world by
applying harmonic calculation to certain positions of latitude and
longitude. It is not necessary to use the grid structure, and such,
for some types of calculation once the harmonic process is
understood. Eventually, when the whole grid has been plotted, the
work will be much easier.
In my second book I stated that the first glimmerings of how true
space travel might be achieved came to me when I uncovered the clues
that led me to the UFO grid which laces about our globe.
I was aware that my calculations were not precisely accurate — in
the strict mathematical sense — but I could see that the system was
based on space-time geometries, and at least there was the best
possible support for this: none less than the theories of Einstein.
Somewhere, I knew, the system contained a clue to the truth of the
unified field which, he had postulated, permeates all of existence.
1 didn't know at the time that this clue had already been found by
scientists who were well ahead of me. I know now that they must have
understood something of the grid system years ago. They knew that
Einstein's ideas about the unified field were correct. What's more,
for many years they had been carrying out full-scale research into
the practical applications of the mathematical concepts contained in
We were told that Einstein died without completing his equations
relating to the unified theory. But in more recent times it has been
said that he did in fact complete his work but that the concepts
were so advanced that the full truth was not released.
The only way to traverse the vast distances of space is to possess
the means of manipulating, or altering, the very structure of space
itself; altering the space-time geometric matrix, which to us
provides the illusion of form and distance. The method of achieving
this lies in the alteration of frequencies controlling the
matter-antimatter cycles which govern our awareness, or perception,
of position in the space-time structure. Time itself is a geometric,
just as Einstein postulated; if time can be altered, then the whole
universe is waiting for us to come and explore its nook and
In the blink of an eye we could cross colossal distances; for
distance is an illusion. The only thing that keeps places apart in
space is time. If it were possible to move from one position to
another in space, in an infinitely small amount of time, or "zero
time", then both the positions would coexist, according to our
awareness. By speeding up the geometric of time we will be able to
bring distant places within close proximity. This is the secret of
the UFOs -they travel by means of altering the spatial dimensions a
round them and repositioning in space-time.
I decided to concentrate specifically on three harmonic values which
appeared to have a close relationship with each other. Previously I
had shown this connection and had truthfully pointed out that I did
not know why the relationship was there at all.
The harmonic values which occupied my full attention:
1703 -This was the four-figure harmonic of 170,300,000,000, which is
the expression in cubic minutes of arc of the mass, or volume, of
the planet earth, and its surrounding atmosphere.
1439 — A four-figure harmonic of 143,900 minutes of arc per grid
second, representing the speed of light in grid values.
2640 — This
figure expressed in minute of arc values is built into the polar
portion of the grid structure, as a geometric coordinate.
I found that when 1 matched these values harmonically the results
were as follows. Zeros to the right-hand side can be ignored in this
form of harmonic calculation:
In other words the difference between the harmonic of mass and the
harmonic of light was the harmonic of 264 (or 2640).It was apparent
that if my calculations were more accurately worked out it should be
possible to find out just what the 2640 figure referred to. After
more calculation the following terms were found:
17025 Earth mass harmonic
-2636 Unknown harmonic
14389 Speed of light harmonic
Checking through some five-figure mathematical tables.
I found to my
surprise that 2.6363 is the square root of 6.95 (from the 1-10
square root tables). In harmonic calculation decimal points as well
as zeros to the right or left of a figure can be ignored; so it could
be said that the square root of 695 was 2636. I could perceive from
this the first steps necessary to solve the elusive equation. 1 had
established that 695 was the harmonic reciprocal of the speed of
light, or 1 /1439 subject to the accuracy of my calculations at the
time. It was now possible to substitute algebraic values -although
obviously a computer would be necessary to solve the true values to
17025 (earth mass)
-2636 square root of speed of light reciprocal
14389 (speed of light)
C = The speed of light, and
Then M = C +
I had the first part of a unified field equation in harmonic values.
To take the next step I first had to go back to Einsteinian theory,
particularly the famous equation E = MC2, where E is energy, M is
mass and C the speed of light.
Einstein declared that physical matter was nothing more than a
concentrated field of force. What we term a physical substance is in
reality an intangible concentration of wave-forms. Different
combinations of structural patterns of waves unite to form the
myriad chemicals and elements which in turn react with one another
to form physical substances. Different waveforms of matter appear to
us to be solid because we are constituted of similar wave-forms
which resonate within a clearly defined range of frequencies — and
which control the physical processes of our limited world.
