Numerical nature of ancient mathematics

Numerical Nature of Ancient Philosophy is Number Squares

Numerical Nature of Ancient Philosophy is Number Squares. There are three varied approaches to ancient mathematics. Today we will only examine “real numbers.” Categories 2 and 3 will be future blogs.

  1. Use of “Real numbers” being numbers 1 – 9.
  2. Synthetic numbers being 10, 110, 1110, 11110.
  3. Repeated “real numbers” as 11, 22, 33…Or; 111, 222, 333…Also; 111,222,333…. to the nines.*

Numerical Nature of Ancient Philosophy is Found in the Phrase “To the nines.”

Lyrics from “Don’t Cry for Me Argentina”. You won’t believe me, all you will see is a girl you once knew
Although she’s dressed up to the nines.

  • Evita (New Broadway Cast Recording)

 

My blog traces the history of “to the nines” to prehistoric times. Number squares were of prime importance. What set the concept and pattern of the number squares in motion was the smallest. It is referred to as the grain of mustard seed in the Bible. It uses the numbers one to nine. Nine becomes the maximum. Higher numbers are synthetic.  For example: Ten is the total of any two opposite numbers around the perimeter of the featured picture.  Examples are 9 + 1 or, 3 + 7. They combine two or more numbers in set patterns. Ten, in the distant past, did not exist as an independent number.  In musical terms repeated patterns on different tones is called a sequence. They musically demonstrate a property we will study in number squares.

J.S. Bach Concerto for Two Violins in D minor, first movement, bars 22-24

 

The meaning of this ancient number square is revealed in the phrase Dressed to the nines.  But the history of nines is much older than this defining quote. Perhaps some 10,000 years older. *”To the nines” is an English idiom meaning “to perfection” or “to the highest degree” or to dress “buoyantly and high class”. In modern English usage, the phrase most commonly appears as “dressed to the nines” or “dressed up to the nines”.[1][2]The phrase “dressed to the nines” is just a specific application of the Scottish phrase “to the nine ” The earliest written evidence of this phrase appeared in the late 18th century in the poetry of Robert Burns. Its meaning is “to perfection; just right.

Much more to come on the featured picture of the Grain of Mustard Seed  and categories 2 and 3. Keep checking the blogs.

Mexican Sun Pyramid has a blueprint

Mexican Sun Pyramid Draws on Platonic Codes

Mexican Sun Pyramid Draws on Platonic Codes. Yes, there is an ancient temple plan. It dates back to Neolithic times. Plato used it. It was employed all around the world in antiquity. I discovered it in a vision while hiking around the loop by Oquaga Lake.  The same Ancient Temple Plan also graces the Mexican Sun Pyramid.  I discovered it by means a vision while hiking around Oquaga Lake. The special character of the lake nature is described in my book of poetry on DSOworks.com: The Oquaga Spirit Speaks. It can be downloaded.

I was walking down the main road by Scott’s golf course when I had the insight that forms the basis of this blog.

Teotihuacán
 Pyramid of the  Sun (click to see picture source)

Coordinates: 19°41′33″N 98°50′37.68″W

Add the length of  the perimeters of the four  triangles ABC, ADC, ABD and CDB.  Each one totals 2520′ ( 738 + 738 + 1044 = 2520) .  Four triangles = 10,080. Next, use pi as 22/7. A circle around diameter of length 10,080 = 31,680.

