Archive for the ‘Geometry’ Category

The Earth Pulse Hydrogen Resonator

January 22, 2013

The Kings Chamber Cavity Resonator

     Now that I have worked out the size of the Kings Chamber in Quantum units, let us see if we can explore the implications of its functions as well, this was one of the most rewarding puzzles I had to solve of recent times. This would become more helpful as I could now scale it to something a lot smaller and useful for experimentation. I have also completed the Quantum Coffer as part of this process, armed with an understanding of quantum arithmetical methods I now could apply my work to just about any Ancient monument that was built to those exacting requirements, this information will surely help give some clarity to date these constructions so we can finally put an end to the time wasting debates that have been festering for the last 200 years.

     It occurred to me a few years ago that the Ancient monuments that are of the most interest were those built pre 3000 BC(my reckoning), as the dating of most monuments are not of that early era, something is distinctly wrong is the way Academia view and date the time-lines of civilizations, each new discovery pushes the dates back further than they would like to admit. To attribute many ancient buildings to a later era distorts the history in a way that denies the true origins of cultural fashions and technological beginnings. As we know writing and mathematics were fully developed at the beginning of the accepted historical time line , not at the end, the Greeks learned from the Ancient Egyptians and the Romans learned from the Greeks, this is also true in India where the Vedic texts have a fully developed society , science, art at the oldest time period. The Aztec’s only rehabilitated the more ancient buildings and a culture they discovered. This brings me back to the Great Pyramid and its function, I can only make assumptions based on facts and some evidence that the Great Pyramid was some sort of machine that was designed by a people that were well versed in structural engineering that surpasses the best efforts of today. The Khemitians as I like to call them , had profound understanding of Astronomy, Geometry and Chemistry, these are evident in the materials, methods and designs of what they have left us, this is a profound and obvious fact that no real researcher can deny.

I would like to forward an idea what the possible usage was for at least part of the mechanism of the Great Pyramid, mainly the Kings Chamber acting as a Cavity Resonator . As I was working with the measurements of the Ante-chamber, I could see that the design vaguely resembled an adjustable resonant cavity mechanism. It seemed there has been a lot of conjecture about what was the original function and design layout of the Ante-chamber, the common view was a sealing mechanism of granite portcullis blocks that were strung up with ropes and made to move up and down locking the treasures of the Kings Chamber from greedy grave robbers. This idea seemed plausible if the Kings chamber really had a King with his treasures to hide, sadly there is no proof that it was ever intended for a dead Pharaoh, a simple fact that no hieroglyphs have been found in the great pyramid can attest to its lack of funerary ritual hieroglyphics that dominate the walls of real graves of the well to do Egyptians and Pharaohs. The scribbles that have been found in the sections above the Kings chamber that were attributed to the builders were the result of a rogue Archaeologists idea of getting some credentials and notification, in reality the markings were of nonsense and of the wrong period.

Christopher Dunn describes a possible Hydrogen power-plant that might be the mechanism of the Pyramid, this interested me a great deal, it started to dawn on me that this is a real possibility. The few clues I found was the sooty deposits in the air shaft in the Kings chamber and the green Dolerite ball that was found by Petrie, the unusual cavity in the South air shaft, and the 4 grooves at the end of the Ante Chamber. The early accounts reveal a few more clues, early accounts attest to finding a 6x4ft slab in the antechamber, now gone, also the results that somebody had blasted their way into the kings chamber passageway, gouging a section from the top part, suggesting this small passageway was tightly closed.

Most researchers attribute the grooves in the wall of the rear of the Ante-chamber to rope clearances or such, where I think it would be ideal to create some sort of piezo vibrator or tuned half pipes to transfer a 7.84 hz tone to the inlet of the Kings Chamber, the inlet for the hydrogen gas would also have been part of the pipe mechanism as well. The Grand gallery could have been a gas fractionator unit that was tuned both acoustically and electrically polarised allowing oxygen to stay in the lower portion while hydrogen could rise into the ante chamber and on through to the Kings chamber via 4 pipes and/or resonators. The action could even have water present allowing water to become part of some sluicing gas production process.

All this is just conjecture at present, the Kings Chamber has 2 shafts, one of those has a unusual cavity that looks like some sort of ball valve system, possibly to allow the valve to close or open when pressure was correct and the other shaft is connected to the outside , possibly connected to another mechanism at the outer exit. The only way for us to discover the purpose is to a build scale model of it and test the many conjectures.

     I have drawn a overhead scaled version with the sonic inlet being the column of gas that  is in the passageway between the Ante-chamber and the Kings Chamber . This is a typical Helmholtz Resonator design, nothing mysterious here, just well engineered for low frequency resonance. The approximate frequency response for Air was a low 2hz, this at first seemed remarkable as a lot of conjecture has been out there in the public for at least 50 years that it resonated at much higher frequencies. If you treat the chamber as a microwave resonator you will have frequencies of about 1.76Mhz, this is a suitable band for communications, but not remarkable in nature.

The most surprising result of looking at the resonant values for the Ante-chamber was a close match of 47Hz, ever though I did not have all the exact measurements for the missing parts. I made an approximate of what has been conjectured by many other researchers, the result was amazing to say the least. I will be working of the Grand Gallery and the Queens chamber as next set of parameters to see if they reveal any evidence of a mufti-chamber pyramidic gasifier that breaks-down water into useful gas energy products such as Hydrogen and Oxygen.

Regards Arto

***Update 22nd October 2016 – I have replaced the drawing, the Helmholtz resonator frequency equation had a typographical error. (bracket was in the wrong place), regards Arto.

The Hidden Code of Bruce Cathie

January 14, 2013

The Hidden Code of Bruce Cathie

Again I am presenting material of importance from my book, one that cannot wait to be presented only revealed. When I first read Bruce Cathies books in the 1980’s Harmonic 33, Harmonic 695 and later The Bridge to Infinity and The Harmonic Conquest of Space,  I was amazed and fascinated by Bruces simple facility in bringing all his explorations into the 144 light velocity and all the harmonic frame work as well.  I loved reading his material and all his exploits.

I could not at first see why he chose 144 as the numbers as the velocity, Bruce had made some assertions about the ancient metric and a lot of biblical and Geomatra references, this made me question the historical reasoning, only later did I find the real reason.  You see this was not a common number when measuring anything linear only area, cubits were the rule in the period Bruce points out, besides the Ancients had no need of a decimal version of PHI and its endless decimal fractions or 143.889,  6.9444 decimals fractions either, they are only used in his methods to justify the use of 144 as light speed, the Ancients built and located to natural prime and whole numbers, this is was gives you the PHI ratio. Who had use of a calculator in 3000BC and surely nature never uses parts of anything only whole quantum units for any process. It seems there is something not quite clear in his explanations and has a possible bogus written on this scheme, let us look at some of those that contain vagueness.

Look at the tables and you will see that Standard Cubits and Fingers become rounded off to whole numbers and surely would become more useful that Bruce Cathie’s numeric web of harmonic decimal fraction values, why create new measures when the Ancient measure of cubits had so much to offer. The use of a light velocity in ancient times did make for great reading, only its use would have been for astronomy and some form of technology, I could see many ancient places that could have used laser cutting such as Sakkara, Machu Pichu and Puma Punka. Why would the ancients complicate the natural whole number science with complex algorithms with multiple decimal places and complex formulas just to put a monument, where a simple whole number solution would explain more and reveal complex ratios that come from its prime quantum nature.

Only by studying the mathematical and geometric works of Euclid, Archimedes and Pythagoras can you see the numeric tricks that Bruce has employed to result in what may seem like almost magical answers. This sort of manipulation has truly some amazing reverse engineering to give you the results you seek.

The methods are not hard or magical, the term used is the intervals of the harmonic discipline, these are named as Sesquitertian ratios, Sesquiquialter comparisons, Multiple Superparticulars and its attendants. Without writing a formal doctorate on the subject, I will just show you the numbers and how they function. You will recognize an abundance of Geomatra numbers and harmonics that a lot of people write about.


As you can see the top row of the Duple table it is pure doubling, nothing very complex, this is how octave work in music, light, radio etc To get the start in next number row you add the first two numbers then place the result in the column under the second number. The process continues for every number pair on the top row, this will now give you the second row, now do the same procedure with this row and this will give the next row, continue with the same process and you will have a table like the one I have made.

As you can see the second table(Triplet) the numbers are tripled, the same process of addition and carry to the next row the sum is the same as the first table, will give you the table the same as I have made.