Einstein believed that M, the value for mass in the equation, could
eventually be removed and a value substituted that would express the
physical in the form of pure energy. In other words, by substituting
for M a unified field equation should result which would express in
mathematical terms the whole of existence — including this universe
and everything within it.
Einstein maintained that the M in his equation could be replaced by
a term denoting wave-form. I had found a substitute for M in terms
of wave-forms of light. So the obvious step, to me, was to replace
Einstein's M with the values of C found from the grid system . The
results are as follows:
I now had a harmonic unified field equation expressed in terms of
light — or pure electromagnetic wave form — the key to the universe,
the whole of existence: to the seen and the unseen, to forms,
solids, liquids and gases, the stars and the blackness of space
itself, all consisting of visible and invisible waves of light. All
of creation is light.
It was now necessary to refine my calculations and attempt to
discover a way to practically apply this initial equation.
The equation is that from which an atomic bomb is developed, by
setting up derivatives of the equation in geometric form, the
relative motions of the waveforms inherent in matter are zeroed, and
convert from material substance back into pure energy.
This explained the workings of a nuclear explosive device, but it
still did not yield the secret of space-time propulsion. The grid
system which 1 discovered by the study of the movement of
unidentified flying objects was harmonically tuned to this basic
equation, yet a UFO does not disintegrate when it moves within the
resonating fields of the network.
There had to be an extension of the equation which so far I had
missed that would produce the necessary harmonics for movement in
In the polar areas of the grid the geometric values of some of the
coordinates appeared to be doubled up. The coordinate of 2545584412
was doubled in the diagonals of the polar squares, with all of its
associated harmonics and other factors appeared to be doubled when
the pattern was projected onto a flat plain.
I reasoned that a way to check this idea was to increase the values
of C in the equation, and observe the changing harmonic of E to see
what relative values might emerge. I thought at the time that a
direct antigravitational harmonic might become evident, but my
recent research has proved this line of thought to be incorrect. In
terms of mathematical values I found what I was hunting for in the
form of two more equations. In the case of one of the equations
erroneously believed that the derived harmonic value related to the
reciprocal of gravity. I know now that what I had hold of was an
equation related to the magnetic field of the earth.
The earth being simply a huge magnet, a dynamo, wound with
magnetic lines of force as it coils, tenescopically counted to be
1257 TO THE SQUARE CENTIMETER IN ONE DIRECTION AND 1850 TO THE
SQUARE CENTIMETER IN THE OTHER DIRECTION (EDDY CURRENTS), indicates
that natural law has placed these lines as close together as the
hairs on one's head.
The spectroscope shows that there is an enormous magnetic field
around the sun, and it is the present conclusion of the best minds
that magnetic lines of force from the sun envelop this earth and
extend to the moon, and THAT EVERYTHING, NO MATTER WHAT ITS FORM ON
THIS PLANET, EXISTS BY REASON OF MAGNETIC LINES OF FORCE.
This I agree with, according to my own research. We are taught in
our schools and universities that the magnetic field passes through
one magnetic pole, then through the body, and out the other magnetic
pole. I disagree with this explanation. I believe that the magnetic
lines of force enter the body at the poles, then carry out a looped
path through the body before passing out the opposite poles.
The flow is not in one pole and out the other, but in both poles,
and out both poles, although the field intensity both ways is
If we can visualize one line of force so that we can trace out its
path we can form an analogy by imagining it to be similar to a piece
of string. First of all we make a loop in the piece of string. Now
imagine it being fed through a fixed position with the loop
remaining stationary relative to a fixed point. With the length of
string as the axis we can now make the loop revolve in a path
which is at 90° to the movement of the string. The loop in fact would
trace out a spherical-shaped form in space.
The lines of force of the magnetic field would form a lattice, or
grid pattern, due to the spin of the planetary body. A good analogy
would be an ordinary machine-wound ball of string. The length of
string has taken on the form of a ball, and at the same time has
formed a crisscross pattern. If we again visualize this as a
physical body being formed in space then we can now imagine a small
vortex being created at all the trillions of points where the lines
of force cross each other in the lattice pattern.