Mexican Sun Pyramid Parallels Plato’s Writings

Plato’s Ideal City uses the same numbers in his desciption of the Ideal City.  He states in Laws V: “(1) Mark off 5040 allotments. They must be cut in two so that “each contains a near piece and a distant piece- joining the piece next to the city with the piece furthest off.”. That totals 10,080 markings of land (5040 on each side of the radius). That equals the total of the sum of perimeters around the 4 triangles of the Sun Pyramid as described above.  A circle drawn around diameter 10,080 has a circumference of 31,680 . As 10,080 x 22/7 = 31,680. The co-incidence goes even further. John Michell explains defines the area of each of its 2520 pairs of rings. The combined area of each of the pairs is 31,680. Both the Mexican Sun Pyramid and the Ideal City use the same number tradition of prehistory.  I refer my reader to The City of Revelation by John Michell pgs. 84-86

Conclusion: At one time there existed a peaceful formula for civilization. Due to some kind of cataclysm, everything was destroyed.  This possibility is discussed by Immanuel Velikovsky (/ˌvɛliˈkɒfski/; Russian: Иммануи́л Велико́вский; IPA: [ɪmənʊˈil vʲɪlʲɪˈkofskʲɪj]; 10 June [O.S. 29 May] 1895 – 17 November 1979) He was a Russian-Jewish independent scholar best known as the author of a number of controversial books reinterpreting the events of ancient history, in particular the US bestseller Worlds in Collision published in 1950.[1] Earlier, he played a role in the founding of the Hebrew University of Jerusalem in Israel, and was a psychiatrist and psychoanalyst.

Conclusion: I think that ancient ruins hold lost knowledge. Uncovering and understanding what’s in these ruins provides possible pathway way to peace. I think we are approaching another Golden Age. How good is that?

Image result for picture of Book cover of John Michell's City of Revelation
John Michell quotes Plato’s Laws V which one of my sources for this blog.

Hidden Heptagon is Found at the Great Pyramid of Egypt

Hidden Heptagon Found Attached to Great Pyramid’s Blueprint.

Hidden Heptagon  Can Be Attached to Great Pyramid’s Blueprint. Or, is it vice versa?  First, what is a heptagon?  In geometry, a heptagon is a seven-sided polygon or 7-gon. The heptagon is also occasionally referred to as the septagon, using “sept-” (an elision of septua-, a Latin-derived numerical prefix, rather than hepta-, a Greek-derived numerical prefix) together with the Greek suffix “-agon” meaning angle.

The featured picture is from my 1st volume, p.393, of The Staff of God. I worked many summer seasons at Scott’s Oquaga Lake House as their piano player. There, a spiritual presence made itself known. I was educated in the ways of the ancients. The Oquaga Spirit Speaks, was one of the results. It relates through quatrains with rhyme the character of this spirit. Here is a sample from the opening poem entitled The Oquaga Spirit:

What a communicator was she
This sprite both blithe and free.
So much she needed an ear,
She ignored my tranquility.

Related image
The incomparable beauty of Oquaga Lake offers strong spiritual sensation for anyone.

NOW FOR THE HIDDEN HEPTAGON

 

Hidden heptagon was relayed at Soptt's Oquaga Lake House.
Scott’s Oquaga Lake House promises and delivers a new and beautiful dimension.

 

 

 

 

 

 

 

To the best of my knowledge, I think I was one of the first to rediscover the hidden heptagon. Even more significant: I think the triangle of the Pyramid’s dimensions originally came from this hiding heptagon. Not the other way around. Every book I’ve seen previously has defined the triangle as giving birth to the Great Pyramid. This involved many geometrical constructions. Here’s the simpler way to draw its dimensions from the heptagon: Set your compass at point “C”, Mark its length AC. Mark point “D” from point “C”. Draw a straight line along ICBD. Connect lines for triangle CDA. You have the essential proportional measures of the Great Pyramid.

More blogs will be written on this topic. Here’s one application. Hebrew language has 3 “mother” letters. It also has 7 double letters. That is, letters with 2 distinct sounds.

  •  A 2nd heptagon can be drawn on the other side of the triangle (not pictured). It’s basic side is defined by line AC. It then extends to the left. The 1st heptagon is on the right.
  • The one mother that gives birth to the 2 heptagons wedged in the lower center between the 2 heptagons. .
  • With the Hebrew language, the 3 mother letters give birth to the 7 double letters. The diagram geometrically defines this pattern.

Possibility exists that I might go to the Lake House once more this summer. There I would recite poetry. Also I would offer expeditions to commune with the spirit, and play the piano.