A careful study of the first and second table will reveal the tripling is also occurring in the first table, only as the diagonal values. This same view has the diagonals of the triple table now creates quadrature. Many more numeric harmonies are present in these tables. An example of this can be shown, if 256 = C1 in music the its octave is 512 = C2, the next octave in now 1024 = C3, this seems logical and simple, now the 5th of diatonic harmony in music is the most concordant next to the tonic, if the tonic 256= C2 then the fifth is 384 = G2, the 2nd is 288, the ratios are 256 x 3/2 for the fifth = 384, 256 x 9/8 for the second = 288. This is how harmonies function numerically, no mystery here, this information dates back at least 5000 years.

The sextuplet table I am including shows you another Geomatra group that are written about, including the Nineveh Constant. This set is in  multiples of 6 , the second row, 7nth element is 1959552.


As you can see these are very simple arithmetic calculations, not requiring PI, PHI or Log, this is how nature creates harmonies and  natural intervals that exist everywhere not just on your piano. If you require more knowledge to pursue, you must create complete harmonic tables  and you must also be willing to understand and make frequency charts covering many octaves.

In the first table and the following table I have created the precise light velocities in:

Meters per second
Miles per second
Feet per second
Nautical Miles per second, Cathie Arc Minutes
Royal Cubits per second
Standard Cubits per second
Fingers per second
Cathie Grid miles per second, Adjusted for maximum
Cathie Grid feet per second, Adjusted for maximum
Art miles per second ( an addition to show how it can be done )
Art feet per second

The Royal Cubit = 525.1816774904 mm
The Standard Cubit = 450.1557235632 mm
The Finger = 18.7564884818 mm

These sizes where chosen as the least rounding error.

I have also created a set of new time scales in seconds, N28, N30 and N34 as N36 is the standard second and N32 is Bruce Cathies Grid second. I could extend this time scales in both directions as required. The Grid , and Art lengths are listed here;

Grid inch = 1.011904379 standard British inch
Grid mile = Grid Inch x 12 x 6000 = 72000 Grid Inches = 72857.1152911442 British Inches


The only problem that Bruce had with these tables is lack of justification on the velocity in a different medium, as he shows that maximum is 144000 minutes of arc per grid second, now for this to be correct he must have either the length of the arc grid mile to be different or the grid second to be slightly different. If he uses the grid second as 8/9 of the normal second as he proposes in all his writing then you will get 143888.868730502 minutes of arc per grid second, to correct this he must change the ratio of the grid second to equal 1.124131787 not the theoretical 1.125 as he suggests. Not to labor the issue we will accept a slight variation that allows the value 144000 to be the speed of lights maximum, this will be the adjustment to the grid mile of 1.1498913398, with the Nautical miles as 1.150779448, on the normal minute arc scale, I will include the maximum values in my tables, to be accurate they should be all equivalent. We know the velocity of light changes with the medium and this is where he can create a variety of values that nobody can question. The absurd idea that PHI reduction is evident is a slight of hand as you can see that 161874.977321814 Nautical miles per sec is very close to PHI (161803.4), this can be used to make fractional values based on this and rounding errors. The values of PHI from the minutes of arc is a result of ratios that are evident in the size of the earth and the number of degrees in s circle, such as;

In these simple equations you can see some of those harmonic numbers and PHI factors appearing at rounding and simplifying.

360 x 27 = 9720
9720 / 6 = 1620

velocity miles per second x multiple ft per mile / length of N mile in ft = Phi

Here is the equations, the way you can fudge these to fit:

186282.397051221 x 5280 / 6076.1154855643 =  161874.977321814
18.63 x 5.28 / 6.08 = 16.18  Simplify
37.26 x 2.64 / 6.08 = 16.18  Halving
36      x 2.7   / 6      = 16.2    Simplify, Halving and Rounding

Just to note 2.64 is the harmonic that Bruce says is inbuilt into the polar grid structure, which is really another factor of 5280/2 ft in a mile. The other harmonics he mentions are 2545.56, which again is 25.4 ratio mm to inches hiding as this value. Two other numbers Bruce quotes regularly are the magnetic field lines crossing in 1257 and 1850 spacing, firstly 12.57 is a half an inch and 1850(6069.5538 ft) is close to meters in a nautical mile(1852 exact), not a coincidence but as designed so he can correlate his data to fit any situation. As Bruce mentions the double cycle of the universe is 360 x 2 = 720 = 1440/2 as you can see he is eluding to the 144 value again. His use of the pentagon and golden triangle geometries  are also used to make it appear to be more of the same harmonics of light  generated from these shapes when he maps his grid points to fit the angles of 36, 72, 144 degrees.

One of the main points on Bruce’s grid map was his Eltanin Aerial , which was a bogus interpretation as this has been confirmed as a sea sponge(Cladorhiza) that has multiple arms and club like ends , this was revealed by Larry Hatch back in 2006. This and many of Mr Cathie’s findings have been exposed by Peter Brookesmith in an article “The Eltanin Enigma”. I will not elaborate here so please check his site here

If the link is broken, there is a you-tube video here:

The Art miles and Art feet are also in whole number harmonic structures, very easy to use as these numbers are called perfect,deficient, super-perfect and superabundant numbers, most common in harmonic sequences.

Art ft   =  1.1383924264 British Ft
Art Mile = 1.2936277573 British Mile = 7761.7665438009 B ft

So the Grid foot also comprises of 12 grid inches, so instead of using B/ft and B/inch you create a new unit that divides exactly 6000 times 12 = 72000 grid inches, this simplifies your figures and also creates a base 2,3,4,6,12 etc for harmonics as you can see from the tables 972, 144, 6 are all part of the harmonic structures.

One of the alarm bells that I heard when first viewing his work was his acceptance of Einsteins work as valid science, as we all should know his equations were the borrowings of others mainly Ruđer Josip Bošković and the hard work of his first wife and the blatant  plagiarism of the work of David Hilbert, perhaps the most brilliant mathematician of the 20th century, and Felix Klein . Albert was a figure head put their by the power hungry establishment to teach us how to believe a metaphysical universe created from a false set of rules and hide the true knowledge and to accept this false dogma for fear of ridicule and banishment so we can serve the elite. He possess no genius that I can find in any of his writing, because it was not his writing that I was reading it was a patchwork of plagiarism from many sources, great men have a core of clear communication that goes beyond stereotypes and speaks to all men, many of the quotes of Einstein were lifted from other people, original thinking was not the premise of this fascist.

We should also be aware of Max Plank as he had reversed engineered his constant so it would fit with the velocity of light, as noted he was quite disturbed by force fitting this by using Boltzmann work and tried to ignore the implications of his earlier work please refer to the work of Charles William Johnson. Together with Einstein they accomplished an early burial to the science of Walter Russell, Nicola Tesla, Victor Schauberger and others like minded Artists, Scientists and Engineers. It seems Bruce was either ignorant of this side show of the establishment or he was just another unwitting puppet that had been used so his work would give credence to the puppet masters agenda, this way the independent researchers started looking in the wrong direction.

Remember it was not Einstein who created the atomic bomb, it was the Engineers who were disciples of Teslas work that made it work, theory had very little to do with its creation only practical men can build such devices. The Tesla rotating brush was the first step, the disintegration of matter by implosion of spherical reflected force was Tesla’s second step, it was this that led men to the atomic era. There are no mysteries on how to create and explode an atomic bomb, only misinformation. The work of Einstein will be long forgotten and relegated to the dust piles of history when the work of Tesla will light the hallways of knowledge for aeons.

As Nikola Tesla quoted in the New York Times (11 July 1935)
“Einstein’s relativity work is a magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king, its exponents are brilliant men but they are meta-physicists rather than scientists. “

Einstein’s formula
Energy = Mass x Velocity of light squared

This simple relationship was obviously borrowed from Newton’s well known equation;
Kinetic Energy = Mass x Velocity squared

The Bruce Cathie Equation is a unique combination trying to include a version of the Fitzgerald contraction,  this being the 1/sqrt(C), this would not help those who are in favor of an Etheric understanding of the Universe. The purpose of the Lorentz-Fitzgerald formula was designed to invalidate Michelson- Morley experiment.

Lorentz Factor = 1 / sqrt(1 – v^2/C^2)

Cathie Equation

E = ( C + 1/sqrt(C)) x C^2

This would validate any slight variations due to variable factors, each variable would be unique to the subject he was describing similar to Carl Munck’s manipulations. I suspect the reason the authorities were interested in Bruce’s work is he was using the powers of the velocity of light in his work, which is what they presented in the scientific community as fundamental constants. They did not want the public to know the level of deception the scientific hierarchy had perpetrated on world regarding the nuclear  situation along with the complicity of the military industrial complex and the theoreticians to hide the real truth.