Each vortex would
manifest as an atomic structure and create within itself what we
term a gravitational field. The
gravitational field in other words is nothing more than the effect
of relative motion in space. Matter is drawn towards a gravitational
field, just as a piece of wood floating on water is drawn towards a
whirlpool. The gravitational fields created by the vortexual action
of every atom would combine to form the field of the completed
The world grid that 1 speak of is the natural grid that is formed by
the lattice pattern of the interlocking lines of force.
The unbalanced field of 1257 lines of force per square
in one direction and 1850 in other does not tell us very much in
itself. But if we use the information to calculate the field
strength over an area which has a harmonic relationship with the
unified fields of space, and if the basic information is correct, we
should find some mathematical values of great importance.
At the time of writing my last book I was not aware of the extreme
importance of the values at that stage of accuracy. 1 was close
enough to see how they fitted into the equations, but a further fine
tuning was necessary to reveal the knowledge locked within these two
The basic unit for harmonic calculation is the geodetic inch, or one
seventy-two thousandth of a minute of arc; one minute of arc being
6000 geodetic feet. If we take the values 1257 and 1850 lines of
force per square centimeter and calculate the field strengths for one
square geodetic inch, the field density is 8326.71764 and
12255.08864 lines of force respectively. The fields being in
opposition to each other. The combined field density is equal to
Allowing for very slight variations in the conversion factors the
difference in field strengths (12255.08864 minus 8326.71764) is
equal to 3928.371. We could say that the resultant field density one
way is equivalent to field 'A' minus field 'B', or 3928.371 lines of
force. This value I found to be the harmonic reciprocal of the grid
The combined field strength of 20581.80628 lines of force can be
harmonically associated with several other interesting facts, to he
demonstrated in other sections of this book.
We can now formulate another equation in order to demonstrate the
association of the earth's magnetic field with the speed of light.
Harmonic equation 2
Field (A — B) = (2C +√(l/2C))
* (2C)2 = 3928.371 harmonic
C = 144000 — 90.9345139
The reduction in light speed of 90.9345139 minutes of arc per
grid/sec. creates a very interesting factor, because:
90.9345139 = 3928371
The reduction in light speed is therefore equal, in harmonic terms,
to the resultant field strength divided by the radius of spherical
mass. In this case the radius being the distance, in minutes of arc,
from the earth's centre to the average height of the atmosphere.
(432 being a harmonic of 4320 minutes of arc).
In my last book, "The Pulse of the Universe", I had shown this
reduction to be equal to three times the gravity acceleration
harmonic as the values matched very closely within the accuracy of
my work at that time. The relationship with gravity is still there
but not so directly obvious.
We can now formulate a third equation by inserting the value for the
speed of light at the earth's surface. By mathematical conversion
this was found to be 143795.77 minutes of arc per grid second, where
one grid second was 1/97200 part of the time taken for one
revolution of the earth.
Harmonic Equation 3
2693645 =√(2C +√(l/2C))
C = 144000 — 204.23
In my third book 1 had again used the gravity factor as the basis
for the reduction, making the value equal to 6G. I feel that this
new approach based on extended knowledge is the more correct one,
although, as above, the gravity factor is not so obvious. 1 believe
that there is yet another factor in the light reduction process to
be found but this will require further research.
The research will be extended until all the answers are in but the
results appear to back up my belief that as the harmonic of light is
fractionally decreased, the energy which is released is converted to
form physical matter.
From this we can get a glimmering of how an unidentified flying
object is able to create a series of resonating frequencies which
alter the physical properties within and around it, thus causing a
change in the space time frames of reference in relation to the
earth or other planetary body.
As I have stated in my previous publications, natural law is not
erratic. The universe does not rely on chance to manifest within
itself the physical substances which we perceive and call reality. A
very strict ordered system of mathematical progressions is necessary
to create the smallest speck of matter from the primeval matrix of
During my years of research into the complexities of the earth grid
system I have gradually built up a picture in my mind of the
possible geometric combinations necessary to form matter from
resonating, interlocking waveforms.
Matter and anti-matter are formed by the same wave motions in space.
The waves travel through space in a spiraling motion, and
through positive and negative stages. Matter is formed through the
positive stage, or pulse, and anti-matter through the negative pulse.