L’image contient peut-être : ciel, arbre, crépuscule, plein air et nature
Every season has its beauty at Scott’s

 

Neolithic number eight is on the piano keyboard.

Neolithic Number Eight Permeates the Great Pyramid of Egypt

Neolithic Number Eight Permeates the Great Pyramid of Egypt. Also the modern piano keyboard. Here’s how.

  • First use of eight (8). The featured picture illustrates an octahedron.  It is a symmetrical, eight-faced, triangulated figure. All angles at their corners are 60°. Bisect the featured picture across the square at the center. The bisected octahedron then becomes two square based pyramids.  The above I call the positive. The below I call the negative. All square base pyramids imply an attached equal and opposite pyramid.  The mere existence of any square base pyramid, implies a counterpart. Granted, the Great Pyramid of Egypt has differing angles. It uses isosceles triangles.  But, the extra four reverse-faced pyramid is still implied. When they are joined, the square bases become internal. They literally disappear. There no longer is a separated square base. We have our first usage eight. As,  4 faces (postive)  + 4 (negative) faces = 8.

2nd Usage of Neolithic Number Eight

  • Image result for picture of the book cover by John Michell the View Over Atlantis
  •  Each side of the square base measures 440 shorter Egyptian cubits. Shorter cubits are 1.718…feet. A more encompassing measure is the Great Cubit. It measures 55 shorter Egyptian cubits. Thus each side of the Great Pyramid of Egypt is 8 Great Cubits. 440⁄ 8 = 55.  Reference John Michell, The View Over Atlantis. Therefore the Great Pyramid is 8 x 8 Great Cubits.

Neolithic Number Eight and Musical Octaves on the Piano Keyboard

  • Last, but not least. We will tie the Great Pyramid into concert note A-440 and its octaves. Its essential measures come from octaves of the concert note A 440. A higher octave doubles the vibrations per second. The lower octave cuts them in half. The lowest note on the 88-keyed piano is “A”. It vibrates 27.5 times per second. On the Steinway below, it is the furthest note to the left.

The musical keyboard of a Steinway concert grand piano

Here’s the connection. The height of the Great Pyramid is 275 cubits. Neolithic builders freely multiplied and divided by 10’s. This is because 10 ten was considered a synthetic number in antiquity. Reason: It totaled any two opposite numbers on the 3 x 3 number square. Diagram is below.  4 + 6 = 10. Or, 9 + 1 = 10. Etc. We now have the following:
  1.  The note A,  underneath Steinway’s name, vibrates 440/per second.
  2. The lowest note on the piano, also an “A” vibrates 27.5 /second.
  3. The length of any side of the square base on the pyramid is 440 cubits.
  4. The height of the truncated Great Pyramid of Egypt is 275 cubits

Image result for picture of the 3 x 3 number square on dsoworks.com

 

 

Numerical nature of ancient mathematics

Triple Grand Unity of Chemistry, Geometry and Number Squares

Triple Grand Unity of Chemistry of Geometry and Number Squares. They are also called magical number squares. It’s time to regain contact with mankind’s past. Magic number squares date back to prehistoric times. Wikipedia’s definition of the square is as follows:  In recreational mathematics, a magic square[1] is a {\displaystyle n\times n}n\times n square grid (where {\displaystyle n}n is the number of cells on each side) filled with distinct positive integers in the range {\displaystyle 1,2,…,n^{2}}{\displaystyle 1,2,...,n^{2}} such that each cell contains a different integer and the sum of the integers in each row, column and diagonal is equal.[2] The sum is called the magic constant or magic sum of the magic square. A square grid with {\displaystyle n}n cells on each side is said to have order n.

triple grand unity of number squares, geometry and chemistry
The periodic charted was coded longer than 10,000 years ago on the simplest number square.