I hope this small snippet can elucidate the unwitting attempts by Mr Cathie over the decades in trying to steer you in unwillingly to a cult-e-sac of misinformation, not much different than the establishment has done for the last 100 years. I am an advocate for what Bruce has tried to do, but his efforts have not been realized by many researchers, scientists or engineers and have not resulted in usage that produces any advantages in designs or concepts. Not to deride his work as I have built many Tesla coils using Bruce’s numeric guidance and the results are no different than using, millimeters or inches, as to the advantage I have gained from his work it is primarily by using frequency tables that are clearly of harmonic content. What you gain from Mr Cathie’s work is the truly amazing value in understanding harmonic concepts and musical ratios that the Universe is built from Regards Arto

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Decoding Carl Munck

January 3, 2013

Decoding Carl Munck

by Arto Heino (c) 1994-2013

      When I first viewed the work and videos of Mr Munck back in to early 1990’s, I thought wow this guy has stumbled on to something, I better check it out. After my initial studies I was not convinced at his methods, so I persevered and allowed time to adjust to his methods so I could begin to find the code just as he had.

      At first I was excited and found a few interesting sites I could apply this work on, that is when I decided to write a spread sheet so I could verify the Latitude , Longitude and Geomatra number with accuracy, just as Carl had done. Hidden in his mathematical multipliers was his secret to making you see what he wanted you to see, the numeric decimals he attached and multiplied was nothing but a tricky way to make it look as if harmonics and numeric codes were present, by reverse coding. Here is his method exposed and laid bare for all to see. I hope you can appreciate and understand that nobody in the last 20 years has questioned his means and methods, the main reason I would say is he did a fine job of cryptography, the other reason would be that he filled a wishful thought about the abilities of ancient man, that of his greater knowledge, something which I am still in concordance with, except this knowledge is not based on anything hidden and coded, only on deeper perceptions on what is already given and in front of us.

I will first find a location that has some ancient importance as Carl Munck had decoded and a version that is the exact position, also my back yard as a major grid point on the Earth just to show this fallacy. Each I will give special properties just as Carl did.

Panther Mound

The Panther Mound is in the Everglades of Florida, and by Carl it has a close relationship to The Great Sphinx. The Panther Mound can only be recognised from the air.

Geocode for Panther Mound: Latitude: 25.573164 – Longitude: -80.7589528

Here are Carl P. Muncks latitude/longitude coordinates for the Panther Mound:

80 deg 45 min 46.886 sec W.Greenwich, Longitude ,

this is a close match to the real location

80 deg 45 min 32.23008 sec W.Greenwich, Longitude,

this is the current real location

The difference of 14.65592 Seconds, this equates to 452.668607488 meters(at equator)

25 deg 34 min 3.5 sec North, Latitude,

this is also a close match

25 deg 34 min 23.3904 sec North, Latitude,

this is the current real location

The difference of 19.8904 seconds, this equates to 614.34285056 meters(at equator). This is at least 1/2 of a kilometer from Carl Munck;s calculated position. So something must be wrong with his numbers, his data, his calculations or all of the above.

Now this part is to makes it look like a genuine discovery, but this subject has been talked about and debated for more than a century, ever since they first were deciding where to put the current meridian, the current prime meridian at based at the Royal Observatory, Greenwich which was established by Sir George Airy in 1851, then again in1884 in the conference of the Meridian in Washington , one of the proposals was the Pyramid of Giza. The need was originally for navigation in the open seas. The ancient Earth prime meridian (as said by Munck) passes through the center of The Great Pyramid, we add 31 deg 08 min 0.8 sec onto the W.Greenwich longitude, to adjust to the ancient longitude, personally I find this a great location for a meridian, as its location and culture has endured thousands of years, Greenwich will be just a forgotten memory when the pyramids will still be standing, reminding us of their builders.

80 deg 45 min 46.886 sec W.Greenwich

+ 31 deg 08 min 0.8 sec Variance in prime meridians

= 111 deg 53 min 47.686 sec W.Giza

80 deg 45 min 32.23008 sec W.Greenwich, Longitude, (real)

+ 31 deg 08 min 0.8 sec Variance in prime meridians

= 111 deg 53 min 33.03008 sec W. Giza (real)

Now to figure out the Grid Longitude and the Grid Latitude of the Panther Mound. Muncks general rule is to multiply the site’s centered (for both longitude and latitude) number of degrees X number of minutes X number of seconds.

Grid Longitude

Grid Longitude 111 deg x 53 min x 47.686 sec = 280536.738

Grid Longitude 111 deg x 53 min x 33.03008 sec = 194315.96064 ( Real)

Muncks reverse PI tables told him that this adjusted number was VERY close to the multiplied product of a Gematrian number ‘times’ (PI to the 4th power).

The Gematrian number = 2880

The derived number = 2805.36738

The Actual value = 1943.1596064

An Invented Geomatra Number = 6267

So he used the derived number as a base with the PI table, this is the part that makes it look like a discovery.

2880 x (PI 4th power) = 280538.1822 W.Giza

= 111 deg x 53 min x 47.68624548 sec W.Giza

So we will create our own Geomatra number that makes it look real

6267 x (PI 3rd Power) = 194316.335955438973

= 111 deg x 53 min x33.0301437966 sec W.Giza (created)

Grid Latitude

Grid Latitude 25 deg x 34 min x 3.5 sec = 2975

Grid Latitude 25 deg x 34 min x 23.3904 sec = 19881.84 (real)

Muncks PI table showed this number as being close to the multiplied product of another Gematrian number ‘times’ the Cube of Pi.

96 x (PI 3rd power) = 2976.602561 North

= 25 deg x 34 min x 3.501885366 sec North

So we will create our own Geomatra number that makes it look real

65 x ( PI 5th power) = 19891.2795110432944620

= 25 deg x 34 min x 23.4015053071 sec North (created)

Grid Point Value

To figure his Grid Point Value, take the ratio of Grid Longitude to Grid Latitude , always greater-than-one .

280538.1822 / 2976.602561 = 94.24777961

= 30 x Pi

This result suddenly made many become followers and converted the undecided into the horde of lemmings that become indoctrinated to the numeric religion of the romantic notions of Geomatra. Here is now the door opener for those brave enough to face this truth.

194316.335955438973 / 19891.2795110432944620 = 9.7689208906 (created)

this value approximates 3 x pi = 9.4247779608 or I could choose Pi squared = 9.8696044011

either one of these values are close enough, now let us work in reverse, I will do both just to prove his method:

187470.89274718436522 / 19891.2795110432944620 = 9.4247779608 ( 3 x Pi)

195 x ( PI sixth power) = 187470.89274718436522

= 111 deg x 53 min x 31.8665464469 sec W.Giza (created)

This will give the result that makes it look brilliant and something unique, also it was not far off from the last value.

Here is the version with Pi squared

196319.0598054914843884/ 19891.2795110432944620 = 9.8696044011 ( Pi squared)

65 x ( PI seventh power) = 196319.0598054914843884

= 111 deg x 53 min x 33.3705694043 sec W.Giza (created) (very close to exact)

65 is the line number value for the magic square of 5, which they call the square of Mars.

This result will make the crowd dance in the isles, also it was not far off from the last value, this is what makes is look plausible. The Grid Point Value of any site like the Panther Mound that have values PI adjusted in the seconds decimals will always be some multiple of PI, easily designed to match Giza.

Here are two locations on the earth, one is arbitrary the other is my back yard next to my shed. I have interesting structure I built for my external Tesla coil, a ground system, it has a precise and real location:

Back Yard

Latitude 33.9027206155 South

Longitude 150.8998518137 East

Arbitrary Location (opposite side of globe)

Latitude 33.9033671156005 North

Longitude 150.899849953205 West

Using Munck reverse coding and numeric tricks, and not even using a PI table as Munck would have I have found this to be one of the most important grid points on Earth next to the Great Pyramid.

150 deg 54 min 18.447905898 sec Longitude West

+ 31 deg 08 min 0.8 sec Variance in prime meridians

=181 deg 62 min 19.247905898 sec Longitude West Giza

Grid Longitude = 181 x 62 x 19.247905898 = 216000 = 60 x 60 x 60

33 deg 54 min 12.1212121212 sec Latitude North

Grid Latitude = 33 x 54 x 12.1212121212 = 21600 = 60 x 60 x 6

Grid Point Value = 216000/21600 = 10 =decahedron is a polyhedron having 10 faces.