Each spiral of 360° forms a single pulse. The circular motion of an
electron about the nucleus of an atom is therefore an illusion. The
relative motion of the nucleus and electrons through space gives the
illusion of circular motion. The period during the formation of
anti-matter is completely undetectable, since obviously all physical
matter is manifesting at the same pulse rate, including any
instruments or detectors used to probe atomic structures.
The period or frequency rate between each pulse of physical matter
creates the measurement which we call time, as well as the speed of
light, at the particular position in space of which we are aware, at
any given moment.
If the frequency rate of positive and negative pulses is either
increased or decreased, then time and the speed of light vary in
direct proportion. This concept would explain time as a geometric, as
Einstein theorized it to be.
A rough analogy of physical existence can be made by reference to a
strip of motion picture film. Each frame or static picture on the
film strip may be likened to a single pulse of physical existence.
The division between one frame and the next represents a pulse of
anti-matter. When viewed as a complete strip, each frame would be
seen as a static picture — say one at either end of the strip — then
the past and the future can be viewed simultaneously. However, when
the film is fed through a projector, we obtain the illusion of
motion and the passage of time. The divisions between the static
pictures are not detected by our senses because of the frequency, or
speed, of each projection on the movie screen. But by speeding up or
slowing down the projector, we can alter the apparent time rate of
the actions shown by the film.
To continue this analogy: our consciousness is the projector. The
conscious T am' part of our individuality passes from one pulse of
physical matter to the next within the framework of the physical
structure which we term our body, thus giving the illusion of
constant reality, and the passing of time.
It is logical to assume that we have a twin stream of consciousness
on the anti-matter side of the cycle, which in fact creates a
mirror-image of our own individual personality. (This postulate has
already been put forward by scientists). The frequency of
manifestation of both streams of consciousness, that is, the plus
and the minus 'I am', would position our awareness of the illusion
of reality at a particular point in space and time. In other words,
if the frequency of pulse manifestation is altered, even
fractionally, our awareness of reality, in the physical sense, will
shift from one spatial point to another. In fact, we would travel
from one point in space to another without being aware that we had
traversed distance in the physical sense. This would be space travel
in the truest sense.
Let's look at another analogy: we can consider a simple spiral
spring as representing the wave motion of an electron through space.
Every second 360° spiral of the spring represents the path of the
electron in physical matter, while the opposite applies to
The theory outlined above explains why light has been described as
being caused by both a wave motion and a pulse. Both explanations
A pulse of light is manifested when the energy level of the atomic
structure is altered by outside influences (theory of Max Planck).
In the physical plane, the electron of the atomic structure appears
to jump from its orbit. According to my belief, the electron does
not jump orbit. But this is the illusion we obtain, since we are not
equipped to perceive the path of the electron during the anti-matter
cycle. What actually happens is that the radius of the spiraling
motion is increased or decreased in order to absorb or release the
energy imparted to, or removed from, the atomic structure. If the
energy is imparted, then the electron must extend orbit in order to
maintain balance in the system; and vice versa. Light, or any other
radiant energy above or below light frequency, is therefore
manifested by undetectable changes in the radius of the spiral
motion of the electron during the anti-matter cycle.
If this hypothesis is correct, movement from one point in space to
another point, regardless of apparent distance — in other words,
true space travel — is completely feasible. By manipulating the
frequency rate of the matter-anti- matter cycle, the time and speed
of light can be varied in direct proportion to any desired value.
All the mathematical evidence amassed so far indicates that the
maximum number of individual elements to be found in the universe
144. Each of these elements will have, in theory, six isotopes,
which will make up a completed table of separate substances
numbering 1008. An isotope is an atom of the same element which has
a different nuclear mass and atomic weight.
Mathematically, the progression would create 144 octaves of
separate substances giving a theoretical value of 1152. The
difference between the total number of substances (1008) and the
harmonic value in octaves (1152) would be 144, the light harmonic.
Once the precipitation of physical matter has occurred, the buildup
of substances takes place according to a very well ordered
mathematical sequence. Light-waves, guided seemingly by superior
intelligence, form intricate interlocking grid patterns which
graduate from the simple to the more complex, as the elements from
hydrogen at the lower end of the scale, to element 144, come into
When we think of reality we must think of mass in relation to any
physical manifestation, and the smallest particle of physical matter
that we are aware of is the electron. Therefore electron mass must
be the starting point in our quest for a feasible theory to explain
the structure of matter.