First note the vertical pattern of numbers on the periodic chart:

  • Lithium (atomic number 3) minus a hydrogen atom (atomic number 1) = 2.
  • Sodium (atomic number 11 under lithium)  minus the 3 = 8.
  • Potassium (atomic number 19 under sodium) minus the 11 = 8.
  • Rubidium (atomic number 37 under potassium) minus the 19 = 18
  • Cesium (atomic number 55 under Rubidium) minus the  37 = 18
  • Francium (atomic number 87 under Cesium) minus the 55 = 32.

Here’s the Triple Grand Unity of the Neolithic Times

Egyptians knew all about this triple grand unity. It's all to be found documented at the Great Pyramid.
The main purpose of the Great Pyramid is to show the many ways that number squares can be used. This is lost knowledge.

Now, let ‘s look at the grid lines of the 3 x 3 number square. It is pictured just under the excerpt from the periodic chart above. . Only number 2 is found directly. Numbers 8, 18 and 32 come as square roots of whole line segments of the grid. Here’s how it works:

  • A to F (on the dotted line segment on the left side. Any side will due, of course.) = 2
  • The diagonal from points “A” to “E” (where the two dark lines meet at right angles) equals √8.
  • Line BD (the entire diagonal of the complete square) equals √18
  • Finally triangle ABD or CBD equals √32.

The numbers of the magic square  and the periodic chart  are the same:  2.8.18 and 32. A number of my blogs are about how number squares mathematically display elemental properties. Was this knowledge known to the Neolithic cultures that used number squares? Was there an advanced civilization at one time in the distant past that was destroyed? Possibilities are many. More blogs in the future will deal with this.

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Neolithic Periodic Chart is Number Squares

Neolithic Periodic Chart is Number Squares, Here’s How

Neolithic Periodic Chart is Number Squares. Do number squares point to the existence of a super advanced civilization? Did Atlantis once exist? Was this knowledge destroyed whe the library at Alexandria was burned down? Anyone with a mathematical mind should say yes to all the above. Study the two number squares of the featured picture. Each of the number squares had a planetary association.

  • The charactertistic number is what any two opposite numbers total. Any two opposite numbers on the 9 x9 square above total 82. This number number square of the Moon defines the atomic number of the ash of nuclear fission. That is lead-82.
  • The characteristic number on the 5 x 5 number square is 26. Iron has a 26 atomic number. Iron defines the limits of nuclear fusion on stars. When enough iron is fused at the core of a star, the star explodes.  That is what creates the heavier elements.

What’s So Special About This Aspect of the Neolithic Periodic Chart

These numbers (26 and 82) point out a relation of fission to fusion. It does so as the ratio of a circle to a diameter. The number π is a mathematical constant, the ratio of a circle‘s circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter “π” since the mid-18th century, though it is also sometimes spelled out as “pi” (/p/).

A diagram of a circle, with the width labeled as diameter, and the perimeter labeled as circumference

 The circumference of a circle is slightly more than three times as long as its diameter. The exact ratio is called π.  π is commonly defined as the ratio of a circle‘s circumference C to its diameter d:[8]
Let’s look once more at the two characteristic numbers. 1st on the 9 x 9 we have 82. Then on the 5 x 5 we have 26. Next, 82÷26 = 3.1538461…Using number squares, this becomes a close approximation of pi. Pi = 3.14159…What is even more remarkable is how the 3 x 3 number square ties into the formula. Look at the middle vertical column.
  • The top number is 9. When squared, it becomes the basis of the 9 x 9 square.
  • Just underneath we have the central 5. It becomes the basis of the 5 x 5 square.
  • The 1 represents the atomic number of hydrogen.  Number one  is unchageable by squaring. It is the the basic building block of all the elements. The central  9-5-1 column of the 3 x 3 number square is animated in the fisssion-fusion process by their squares.  Ancients knew this. It’s about time we did.
Image result for pictures on DSOworks.com

 

Greco-Hebraic Bond Through THis Design

Greco-Hebraic Bond by Number 3168

Greco-Hebraic Bond by Number 3168. This “3168” figure is virtually ubiquitous throughout the ancient world. John Michell discusses 3168 in City of Revelation. Chapter VII is entitled: 3168, the Perimeter of the Temple.  He also discusses how the number ties into measurement. Here is a brief excerpt.