My Back Yard

150 deg 53 min 59.46652948sec Longitude East

– 31 deg 08 min 0.8 sec Variance in prime meridians

=119 deg 45 min 58.66652948 sec Longitude East Giza

Grid Longitude = 119 x 45 x 58.66652948 = 314159.2653654 = Pi x 100000

33 deg 54 min 9.7942157802 sec Latitude South

Grid Latitude = 33 x 54 x 9.7942157802 = 17453.2925203 =  Pi x 5555.5555

Grid Point Value = 314159.2653654 /17453.2925203 = 18 = 6+6+6

My Tesla coil has wire wound in a coil of 2160 turns(18 x 120) and resonates at 216000hz(18×12000), the Earth system I made has 8 radial arms 1 vertical down and a vertical up for the coil which makes 10, it also has 10 turns for the primary coil tapped at 6, the top load could be shaped as a decahedron (which has a icosahedral symmetry of order 120). As you can see I can make fanciful additions, even though all the numbers are correct and accurate, my Tesla coil is also real and its numbers are provable. The only difference is that if I moved it 50 mm in any direction the whole number stack falls apart.

These are based on mathematical tricks that any body with a calculator can create, the problem is the amount of people that have been seduced by the fantasy that there is a hidden code that we must decipher in these ancient sites. The real code is not hidden at all but in plane sight, and you cannot call it a code as much as Carl would like you to believe. The reasoning is a clear headed understanding of the workings of the Universe based on pure natural prime geometry and natures proportions and not religious, ceremonial or Geomatra numbers as most try to make you believe. The very nature of Geomatra numbers act as lures to those who are seeking symbolic meaning and purpose to them. Attaching the velocity of light to 144 is a simple example of this, as this is one of those special numbers that are coded into our history. That does not mean that these numbers do not have some significance to our past, they do, it is just they should not be muddied by superstitious beliefs and foolish notions. Number Theory, Atomic physics, Crystallography and our understanding of electrical phenomena are true pointers for the use of these numbers.

      The decimals placed after the whole number seconds are where he hides the PI and Geomatra numbers, when shown on a map this equates to distances under 1 meter,this allows you a great variation of choices to match the particular monument. A good example of this method is to show how numbers actually can do this. I am not a cryptographer as Carl is, but my methods unveiled his number game almost 10 years ago, a similar trick was used by Bruce Cathie, I have sat on this just hoping these guys would fess up and tell the world about their number game. This is when I realized, the purpose behind the deception, they believe their methods would guide any researcher to non-answers and permeate the underground researchers with false leads, 99 percent of the discoveries and conclusions they these types of writers have on the work of people like Schwaller de Lubicz and the engineer Nicola Tesla and his unfinished work have been a total fallacy. Only real Tesla engineers like Eric Dollard have pointed us in the right direction and the work of Christopher Dunn on clues left by ancient engineers proving Schwaller’s notions of an enlighten ancient past.

More Tricks

If the number you want in the final answer is 144 then you find what constitutes the parts that can multiply into this number, look at the huge pallet of numeric interplay that can be found in a simple number.

12 x 12

2 x 6 x 2 x 6

2 x 3 x 2 x 2 x 3 x 2

10 x 14.4

2 x 5 x 14.4

8 x 18

2 x 2 x 2 x 6 x 3

6 x 24

5 x 28.8

4 x 36

3 x 48

20 x 7.2

2 x 10 x 7.2

2 x 2 x 5 x 7.2

3 x 4 x 5 x 2.4

(1 x 2 x 3 x 4 x 5 x 6)/5

(1 x 2 x 3 x 4 x 5 x 6 x 7)/ 35

19 x 3 x 2.5263157894736842105263157894737

This last addition lets you see how to hide the intent in the numbers after the decimal point.

19 x 3 x 2 = 114 differential = 144 – 114 = 30

19 x 3 x 2.5 = 142.5 = 144 – 142.5 = 1.5

19 x 3 x 2.52 = 143.64 = 144 – 143.64 = 0.36

19 x 3 x 2.526 = 143.982 = 144 – 143.982 = 0.018

19 x 3 x 2.5263 = 143.991 = 144 – 143.991 = 0.009

Here is the same number with a hidden PI

2 x 22.918311805232928350719261925642 = 45.836623610465856701438523851284

PI x 45.836623610465856701438523851284 = 144

Now I will hide PI and reveal PHI(1.618034) in the same number

4.8 /PI = 1.5278874536821952233812841283761

( 15 x 4.8 x 1.5278874536821952233812841283761 )x PHI x PHI / 2 = 144

144 / ( 15 x 4.8 x 1.5278874536821952233812841283761 ) = PHI x PHI / 2

If Carl Munck could show how the ancients manipulated his values without a calculator I would probability would have been more convinced of his Code and not question his methods. The fact is clear his methods must be manipulated in inches and many decimal places at the seconds and PI and PHI are always involved, tweaking the bits so it fits in to his code. These two simple facts alone should make you question his results.

I propose the ancients didn’t use or need any values after the decimal point, they had no need for the AVERAGE value of PI or PHI, because they used prime numbers as a base property of all of their work, a slow dawning of understanding that only now we are beginning to appreciate. One main clue is the earthquake proof walls that exist in every ancient site on Earth, these were designed using prime number law not by some PI/PHI fudge factor. PI and PHI come out of using whole number values that are manipulated through simple arithmetic, and the use of normal and didactic fractions is paramount to this understanding.

The clear knowledge of Quantum Arithmetic and its true roots in Ancient Egypt, Sumer, Gobekli, Angkor, Mayan and other ancient civilizations are what we should be looking at, not some tricks of code that have no meaning except to promote disinformation and enrich the promoters.

One of the Carl’s codes secret is not to use whole prime numbers as they cannot be derived from other numbers, he always uses perfect,deficient, super-perfect and superabundant numbers along side decimal fractions. This keeps the Geomatra numbers easy to transform, hiding PI and PHI in the decimals. This is again will show either the ancients didn’t understand prime numbers or Mr Munck avoided using only whole numbers and prime numbers in his code, the later seems to be the case.

This is only a part transcript, in the full version I breakdown many Ancient monument and show you all the tables and spread sheets used, if you want to read more please buy my up coming book “Talking to the Birds”, Regards Arto.

The Great Pyramid – A Quantum Solution

December 21, 2012

Quantum Numbers for the Pyramid of Alnitak

by Arto Juhani Heino (c) 2012

 I am One that transforms into Two

I am Two that transforms into Four

I am Four that transforms into Eight

After this I am One

(Coffin of Petamon, Cairo Museum no: 1160)

 Finally I have unearthed the Quantum Arithmetic set of numbers for the Great Pyramid. I have been working on this for a number of years(1988), only now have I discovered some of the methods of the underlying geometry to build such a complex structure from only two numbers. The deep understanding of geometry by the Ancient Khemitians(Egyptians) should make our current system of calculus of approximates seem poorly suited for simplification and shorthand. All the pyramids can be constructed from this understanding, and if these insights become common knowledge then we have entered a new paradigm of Art, Architecture and Science.


The first two numbers and a ratio translation number are all the information required to reconstruct the Great Pyramid’s elusive design. There has been many theories about what constituted the design and the actual numbers used to build the structure, each one has failed to show the true beginning of the numeric journey. I found many ideas quite amazing and interesting how they weave their numeric code into the design.

There are many amazing and promising designs I have encountered, great work using pure geometry to crunch those angles and make it fit, sadly there are many devices used that are artificial and eludes to squaring of the circle, a pursuit rooted in the misunderstanding between a curved line and a straight line, two different forms of measure. The constructs used are the same devices used by generations of geometers who construct perimeters of different types, rooted in Phi and Pi. Just remember PI and Phi are not quantum units they cannot be used without resorting to approximations, you cannot build wholeness from endless fractional decimals, this is a modern illusion. I have included the Phi relations in Diagram 1 so you can crunch your own numbers and design a Golden Pyramid, based of PHI. The short list is a PI Pyramid, a PHI Pyramid and the Quantum Pyramid, all three are valid and related to each other, only the Quantum Pyramid is exact solution the other two are approximations.

Here Listed here are some of the Pyramids investigators and a brief of their work.

Leon Cooper -The Architects Plan

Ole Jergen Bryn Apex – Retracing the Egyptian Pyramids

John Cadman- Engineering Science and the Great Pyramid

David Furlong-The Key to the Temple

Samuel Laboy -The Perfect Symbol

Tim G. Hunkler- Symbolism and Coincidences of the Great Pyramid

Christopher Dunn -Giza Power Plant

Graham Hancock-The Orion Mystery

Mark Lehner- The Complete Pyramids

I.E.S. Edwards -The Pyramids of Egypt

Now that you can see some of the Writers, Archaeologists, Engineers and Investigators that have have walked this well worn ground and have not found the first principals, the reasons of structural placement and the functional meaning matching the form. They are all right in their conclusions , as this Pyramid includes ALL of these views and ideas, only their conclusions are but a different view point on the same thing. The main problem is the teaching of maths and geometry in schools, treated like a adjunct to abstract notions in finance and computer modelling. Only very few investigators in pure mathematics bothers to find out why numbers works in nature this way and why some solutions have multiple equations and some need calculus to try and figure it all out.