The average radius of action of the electron around the atomic
nucleus must also have a constant harmonic value in order to set up
a system of expanding spheres which encompass the structure of each
element. As the number of protons in the nucleus increases with the
buildup of each element, the spherical space which houses the
electron shell must expand to accommodate an equal number of
electrons. Although the protons and electrons are nothing more than
extremely concentrated wave-forms, we consider them as physical
particles in order to build up a picture of our model.
electron cloud, or shell, expands outward from the nucleus, we find
that it can accommodate only eight electrons. The shell is then
filled up and
another expansion must take place in order to form a new shell or
harmonic-zone, which again builds up to a maximum of eight
electrons. As the magnitude of the harmonic resonance intensifies,
heavier and heavier elements are produced until we reach a maximum
of 144 elements. The light harmonic is then equal and the cycle has
been completed. The whole series is a repetition of octaves of
wave-forms forming more and more complex structures.
In my earlier work I had assumed that the harmonic radius of the
atom was equal to the mass ratio of the proton and electron. I now
realize that although I was on the right track, the theoretical
mode! demonstrated was partly in error. This necessitated another
search into the physics books and I now feel that the following
calculations based on the experimental values are getting close to
It would be logical to base the harmonic interaction on the
geometric structure of the hydrogen atom. If harmonic equivalents
can be derived from the basic values established by experimental
physics, and remain within the laid down tolerances, then almost
certainly a new theory should be evident. Especially if the harmonic
values closely match those found in the unified equations previously
The distance given between the electron and the proton in the
hydrogen atom is approximately 5.3 x 10-11 meter. (Physics Part 2,
Halliday & Resnick) I have discovered that a value of: 5.297493 x
10-11 meter fits in very neatly with the previously established
harmonic terms. If we convert this value into its geometric
equivalent, then: 5.297493 x 10-11 meter = 17.15150523 x 10-11
geodetic feet = 205.8180628 x 10-11 geodetic inches
The radius of the hydrogen atom is therefore very obviously tuned to
the harmonic value of 20581.80628, which is the number of magnetic
lines of force per square geodetic inch. The diameter of the
hydrogen atom would be, 411.6361256.
If we calculate the circumference of the atom in terms of harmonic
geodetic feet then: 17.15150523 x 10-11 geodetic feet radius =
34.30301 harmonic diameter = 107.7660 harmonic circumference.
Now if we allow spacing on this circumference for eight electron
107.7660 divided by 8 = 13.47 units
But an electron has only half a spin value; the other half taking
place during the anti-matter cycle, so:13.47 x 2 to allow for the
double cycle = 26.94
Allowing for the accuracy of the conversion factors etc. would
harmonic geometries of the hydrogen atom comply fairly
closely geometric energy value derived from the unified equation
(2693645). A make with the the computer program set up for curved geometry should, in theory, show
a perfect match.
We can now use the hydrogen atom as a base line to form a
theory regarding the formation of the complete atomic table of
elements. I believe that the harmonic radius of 205.8180628 units
would remain constant throughout the whole range of elements. The
orbits of electrons in all substances taking up harmonically spaced
positions to the power often. In other words by shifting the decimal
point to the right or left of this basic harmonic, the orbital radius
of all electrons can be calculated. (See diagram 5).
This would apply to the whole range of 144 elements and their
isotopes. Physical reality, as we perceive it, being manifested by
the concentrated interlocking of harmonic wave-forms, which are
built up progressively from a foundation of fundamental
The square of the diameter of the hydrogen atom (4116361257) is
equal to the harmonic of mass at the centre of a light field,
1694443. This value also shows up in the cycle of element formation
due to the introduction of neutrons into the atomic nucleus. It is
stated in the physics books that the maximum number of neutrons that
can be contained in the atomic nucleus is
1.6 times the number of protons.