  • 31,680 inches = ½ mile.
  • 31,680 feet = 6 miles
  • 31,680 furlongs (660 feet) = radius of the Earth (3,960 miles).
  • By an ancient science called gematria, the Greeks equated 3168 with “Lord Jesus Christ.” See City of Revelation p.82. This is found in the ancient Greek practice of equating numbers and letters called gematria. Hebrew does the same. So do many ancient languages.
  • Image result for picture of City of Revelation by John Michell

Greco-Hebraic Bond is Quite Unique

In my featured picture above we have the blueprint and numbers of “the ancient temple plan.” Here we find the Greco-Hebraic bond. This is a source of ancient building. The idea was to draw on the numbers of this blueprint. Whatever units of measure you used didn’t matter. The idea was to draw on the numbers. It could be numbers in shorter Egyptian cubits (1.718 feet) , Palestinian cubits (2.107 feet) , English yards (3 feet) or even megalithic yards (2.72 feet).  Please notice the outer hexagon  numbers 528 on each side. Multiply number 528 by the 6 sides of the hexagon and we have: 528 x 6 = 3168.

Image result for pictures of Oquaga Lake
A spirit hovers around pure, spring fed Oquaga Lake

You are probably wondering how or where I discovered this ancient temple plan. I found it on beautiful Oquaga Lake. While I was hiking, the Oquaga Spirit offered me the vision in the featured blog picture. This spirit has became a part of my life. This is true even when I am away from Oquaga Lake. I’ve memorized every poem this spirit has dictated. I recite the poems to myself daily. The result was the poetry book entitled, The Oquaga Spirit Speaks. From the Greco-Hebraic bond to wisdom about number squares, the spirit freely offered knowledge to me. In turn I am sharing her knowledge with you.

 

 

fourfold celebration is lucky here's why

Fourfold Celebration While You’re on the Subject

Fourfold Celebration While You’re on the Subject. Why fourfold? The answer goes back to at least Mesolithic times. That is, 9,000 B.C. Number squares were at the basis of ancient cultures. The 1st possible odd number  square is 3 x 3. It has one number at its center. Then comes 4 x 4. It has 4 numbers at its center.Below are the classic outlays of these number squares.

Related imageImage result for 4 x 4 number square on DSOworks

Genesis 1:1  is based on these 2 number squares. God described everyday of creation in the Torah as “good”. In Hebrew the  letters double as numbers.  An example: There was no separate “A” and #1. The Hebrew “aleph”  “אָ”,was both “A” and #1. In this manner, the  word for good, Tov, totals 17. Look up the Greek word, gematria. It defines the common  shared symbols by number and letter.  In Genesis everyday of creation is  described “Tov”.  (good), טוֹב.  it is formed by the math 4 x 4 number square.  Any row of 4 numbers totals 17. Also:

  • All potentialities for creation lie at the 4 fold core of this number square;
  • The numbers 1 to 16 total 136. Add them one after the other.
  • Now look at the square’s 4 central  numbers. Cross multiply each set. Then add them. As-  (10 x 7)  +  (6 x 11) = 136.

Next consideration.  The he 3 x 3 number square defines limits. It confines as it is, at least on appearance, the smallest number square.  On the last day of creation, God used the adjective “very” with the word, good.

“טוֹב “מְאֹד, “Very” has a 45 gematria.

Genesis I: 31 And God saw every thing that He had made, and, behold, it was very good. And there was evening and there was morning, the sixth day. Very “מְאֹד” in Hebrew has a 45 gematria. The numbers 1- 9  total 45. It defines the 1-9 square of three. God limits by this number square. Fourfold blossoms into full potential. The 3 x 3 number square is the smallest. When creation is finished, God draws on the 3 x 3. It limits. Thus, the final day is described as: טוֹב מְאֹד. “Very good.” He created, but he also stopped.