The only problem with invented mathematics are the results are not an arrow to the question what the Pyramid originally imposed upon mankind, only some numeric abstraction that has no basis in the natural world or order of the universe. Empirical results cannot give mankind much headway in answering our future dilemma. only the enlightened human being who understands the inner needs on the living system can know the path we must make to change our current perceptions on the nature of our reality and survival.

One question is why does the circle have only one center and the triangle have more than 6000 and the list grows. These things seem trivial, remember it is not the answer that matters but the question that is important. from questions arise the underlying principles that makes these geometric constructs work.

Here Listed is the basic Quantum Arithmetic equations that you need to design the correct pyramid. I recommend all researches to use these numbers to correct their models, as this is the pure whole number set that you cannot fudge to fit, they are absolute and cannot be corrected by any small decimals using Phi, Pi or Log. They are a constant and the roots to these the higher dimensions can be translated to any unit of measure by using a conversion ratio. We are dealing with whole number solutions and the ratio Phi is only a derived number, in the natural system you can refer this to the root numbers in Fibonacci series, where the oscillation about the Phi point generate amazing geometry. Pi is also a ratio and cannot have an exact solution so we will not use it as the value 3.1415727…..but as a series of ratios like the Phi point. Here is a list between 1.25 and 1.75 that you should recognise as common usage by Engineers, Geometers and Mathematicians.

5/4 = 1.25000000000000000

9/7 = 1.28571428571428571

4/3 = 1.33333333333333333

3*HDp/WDp = 1.350272105524200

e/2 = 1.35914091422952261 = Natural logarithm/2

7/5 = 1.40000000000000000

SQR(2) = 1.41421356237309504

10/7 = 1.42857142857142857

3/2 = 1.50000000000000000

163/107 = 1.52336448598130841 = Alintak fraction 56+107 = 163

Fg/3 = 1.55640053636766355 = Feigenbaum constant /3

168/107 = 1.57009345794392523

PI/2 = 1.57079632679486619 = PI/2

Wp/Hp = 1.571031746031750 = Pyramid Width/Height

11/7 = 1.57142857142857142 = Refer Plato also 11! / 7! ^2

8/5 = 1.60000000000000000

PHI = 1.61803398874989484 = PHI

2*HFp/WFp = 1.6188431422076200 = Quantum Pyramid Face Height/Width

5/3 = 1.66666666666666666

12/7 = 1.71428571428571428

265/153 = 1.73202614379084967

SQR(3) = 1.73205080756887729

1/V = 1.73245471460063347=  1/ Euler-Mascheroni constant

100/Rad = 1.74532925199432957 = Radian

3/4 = 1.75000000000000000

Fg = 4.6692016091029906718532038204662 = Feigenbaum constant

e =2.7182818284590452353602874713526 = Natural logarithm

V =0.5772156649015328606065120900824 = Euler-Mascheroni constant

Rad = 57.295779513082320876798154814105 = Radian = 180/Pi

A series of Quantum versions, some are exact, most are approximates:

5/4 = 9/7, 35/28, 180/144, 6300/5040, 8201/6561

4/3 = 9/7, 37/28, 192/144, 6720/5040, 8748/6561

Sqr(2) = 10/7, 40/28, 204/144, 7128/5040, 9279/6561

3/2 = 11/7, 42/28, 216/144, 7560/5040, 9842/6561

Fg/3 = 11/7, 44/28, 224/144, 7844/5040, 10212/6561

PI/2 = 11/7, 44/28, 226/144, 7917/5040, 10306/6561

11!/(7!)^2 = 11/7, 44/28, 226/144. 7920/5040, 10310/6561

PHI = 11/7, 45/28, 233/144, 8155/5040, 10616/6561

5/3 = 11/7, 46/28, 240/144, 8400/5040, 10935/6561

Sqr(3) = 12/7, 48/28, 249/144, 8730/5040, 11364/6561

1/V = 12/7, 49/28, 249/144, 8732/5040, 11367/6561

100/Rad = 12/7, 49/28, 251/144, 8796/5040, 11451/6561

7/4 = 12/7, 49/28, 252/144, 8820/5040, 11482/6561

PHI = 1.6180339887498948482

PHI = 11/7 = 1.5714285714285714285 below

PHI = 45/28 = 1.6071428571428571428 below

PHI = 233/144 = 1.6180555555555555555 above

PHI = 8155/5040 = 1.6180555555555555555 above

PHI = 10616/6561 = 1.6180460295686633135 above

As you can see these ratios converge to the irrational value PHI, as a abstract. This cannot be used a a building block only the two convergent whole numbers are usable as true constructs of concrete reality.

PI = 3.1415926535897932384

PI = 22/7 = 3.1428571428571428571 above

PI = 88/28 = 3.1428571428571428571 above

PI = 453/144 = 3.1458333333333333333 above

PI = 15834/5040 = 3.1416666666666666666 above

PI = 20612/6561 = 3.1415942691662856271 above

As you can see these ratios converge to the value PI, again it is an irrational abstract. This cannot be used a a building block as the value is not a whole number, only the two convergent whole numbers are usable as true constructs. These lists are guide lines to investigators to look for whole number relations that can be used to create whole forms without PI/PHI, only this type of knowledge can help you realize the hidden potential of Quantum Arithmetic.


The diagram 2 illustrates the Pyramids design is based only on the properties of the Quantum Triangle Unit and the centers that are generated from such a triangle and the circular distances(radii) from points. There is no esoteric magical number or Pi / PHI related ratio grid and the use of any design constructs are removed and only the pure triangle geometry is allowed. This constraint is to eliminate the modern propensity to try and own and control the geometric space by artificial means, this allows the clean use of the quantum numbers that you have begun the construction with and not to wander into transcendental number schemes, this would only cloud the underlying integer structure and clear definitions that are created by staying to the whole number constraint.

The numbers contain the constants of the geometry of the triangle and all the units derived from these base units for the construction of circles squares and many other forms.

b     e      d       a

70   37   107  144

B          E          D           A

4900   1369   11449   20736

C          F            G            L

7918   10080   12818    6651120

H           I             J            K

17998  2162    7490     15408

W           X            Y            Z

19367   3959      9287      16777

Some of these numbers you might recognize if you are a student of Geomatra and the hidden meaning behind numbers. I am sure the number 37, will ring a bell to those mathematicians who will also recognize 107 + 56 = 163, these numbers are called “Almost Integer”, these types of numbers are found in the Quantum Pyramid in abundance. Some of these number are 25, 37, 43, 58, 67, 74, 148 etc. Why are these numbers important as a large class of these irrational numbers can be found using the theory of modular functions, a few examples are given by Ramanujan (1913-14). Such approximations were also studied by Hermite (1859), Kronecker (1863), and Smith (1965). They can be generated using some properties of the j-function. How this relates to to the Quantum Pyramid is fascinating as the mathematicians where searching for an underlying structure to prime numbers and number theory in general, these crossings can only guide our understanding.

There are a minimum of three basic triangles in the pyramid and a minimum of one square :

1 BH Base width x Height

2 DH Base Diagonal x Height

3 BS Base Width x Face slope

Each Triangle has a minimum of three quantum parts

1 BHQ1 C+C,G,G

2 BHQ2 Q,G,D

3 BHQ3 G,D,M

Each Triangle Has a minimum of 5 Centers, depending on the type of triangle , some centers coincide.

1 CEcent Centroid

2 CEinct Incenter

3 CEcrct Circumcenter

4 CEorth Orthocenter

5 CE9pnt 9 Point Center

Each Triangle Center Has at least a Circle associated with it.

1 CRcent Centroid**

2 CRinct Incircle

3 CRcrct Circumcircle

4 CRorth Orthocenter**

5 CR9pnt 9 Point Circle

Each center and circle will have lines either connecting each other, tangent from centers to all circles, from each point in each triangle. from each point in each triangle and each circle center and from each point of each triangle to the tangent of each circle. Quite a lot of these values generated by the line point/tangent co-ordinates will have direct relationships to the quantum set.


























































The list above is only a short version of the centers and points that could be used to build these structures, these are only basic guides that will be in harmony with the quantum numbers that you started with. These guides are allocation design parameters and the purposes of the shafts and cavities that you build, each will reflect the meaning of the geometric center that is used and the numeric harmony it has with the quantum number set. As mankind has forgotten the inner meaning and names of these hidden geometries, we will give names to each as we find them, just as the ancients did.

This List is relative to the diagram 2 showing the pure geometric reasoning for placements of internal section of the design.