The theory of harmonic formation agrees
with this. If the ratio of protons and neutrons in the basic
element is taken as
1:1 then as each isotope is built up due to the introduction of
neutrons we have the mathematical progression of 1:1, 1:1.1, 1:1.2,
1:1.3, 1:1.4, 1:1.5, 1:1.6, for the element and the six isotopes;
then as the harmonic increases to 1:1.694443, and above, towards
1:1.7, we get the formation of the next higher element. The cycle
would then repeat itself.
The rest mass of the proton is given as 1.67252 x 10-27 Kg, and a
mass ratio of 1836 is laid down for the proton and electron. I
believe that the harmonic values approach those found in the unified
equations when the atomic structure is accelerated towards the speed
of light. According to Einstein the mass increases, and I believe
the mass of the proton increases towards the 1694443 harmonic. If
the energy level is built up above this point a condition would be
reached where a change in physical state would occur. That is, the
harmonic would be approaching 1.7 to 1.7018, the surface mass
harmonic for an atomic structure, and a change would be triggered.
A gravitational connection with mass becomes evident when the normal
gravitational acceleration is converted into grid equivalents. The
physics books state that gravity acceleration varies according to
latitude on the earth's surface, and also with altitude, or distance
from the centre of the earth. The variation at sea level from 0° to
90° latitude is equal to 32.087829 feet/sec2 to 32.257711 feet/sec2.
I decided to calculate the grid gravity acceleration at latitude
52.8756° which is 37.1244° from the geometric pole. The reciprocal
harmonic of this position (371244) is equal to 2693645. The
interpolated standard gravity acceleration at this latitude is
The grid time factor I discovered has stood up to scrutiny over the
years and is based on 27 periods for one revolution of the earth.
Normally we use 24
periods of one hour each. The 27 periods, I call 27 grid hours. A
grid hour is slightly shorter than a normal hour, and is divided
into sixty grid minutes, each of which is equal to sixty grid
Therefore for one revolution of the earth we have a standard time of
86,400 seconds as against a grid time of 97,200 grid seconds. The
ratio is 8:9.
So: 32.194417 x 6000 x 8 = 28.24071667
If this acceleration factor is multiplied by 6 then:
28.24071667 x 6 = 169.4443
1694443 harmonic = (C +√(1/C))
Where C = 143000 minutes of arc
So harmonically, gravity acceleration is equal to:
(C +√(1/C) )/6 At the centre of a light field, forming spherical
As my own research has shown me that physical reality is manifested
by the harmonic nature of light, it appears logical that a vehicle
constructed to the principles of harmonics will be required to set
up the space-time fields necessary. If this is so, then the first
criterion will be that the vehicle must resonate in perfect harmony
with the complete table of elements in our physical universe. If it
does not, then it would be more than probable that any element or
particle of matter not in harmonic resonance within the vehicle
structure, or payload, would be left behind when the space-time
field was activated. The results would be embarrassing, to say the
It would be impractical to construct a vehicle made from an alloy of
the whole range of 144 elements in the theoretical atomic table.
Apart from this, such an alloy is no doubt a physical impossibility.
The clue which suggests a method of overcoming this problem is the
way matter is built up in octaves of wave-forms. If an octave of
elements could be combined, which would set up a resonating field
tuned to all the elements in the table, and the unified fields of
space then, maybe, we would have a method of crashing the time
I put forward the following proposal for consideration. If an octave
of elements is the answer let us make a selection from the
theoretical table of elements of 144. If we divide 144 by 8 we get
divisions of 18 units, therefore we will select each of the elements
we require, 18 units part, as follows:
Atomic number 18: argon
number 36: krypton
Atomic number 54: xenon
Atomic number 72: hafnium
Atomic number 90: thorium
Atomic number 108: X
Atomic number 126: Y
Atomic number 144: Z
Total number 648
It can be seen that the total harmonic value of the atomic numbers
of the combined elements is 648. The square root of this number is
25.45584412, the harmonic of which is found in the polar sections of
the world grid. Three new elements just recently discovered have
atomic numbers of 116,124 and 126. Do the scientists know something,
and are they now looking for numbers 108 and 144.
The circumference remains a constant harmonic of 107766085 giving an
electron spacing harmonic of 1347076. By doubling this harmonic to
allow for the matter and anti-matter cycle we have a value of 2694
which closely complies with unified field equation (3) 2693645. A
full computer program should make these values match exactly.
Harmonic values based on the Hydrogen Atom.
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