Posts Tagged ‘Quantum Arithmetic’

Live Interview

December 14, 2013

Hi Fellow researchers ,

Adam Bull has released a 4 Hr interview on Youtube, it is informal and free flowing, about my book “Talking to the Birds”.

Here is the Link-

Here is the Press Release:

After many years of research, personal discovery and seeing the world through the perception of an Artist, one who by his very nature must understand something very deeply before he renders its likeness, Arto Heino has released his first volume “Talking to the Birds”. The subjects covered in his book are as varied as his pallet, he shows a different perspective about each subject he studies.  Volume I, A compilation of his best works, you will see the many different hats he wears as he sifts through a broad spectrum of knowledge with a profound insight into several pieces of hidden information ignored by most other researchers.

To understand the author of this work is to peer into layers of understanding that have not been lifted in most researchers lifetime. In the chapter on Archeo-Astronomy Arto looks at some of the basic assumptions about the nature of man’s history and came to some simple conclusions, the evidence he uses is not a rehash of another theory but new and startling revelations about the cyclic nature of our consciousness. The artist and writer Arto Heino shines the light where few others have on past ancient artifacts and current sciences that should give you a new way to see the past.

As a young child, Arto found meaning in natures chaos and his deep connection to some of its hidden attributes long before he articulated his understanding to others. Books gave him one of the tools to peer into history and find those who could help him guide his vision, great artists like Leonardo Da Vinci took him to a simpler way of personal scientific and artistic discovery. To show some of what he has learned from the master he gives a brief insight into one of Da Vinci’s more famous artworks.

The lure of electricity is never far from his thoughts, he has several chapters that deal with Electronics, Invention and Machines they cover some of the most important works of Nikola Tesla. Arto shows his own artistic method of understanding the circuits of Tesla and removes a lot of the mystery that surround his work. The circuit models by Arto are more like artworks that have a landscape of parameters and clues to other possibilities. He pries into some of the mystery that surrounds the work of Lester Hendershot, Don Smith and Henry Moray, giving  new insights that could help to guide other researchers to new conclusions.

The nature of the geometric abstraction is not just pretty patterns like most modern conveyors, to Arto this is where you can find a deeper connection to the sciences. He sees a simple form such as a triangle as a new beginning to a new and non-complex form of mathematics, Quantum Arithmetic. As he implies he is only expanding on something that the geometers have tried to bury, Arto shows some of his studies in Quantum Arithmetic and the expansion of a new type of geometric discovery, where he applies it to the Giza pyramid, the Kings chamber and an Egyptian artifact that has alluded many archaeologists and geometers for the past 80 years.

The surprise in the book is not just his varied perspective of technology but in one chapter Arto lifts the surface off our modern paradigm, he includes some of his more popular cartoon images to highlight the high paced and disturbing reductions of our elite. Arto as an artist and a musician gives those inclined an interesting group of studies.

If you would like a copy of the book –

Also Available from –

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

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


Contra-Cyclic Harmonic Archimedean Geometry

October 5, 2012

Here are some of the files I have released in the Energetic Forum recently. In them I am dealing with a geometry that has been used in many types of machines for thousands of years ranging from Archimedes all the way to Da Vinci, Huygens,  Bessler,  Keely, Russel, Constantinesco and to all the late 19th century mechanical inventions and now to the whole free energy fraternity that seem to think these things have not been discovered before or even understood by previous generations. I am a wittiness to a unique renaissance in this type of research as seen by a multitude of patents, designs and inventions  in torque conversions and unique mechanical advantage systems.These reveal the simple but hidden aspects of geometry, as I have seen by perusing hundreds of patents and engineering catalogues,  still I find nothing historically new but a creatively variant and diverse  application of a multitude of designs, utilizing a hidden pallet that engineers need to know about and define as a branch of dynamic geometry.

Nicola Tesla hinted at the electrical version of this higher geometric typology, most of his inventions had this at its center, where logarithmic curves are not approximated and linearized. The etheric geometric relationships of these phenomena has been elucidated by Eric Dollard in his many publications, videos and writing, showing a precise 4 quadrant nature to electrical phenomena, no Einstein or Maxwell misunderstandings and disinformation required here . What is the core of this version of science, engineering and understanding?, it is ancient geometry of course, or as some call “Sacred Geometry”, the same as ALL the crop circles around the world. The geometry of Archimedes, toroids, pendulums, spherical geometry, Huygens Evolutes and Caustics, Bruce Cathie,  versins, haversins, Quantum Arithmetic(as per Ben Iverson, Not Quantum Physics)  and  Great Pyramid geometry could all be involved. The new branch would be viewed as 3d dynamics that cover those geometries of spherically rotating pendulum, single,  double and triple stages with optional locations of pivoting axis, that could be called an upside down rotating spherical pendulum.

The machine designed by Sixto Ramos reveals this type of geometry very clearly, it relates to the Archimedean twin circle(fibonacci/golden) geometry, as you can see toroidal geometry is also involved. Looking at the forms created in its action you can see a part of the conchoid of de Sluze family of curves.

As you can see I have added an extra pointer in the geometry that relates to the great pyramid. This I will carry through to the Ucros device.

George Constantinesco must be included in this array as his devices are the most elegantly designed and understandable from all the types of these torque converters you will ever see.

To conclude these machines , I have a design that uses the hyperbolic curve as the geometric element in the design, accomplishing the similar results as the Sixto design.

Here is a geometric diagram that includes the Archimedean twin circles and the basic geometry of the Ramos machine  I hope this will help in understanding some of the ideas shown here.

I would love to include the section relating to Veljko Milkovic as his inventions has gravitation as the other inlaid geometry. Some of these diagrams and graphics here are included in one of my chapters in my book “Talking with the Birds” Vol I & II. **note** Volume I of my book is now available at, please check here.