C1 Circumcircle

C2 Incircle

C3 Centroid Circle

C4 Nine Point Cicrle Ztr

C5 Incircle 2nd

C6 Incircle 3rd

C7 Tan L4/L2/ Diam H

C8 Apex circle

C9 Quantum Zline Circle

C10 Diam = H

C11 Incircle Ztr

C12 Incircle 2nd


L1 Central axis

L2 Triangle slope

L3 Triangle Base Line

L4 Triangle slope

L5 3 point Angle 1/2 division Main tr

L6 Angle 1/2 division Ztr

L7 Circumcircle center/L4/

L8 2 point Angle 1/2 division Main tr

L9 Point 21/Point 6/Point 11/Zline Circle/L1/L12

L10 Point 8/point 13

L11 Point 18/Point 17/ Point 20

L12 Point 10/ Incircle 2nd center/point 21

L13 Point 8/

L14 Quantum Zline

L15 Point 7/Point 13/Point 15/C7


1 Cross L2/L4/L1 Apex

2 Cross L2/L3/L8 Main Tr corner

3 Cross L2/L3/L5 Main Tr corner

4 Tan C3/L2

5 Cross L5/L2 Circle center Diam=H

6 Cross L2/C9/L9

7 Cross L4/L8

8 Cross L4/L7/tan C7

9 Cross L3/L16/C9

10 Cross C5/tan L3/L12

11 Cross C9/L14/

12 Cross L1/L9

13 Cross L10/C7

14 Cross C5 center/L12/L8

15 Cross L1/Center C1

16 Cross L1/Center C2/C10/Centroid of Main Tr

17 Cross L6/L11

18 Edge Incircle C5/L11

19 CrossL1/L7

20 Center 9 Point circle C12/L11

21 Cross L12/L9/C9

22 Cross L14/C6/L7

The early Egyptian deities were all on a equal footing and each reflected a particular type of action and philosophy, this will have to be rediscovered again before we can realize the subtle reasoning that the ancients had with the structural form allocations. The clear truth starts to dawn that the Khemitians NEVER used the pyramids as a tomb for a Pharaoh, because at the time they were built there were no Pharaohs only an enlightened mankind that left a legacy to the future. The legacy of pure geometry and number that is immutable and is aligned with the actions and harmony of the universe.

The Khemitians left a structure that was filled by the early Egyptians and slowly converted in to the religious worship that was never part of the original designs of the Khemitians , they knew their legacy would be followed if they stuck strictly to geometric rules and numeric constraints, eventually the true knowledge would rise from the observations of the art and architecture, even if the the civilization that embraces them have lost the original meanings. An example is the sun sign on the heads of many deities, these are never shown as circular only as ellipses, and if observed without preconceived notions they would be understood as Quantum ellipses.


The diagram above is the  BHQ3 = G,D,M

PyraPict1aThe diagram above is the  BHQ1 = C+C,G,G


The Diagram above is the BHQ2 = Q,G,D

The Origins of Geomatra Numbers

As you are aware there has been a New Age numeric enlightenment towards ancient monuments and the associated location and the dimensions of them. These ideas are from numerous sources old and new and they place importance to different numbers and quantities, as you know if the values are PHI related then you can be sure they have a common background in Quantum Arithmetic. The list is very long and the variety of scared numbers is very long and grow longer with each generation, it looks like we should find the source to this attachment to these special numbers. Here is a short list and some of the background of its attachment.

7 = Days

8 = Eightfold Path

9 = Egyptian Gods

11 = Master numbers in modern occult numerology , it denotes hidden dangers and great trials and difficulties.

12 = 12 Links of Dependent Origination, 12 Powers of Buddha

13 = Natures number

32 = Parts of the Body. 32 Physical Marks, 32 Characteristics Which a Great Man can be Recognised found on Buddha.

37 = Factors of Enlightenment, 37 things that are conducive to awakening. Mark the perfect man, and behold the upright: for the end of that man is peace. That’s Psalms Chapter 37, Verse 37.

40 = days and nights of darkness,

52 = Mental Formations. These range from greed and hatred to discretion and balance of mind. Weeks in the year.

144 = Light

153 = Bible, miraculous catch of fishes

216 = 6 x 6 x 6

288 = Double light, the Kingdom of Heaven.

360 = Degrees of the circle

432 = Consecration (also the square root of the classical speed of light, 186624 miles per second). Luke 8:15, Revelation 2:17, etc.

396 = Classical earth radius (3960 miles).

576 = Prophecy and Gospel.

666 = Sign of the beast

864 = Time , the source of light and life, Most Holy. Diameter of the sun=864000 miles

888 = Jesus

1152 = Witness (576 x 2). Biblical references include Luke 14:26, Revelation 3:12, 12:11 and 19:9.

1296 = Circle of space (360 x 60 x 60). 1296 was also Plato’s favorite number.

1440 = minutes in 24hours. Light

1548 = Priest of God.

1728 = 12x12x12 , A-flat in music.

2160 = Diameter of the moon: 2160 miles

2304 = False Christ’s and False prophets (1 Cor. 14:22, Mark 13:12).

3168 = Lord Jesus Christ.

3888 = New Jerusalem (Rev. 21:2, 1 Cor. 12:27, Luke 8:21, etc.).

5040 = 7!

5184 = 72 x 72, Victory over the beast (Rev. 15:2).

25920 = The Great Year

There are many more than I could list, a common sequence is those numbers that divide by 3, and 7. The mental attachment to these and other numbers are a symptom of hundreds of years of subtle religious reinforcement, financial methodologies and forceful masonic application each using the influence as a form of magical control over the general public, if you are one of those who have this affliction then you are in good company.

The main source of the western Geomatra is the Hebrew alphabet and Greek alphabet, as the Hebrew has its origins in Egyptian hieroglyphs, I would say they are related by basic forms and meanings. Then as a consequence of the common heritage the lineage of Geomatra numbers go back to the Khemitians who wrote the first codes of understanding into the monuments and the writings on the early civilizations of that region. Other parts of the world used the same ideas and basic forms , not necessarily the exact same glyphs but similar enough to recognize the same origin, as the local culture was global NOT regional as the establishment want us to believe.

The first sign of enlightenment and awareness is to recognize these numbers, the second is to be see to who is wielding the influence, third is in the clear knowledge that these things can no longer control your actions. At the moment of this , we will have entered the new paradigm and have gone past the hierarchical control from the leaders who wield agendas of enslavement. This was the purpose behind the Egyptian Horus, the complete and enlightened human, a model for all to follow, NOT a God to worship.

Opening the door to this is accepting a new numeric organization, one that has not been taught since the Ancient Khemitians built their Pyramids. Only Pythagoras had tried to pass some of his methodologies and ideas that was taught to him from the Egyptians who kept the knowledge through the ages, only to be misunderstood by many. Archimedes and others who read the manuscripts from the Alexandrian library and passed some of his interpretations back to us.

At the entrance of the new awareness you will have to leave the coded tricks of invented mathematics and walk a narrow path that will lead you to answers that are simpler and full of meaning. It is only truly free men that are not trapped by a wall of numbers built by accountants, lawyers and politicians and the rest of the masonic orders that wield power and influence hidden to most of mankind. Are we ready for such a new journey or are you still comfortable in the entrapment of occultists numeric policies that run our system..

Remember all the valued listed are derived from the b and e roots by simple arithmetic. The first 4 terms are the Roots, the next 12 are derived from the the 4.

b = 70 = d – e

e = 37 = a – d

d = 107 = b + e

a = 144 = d + a


B = 4900 = b x b

E = 1369 = e x e

D = 11449 = d x d

A = 20736 = a x a

C = 7918 = 2 x d x e

F = 10080 = d x d – e x e

G = 12818 = d x d + e x e

L = 6651120 = ( d x d x d x e – e x e x e x d ) / 6

H = 17998 = ( a x a + 2 x b x a – a x a ) / 2

I = 2162 = ( e x e + 2 x d x e ) – d x d

J = 7490 = d x d – d x e

K = 15408 = d x d + d x e

W = 19367 = d x e + d x a

X = 3959 = d x e

Y = 9287 = 2 x d x e + d x d

Z = 16777 = e x e + d x d + d x e

These two are non whole number terms that are used to help solve the Circular and Triangular Equations.

AP-Pi = 5.387334464 = ( 2 x d x e + d x d + e x e ) / 2 x ( ( b x e x d ) / a ) = Arto-Parker Pi Ratio for Quantum Triangles

ICR = 3849.027777 = 2 x ( ( b x e x d ) / a ) = Incircle Radius

Thank you very much for reading an excerpt , and I hope you will enjoy my book, “Talking to The Birds”, Regards Arto


The Kings Chamber

December 14, 2012

Here is the complete numeric code of the Kings Chamber(Resonant Cavity) from the interior of the Great Pyramid(Alnitak), the numbers cannot be fudged and are precise , no allusion to the value PI or the Phi. Using transcendental numbers only gives you approximations, not true values, only Quantum Arithmetic can reveal the underlying order behind these types of structures.