The Fourfold Celebration of Black Elk

Fourfold is at the basis of the vision of Black Elk. We find another fourfold celebration, He was from the Sioux Oglala tribe. Here is a small excerpt from one of my earlier blogs. For the full story click on the blue heading.

Black Elk of the Sioux

Black Elk was a medicine man for the Oglala Sioux Indians. He related his story to John Neihardt.  In 1932 Neikhart published Black Elk Speaks: This is an excerpt. “Younger brother,” he said, “with the powers of the four quarters you shall walk”… (quote from an ancient grandfather speaking to Black Elk  in Chapter 3 of Black Elk Speaks). Never overlook the wisdom of our own American Indians.

 

A triad trinity is at the basis of any keysignature

Triad Trinity and Temples Play Tick-Tack-Toe?

 

Triad Trinity and Temples Play Tick-Tack-Toe. Musical Temples Become a  Reality in Tick Tack Toe Design. Here’s how: Right below is a blurry picture of the tick tack toe board blueprint that includes the basis of both the Holy Temples in Jerusalem. The First Temple based on the middle row of 3 vertical boxes. That corresponds to the pictured middle, vertical row of the C – E – G triad. On the 3 x 3 number square,  that relates to 9-5-1. The Second Temple was built to include the entire nine-boxed tick tack toe board. The 2nd temple extends the dimensions of the 1st to the left and right of 9-5-1. The First Temple was 60 x  20 cubits. According to the Tanach (Hebrew for Bible), he 2nd temple becomes 60 x 60 cubits.

Judaism and much of the beliefs of sacred  antiquity springs from this 3 x 3 board. It becomes apparent when the boxes are filled with numbers one to nine arranged so that any row of three totals 15. These 9 boxes, in a parallel way can also hold the  9 tones of the primary triads that define a key.The triad trinity  is named (Vertically left to right) tonic, dominant and sub dominant. In the key of “C”, the tonic is C-E-G. It  rests on the  central vertical row of the number square pictured  below.  Thus:

  • The triple-boxed shape of the 1st Temple is likened to the  middle 9-5-1 row of the 3 x 3 square.
  • The dominant of G-B-D occupies the same position as the 2-7-6 to the right.
  • The sub-dominant of F-A-C. occupies the same position as 4-3-8 to the left.

When used in combination, a triad trinity can be seen as outlining  the boundaries of the 2nd Temple. They also define the primary triads of C major.  The grid can hold the three primary triads of any key signature. These three key defining triads comprise 9 tones altogether.

Three main triads and Temples in Israel use the same form
Music as a part of service in the temple is quite fitting.

Related image

Triad Trinity is, Top to Bottom and Vertically Left to Right-  Sub Dominant, Tonic, Dominant

Three Main Triads and the Holy Temples in Jerusalem Use the Same Design
Our pattern of three primary triads is sampled here in C major. It uses the same design as the Jerusalem Temples

So Where else in the Grid Do We Find the Concept of  Musical Temples?

  1. The same grid that was the foundation of the  two Jerusalem Temples sets the basic diatonic musical interval of the fifth by vibrations per second. They are A-440 and E- 660.  Take the numbers two at the time. Go around the perimeter either way. Here is how to find the A-440: 49 + 92 + 27 + 76 + 61 + 18 + 83 + 34 = 440. Here is how to find the E- 660. You get the same sum either vertically or horizontally.  (49 + 35 +  81) + reversed as 94 + 53 + 18) + from the other side: (29 + 75 + 61)  + and again reversed (92 + 57 +16) = 660.
  2. The basic musical interval from which ancient and modern musical systems is the musical 5th. Our more modern music uses key signatures of the Circle of Fifths. Ancient music used individual tones derived by the actual fifth. The key or core number of the 3 x 3 number square is 5. Any other number placed in the center destroys its symmetry. This is the basis of its sacred order.