Kings Chamber1f

The original ideas were not coded from computers and approximated with calculus, these tools would not have been needed 10000 years ago. The dawning of a new paradigm in understanding of ancient monuments are written in the quantum code that underlies all of these stone artifacts, if they knew how and why, we can also know, this was their legacy to us. The path to the enlightenment of our ancestors does involves many sacrifices, many more than most modern people would want to endure.

The value to translate from Fingers(Digits) to millimeters is to divide by:

1  Finger     =    18.6871428571429 mm

The value to translate from Quantum Units to feet is to divide by:

1  Foot         =    39.378640776699 QU (Quantum Unit  = 338)

By the research I have here it seems the Cubit(Royal) used for the Kings Chamber is:

1 Cubit (CR)    =    523.24 mm     = 20.6 inches

A quantum unit in not a empirical measure, it is an absolute value that can be derived from number law and prime numbers it does not have a distance measure like meters and feet. This is what the ancient Khemitians (Egyptians)  express as divine , sometimes giving it names like Osiris, Horus, Thoth, Atum etc to explain the amazing qualities of pure numbers. I suspect the nine gods of the ennead are also known as the geometers Nine point circle and all the discipline and understanding that comes from its knowledge and deep connections with the absolute and pure numbers of the universe.

As you can see the use of cubits, hands and fingers are very easy to translate from quantum units, the people from Khemit knew that these measures would not be absolute, only as a translational device. This is the reasons our current society cannot pinpoint why cubits had so many variants, we think that our measures are correct and absolute and the ancients were vague and approximate, I agree this is the case, only if you look at it with a narrow idea of what absolute measure really is, meters or feet are just convenient rulers for our utilitarian needs, just as cubits and palms were to the ancients.

There is a another level of hidden measure here, as the Khemitians did not use  decimal fractions like we do, we must look at another schema that does not rely on our modern approach. It looks like the unique quantum values have been used again, this time to create another cubit measure that can be used for the height and one of the diagonals(D3). This was has been called the standard cubit:

1  Standard Cubit (CS)        =    17.7165385909599 inches

This length reduces the problem required by making the height now 13 CS and the diagonal D3 become double value of 26 CS. These numbers are the first 2 numbers of the Quantum set that I have shown. This alone will tell you the Khemits knew the Quantum code used and that the rediscovery of their methods is complete, no more esoteric geomatra that only confuses the numeric issues by introducing some strange masonic ritual into the understanding of numbers, not that this did not serve the purpose of showing these values as sacred to the hidden code and help perpetuate the use of them through history, thanks to the people who showed their continued reverence and usage in architecture, art and geometry. Here is some more figures that confirm this:

13 x 26 = 169 x 2 = 338

338 X 338 = 114244

A right angled triangle created from a base of 26 CS(D3) and a height of sqrt(33.8) has a hypotenuse that is equal to the floor diagonal(D4), this value is Sqrt(709.8)

7098 = 239912/338 = 1014 x 7 = 338 x 21 = 338 x 7 x 3 = 26 x 13 x 7 x 3 = 169 x 42 = 169 x 7 x 6 = 13 x 13 x 7 x 6

There seems to be some strange idea that the ancient builders used some sort of special ruler to measure and build the structures and maintain the PI/PHI properties, this is just fantasy as you do not need to use these numeric or ruler type devices to measure its proportions, they arrive out of using Quantum numbers as PI/PHI are built from Quantum proportions.

The D4 measure is most interesting it looks like the possibility to translate into whole number measure the Khemits may have used is 26 cubit CS and a didactic fraction 217/338 this is 0.00006015717542851 from being exact, in millimeters this equates to 0.000041959721260mm which is about the thickness of a human hair. This would seem be an acceptable clearance allowing for temperature differentials and seismic activity. As for that number 217, this is another interesting quantity as 216 is 6 cubed, further investigations would seem fruitful in this direction, even though we are only dealing with such a small fractional part, the Khemitians gave us the questions, so we are obliged to answer.

The QA numbers seem almost trivial compared to the modern edifice of mathematics, millions of volumes full of the most complex ideas of mankind, still it seems not to speak as simply and directly as Quantum Arithmetic. The Quantum number set used in the cavity is the part of a series of numbers that have particular properties, such as:

2 x 39 x 13 = 1014 = 39 x 39 – 39 x 13

the common divisor is 13

as 39 = 3 x 13, this only works by multiplying 2 prime numbers and having a common divisor(13).

2ax b = a^2 – ab if b/a is an integer and is a divisor of the other

what if the QA set was 26,12,38,50  then

2 x 38 x 13 = 912 and 38 x 38 – 38 x 12 = 988

38 does not divide by 12 without remainders, this cannot be used in this type of construction, but maybe in another shape or form these numbers are suitable as part of its required building blocks. This particular rectangular cube has harmonic properties just like the Quantum number set has.

My methods are original and the answers speak for themselves. if you doubt the veracity of my approach please by all means find fault with the numbers not me. I am not an Engineer, I am not a Mathematician, I do not hold a degree in any subject; BUT: I am an Artist and this is part of my art, something that I have worked a lifetime to accomplish, I hope what I reveal through my work, we can all gain a better understanding of the world around us.

If you find my work of value please donate via PayPal, as this will afford me to continue in this unique endeavor. Thank you Regards Arto. This and more will also be in my book “Talking to the Birds”.

Saqqara Ostrakon

December 5, 2012


Saqqara Ostrakon a Different and Exact Solution

by Arto Heino 2012

Having solved many numeric puzzles using Quantum Arithmetic, I decided to attack this interesting artifact with relish. It seems everybody had a go at this including Graham Hancock. I am glad to express my delight in the solution that I have found, revealing the true principles of Ancient Khemitian(Egyptian) geometry and part of the foundation of building and pyramid design and the reason for their construction principles. As I will show on a another blog entry, I have found one of the the final keys to knowledge of the ancient Pyramidic geometric cipher, no weird magic number or symbol required, this is truly exciting and I will notify all interested parties when my blog is published.

The Saqqra OstraKon was found at the excavations in Saqqara in 1925, the writing reveals this object has a geometric value. The inscription is a form of shorthand to a larger idea.

3 Cubits, 3 Palms, 2 Fingers = 98 Fingers = 1837.5  mm
3 Cubits, 2 Palms, 3 Fingers = 95 Fingers = 1781.25 mm
3 Cubits, 0 Palms, 0 Fingers = 84 Fingers = 1575    mm
2 Cubits, 3 Palms, 0 Fingers = 68 Fingers = 1275    mm
1 Cubit , 3 Palms, 1 Finger  = 41 Fingers = 768.5   mm

1 Cubit  = 7 Palms = 28 Fingers = 525 mm (using this conversion size in millimeters)
1 Palm   = 4  Fingers = 75  mm
I Finger = 18.75 mm

The small curved line and a few strokes and the numbers above is all that was needed. The 98 Fingers was the first clue, this would be the Perihelion or in QA the J factor. The plane number 98 didn’t fit with any Quantum Ellipse so a multiplication or conversion number must have been used, after a few attempts it looks like the prime number 5 was the cipher.

G _ H  = 490 = 5 x 98
N _ W  = 475 = 5 x 95
D _ Z  = 420 = 5 x 84
R _ B1 = 340 = 5 x 68
T _ C1 = 205 = 5 x 41

Now that I know J= 98 then as in all QA you can work backwoods to find the roots of the ellipse. These are the original root numbers that I found:

b = 2    e = 3  d = 5   a = 8  , these will give you J = 10 and the eccentricity of 0.6

b = 14   e 21   d = 35  a = 56 , these will give you J = 490 and the eccentricity of 0.6

The prime factor underlying the x 7 is a way of finding the other derived numbers in a simple translation as J=98 is not a Quantum root size it is a derivation from a physical measuring system from a Quantum number set.  This diagram should explain the geometry.SaqqaraElli4

The reason I exclaimed the true solution is because of the following hidden variables. The redrawn diagram everybody followed by Battiscombe Gunn is incorrect, looks like his pet theory of 28 fingers between lines was wrong, as you can see by the original carving the lines are not evenly spaced, it was only a crude diagram drawn without a rule, you cannot base the intention of the geometer on a rough sketch,  only on the description he gives and the approximate position of all the lines. All QA requires is some real numbers and an approximate shape to define the correct form.

These are exact values with no decimal fractions:

H _ W  = sqrt(  23376 )
H _ Z  = sqrt( 106624 )
H _ B1 = sqrt( 220800 )
H _ C1 = sqrt( 394896 )
H _ I  = Sqrt( 614656 )

These are the values when J=490, they reveal the correctness of the QA precision  You will never arrive at this sort of numeric clarity using any mathematical tricks, the Quantum Ellipse is a unperturbed form and non empirical.  The values when J=98 re listed below:

H _ W  = sqrt(   935.04 )
H _ Z  = sqrt(  4264.96 )
H _ B1 = sqrt(  8832    )
H _ C1 = sqrt( 15795.84 )
H _ I  = sqrt( 24586.24 )

What we are looking for is the gap sizes, here is J=490

H _ W  = sqrt(  23376 )
W _ Z  = sqrt( 106624 ) – sqrt(  23376 )
Z _ B1 = sqrt( 220800 ) – sqrt( 106624 )
B1_ C1 = sqrt( 394896 ) – sqrt( 220800 )
C1_ I  = Sqrt( 614656 ) – sqrt( 394896 )

Here are the final values decoded and back to empirical finger and metric measure

H _ W  = sqrt(  935.04 )                                    = 30.5784237 Fingers = 573.3454456 mm
W _ Z  = sqrt( 4264.96 ) – sqrt(  935.04 )  = 34.7282374 Fingers = 651.1544523 mm
Z _ B1 = sqrt( 8832    ) – sqrt( 4264.96 )    = 28.6720597 Fingers = 537.6011207 mm
B1_ C1 = sqrt(15795.84 ) – sqrt( 8832    )  = 31.7027812 Fingers = 594.4271479 mm
C1_ I  = Sqrt(24586.24 ) – sqrt(15795.84 )  = 31.1184877 Fingers = 583.4718333 mm

These sizes were not needed by the Khemitian geometer to their requirements only the right angle edge and the curve was needed, only modern calculus require these values as to plot X * Y curves. The Khemitians had no need of such crude mathematical devices such as calculus, they treated the curve as a different type of measure than the straight line. Now we can extrapolate the Cubit/Finger and metric size of the whole ellipse.

Length of the ellipse is = 2450 = 490 x 5 in Fingers = 490 = 17 Cubits 3 Palms 2 Fingers = 9.1875 mtrs

Width of the ellipse is = 1960 = 392 x 5 in Fingers = 392 =  14 Cubits = 7.35 Mtrs

The values are correct as no extra bit of a finger is required, this one of the reasons the Khemitians used these types of measure. The translation into quantum units were simple and there were no fudge factors that required PI, PHI or Log, no fractional decimals, only whole numbers  So the final outcome underlies how truly powerful Quantum Arithmetic is when fully understood and utilized in the right hands, when looking for a accurate solution without errors from empirical measurements and data from approximation using calculus.

These and many more are from my up and coming book “Talking to the Birds”, regards Arto

An article by Battiscombe Gunn
Published in Annales du Service des Antiquites de L’Egypte,
Volume 26, 1926, pages 197 – 202
Printed by the Institute of France, Oriental Archaeology,
Le Caire, France

Diagram was created by Arto Heino using GeoGebra

*** New Addition *** 2021

I can see some are not convinced of my odd methodology, here is ample proof that simplicity was the key.

As the diagram illustrates:
IH = 784
HF = 1470
IF = 1666

Add together to create the perimeter of the triangle, thus:
784+1470+1666 = 3920

Now return back to Finger measure:
3920 / 5 = 784

Now return back to Royal Cubits:
784/28 = 28

Thus if you have a string 28 RC long and joint it to make a loop, then you make two pegs on the ground at the distance of:
1470/5 = 294 fingers = 10 RC + 14 F

You can now trace this ellipse with a marker at a third point when you stretch the string. Refer to the diagram below using the 3-4-5 triangle giving 12 as the perimeter.

I hope that simplifies my reasoning why I use QA to solve these ancient problems. Regards Arto

Quantum Arithmetic

November 22, 2012

This is another brief expert from my book “Talking to the Birds”, I hope you enjoy it. I have included some notes from Ben Iverson as well.

Only a trained mathematician/geometer can recognize the missing elements in the geometric canon, that which has been ignored for the last 60 years, you cannot accidentally or casually find this most unique arithmetic, it is not based just on porisms. It is not number theory or invented mathematics, it does not need calculus, there is no approximations, it does begin its understanding as the trivial terms that most assume to be understood. Let us begin with the trivial terms so we can dispense with all the mystery.

Quantum Arithmetic uses a natural number system which has a base in of all of the prime numbers which occur in the problem you need to solve. All its numbers are interlocked in a geometric arrangement. All numbers are positive integers, no decimal points or irrational numbers. Addition, subtraction, multiplication and division is all that is mainly required, the use of square roots and diadic fractions are also used, they are mainly used to verify the results and find the whole number ratio’s. The ordering into Par numbers can also verify and help understand the internal arrangements.

There are sixteen primary identities. The first four are given the identity of “a”, “b” “e” and “d”. These, are the roots of its given problem, and is the base numbers. The next twelve identities are the upper case letters A through L. They are combinations, of the first four base numbers, and are usually considered as one dimension, higher than the base identities. They will denote linear dimension, surface areas, or volumes, for the three standard dimensions above the roots.

There is also one dimension below the “roots” b, e, d, and a. They are called “quaternions”, and are the square roots of the root numbers. In conventional mathematics, these are called “Gaussian Integers”. They are integers, only when their base number is a perfect square. A problem in QA is well defined and problems solvable when only one of the upper case identities is assigned a value and the name of that identity. All of the values within a problem in QA are intertwined this gives you hundreds of ways to solve any given problem.

The Quantum Number for one figure is the same for all geometric figures. A single quantum number defines the magnitude of the measurements, as they are related between themselves. Different geometric figures can be connected and their dimensions are calculated once for all of the various shapes. The shapes used are:

1 Right triangles

2 Equilateral triangle

3 Isosceles Triangles

4 Triplet circles (Koenig Series)

5 Triplet Squares (Koenig Series)

6 Ellipses

Each shape is calculated from a single Quantum Number. The one requirement is that the second and third integers of the Quantum Number must be prime to each other. These are in the Fibonacci sequence. They derive from Euclid VII, Proposition 28. The first and fourth integers become, “Sum and Difference” numbers.

All Quantum ellipses will give the value one when you apply the Steiner Inellispe porism. The numeric laws it contain can be geometrically reconstructed with s0me of the most excellent programs such as GeoGebra, First you need to understand the construction of the “Quantum Ellipse”. The usual 2 foci and semi-major length/third point will not suffice only Conic section ellipse will create the correct elliptical form, if you have 5 points that are aligned to the quantum arithmetic standard. I hope some of these diagrams will help clarify all the parameters. The best way to construct an ellipse of this sort is to start with a string with length 3+4+5=12 a Pythagorean triangle. This method was re-discovered by James Clerk Maxwell in the mid 1800’s.

This type of geometry had been developed by Ben Iverson from the 1950’s through to to 1990’s extended by Dale Pond and myself over the last 20 years.

After many calculations and with the application of Quantum Arithmetic, I have created a beginning for the foundation of the Quantum 120degree Isoceles. The smallest integer units begin at the 4 digit root numbers, which means some calculations are up to 20 numbers long This study has revealed the Quantum Equilateral also within its perimeter, having now multiple Z line integers.

Listed below is the some of the raw data for one of the smallest Quantum Isosceles 120 degree Triangle, the added Var1,Var2,Var3,Var4,Var5,Var6 are part of an incomplete data list, you can ignore them or just make each equal zero.

b = 2646 = d – e

e = 4343 = a – d

d = 6989 = b + e

a = 11332 = d + a

B = 7001316 = b x b

E = 18861649 = e x e

D = 48846121 = d x d

A = 128414224 = a x a

C = 60706454 = 2 x d x e

Fe = 29984472 = d x d – e x e + Var1

G = 67707770 = d x d + e x e

L = 151687580848524 = ( d x d x d x e – e x e x e x d ) / 6

H = 90690926 = ( a x a + 2 x b x a – a x a ) / 2

I = 30721982 = ( e x e + 2 x d x e ) – d x d

J = 18492894 = d x d – d x e

K = 79199348 = d x d + d x e

We = 109552575 = d x e + d x a

X = 30353227 = d x e

Ye = 79568103 = 2 x d x e + d x d + Var2

Ze = 98060997 = e x e + d x d + d x e + Var3

Wib = 328657725 = 3 x ( d x e + d x a )

Fi = 109552575 = d x e + d x a + Var4

Yi = 219105150 = 2 x ( d x e + d x a ) + Var5

Zi = 109552575 = d x e + d x a + Var6

Wis = 189750626 = ( d x e + d x a ) x sq 3

Wh = 94875313 = ( ( d x e + d x a ) / 2 ) x sq 3

Thank you

Regards Arto