So How Did I Discover This Approach to the Trinity of Triads?

There is an American Indian spiritual presence on Oquaga Lake in the Catskill Mountains. For years I had been the piano player at Scott’s Oquaga Lake House. This spirit would accompany me on walks in wilderness. I call on it by the name of the Oquaga Spirit. On my product page of DSOworks I have some 80 of her poems. It is called, The Oquaga Spirit Speaks. I also have a free thumbnail of me reading the spirit’s poetry. It is on the front page. Here is a sample couplet: If it’s life you wish to live and enjoy to the marrow, then get thee a walking stick and hear the morning sparrow. 

Oquaga Spirit Speaks

3 Measuring Rods of the Great Pyramid

Octahedron Unifies Space Time in Ancient Cultures

Octahedron Unifies Space Time in Ancient Cultures. It does so from an Earthly viewpoint. First of all, what is an octahedron? It is one of the 5 regular polyhedrons. The other 4 are the tetrahedon, icosahedron, cube and dodecahedron. However you view any one of them, it is totally symmetrical. . Together they are also called the Five Platonic Solids. How is the octahedron identified? By its number corners, edges and faces. It has the following:

  • 8 faces
  • 6 corners
  • 12 edges
  • These total 26 topological features. See the featured picture above

Hexahedron.png
Cube
(dual polyhedron)

The octahedron has a non- identical twin brother (or sister). It is called a cube. They don’t look alike. But consider this. The cube has:

  • 8 corners
  • 12 edges
  •  6 faces

The twelve edges are the same in both. Whereas, the number of faces and corners trade places. They are as closely connected as twins. The octahedron pictured below contains a cube. The 6 corners of the octahedron have their points touching the center on the 6 faces of the cube.  For that reason, they are called dual polyhedrons.

File:Dual Cube-Octahedron.svg

So How is it That the Octahedron Unifies Space Time?

Unfortunately, the Egyptian Library at Alexandria was burned down. Its wisdom describing prehistory was destroyed.  Both the cube and octahedron were considered to be harmonious figures. This thought actually goes back to at least 11,000 B.C. Why harmonious? Because of the numerical relationship of its topology.

  • 12 is one-third greater than 8
  • 6 is one-third less than 8.
  • Eight is the number that defines the musical octave. That is the most harmonious and fundamental overtone of the entire overtone series. Guy Murchie thoroughly explains this in his two volumes of The Music of the Spheres.

How Does This Knowledge Date Back to Prehistoric Times?

The holiest sites of antiquity were designed as cubes or square base pyramids. The square base upright pyramid is found in the top half of the octahedron. Although the bottom half is not there, it is implied. As a cube, the Biblical Holy of Holies was set in back third of Solomon’s Temple. The total  rectangular perimeter of  the temple was 60 x 20 cubits.  The 20 x 20 cubit back  third becomes cubic. Also, the Ka-aba in Arabic literally means, cube. 

Much of the  world order of antiquity was destroyed. The cause was invaders from Afghanistan. The invaders were called Kurgans.  Riane Eisler discusses this her The Chalice and the Blade.

chalice-blade-cover
An award winning book by a great author

What was the purpose of these Holy Sites? – To spread harmony and peace throughout the world. This was effected by their geometric harmony. Since many were destroyed, war has ensued. In unity we find peace. In division we find war. The octahedron unifies space time. It defines space as a geometric form.  How does it define time? Each vertex of the regular triangles holds 60°. The 4 upper triangles of the octahedron have a total of 12 vertices. 12 x 60° = 720°. The lower 4 triangles total 12 vertices. They  also total 720°. The upper 4 triangles represent the 720 minutes in 12 hours of daytime at the equinox. The lower 4 triangles represent 720 minutes contained in 12 hours of nighttime also marked by the equinox.

Conclusion: Look for harmonious  models. Base civilization on  these models. Peace follows. The ancients did in through geometry. The same can also help us today.