Three Square Code Structures Stonehenge. Life often offers us the polarity of opposites. Something stands in opposition to something else.

This tiny number square gives rise to the pillar arrangement at Stonehenge. It was used in countless ways by ancient historic and even prehistoric civilizations. Currently we are entering a new age. It will be marked by peace and plenty. This is also known as a Golden Age. The same arrangement that formed the Palestinian cubit and the Egyptian cubit also structured the pillar arrangement at Stonehenge. Some information I quote from my own internal link below:

Abu Mūsā Jābir ibn Hayyān explains how this number square was divided into various corners and gnomons. I show how the dotted points below were the options that were used for the appropriate Egyptian and Palestinian cubits. It was also used for builiding Stonehenge.

Multiply the 4 corner numbers: 5 x 7 x 1 x 6 = 210. The Palestinian cubit is 2.107 feet.

Multiply the remaining five numbers which are called the gnomon: 8 x 3 x 4 x 9 x 2 = 1728. The larger Egyptian cubit is 1.728 feet.

15th-century European portrait of “Geber”, Codici Ashburnhamiani 1166, Biblioteca Medicea Laurenziana, Florence

Three Square Code Uses Lower Right Corner and its Gnomon for Stonehenge

Numbers in a row are called a sequence. Sequence is also used in music and dance. Stonehenge uses 5,6,7, and 8:

5 x 6 = 30. This numbers inner stone circles.

7 x 8 = 56. This numbers the outer holes.

Plan of the central stone structure. The stones were dressed and fashioned with mortise and tenon joints before 30 were erected as a 108-foot (33 m) diameter circle of standing stones, with a ring of 30 lintel stones resting on top.

For fun, add 5 + 6 + 7 + 8 = 26. Now, let’s look at the two products and one sum we created from consecutive numbers 5,6,7 and 8: They are 30, 56 and 26. Any beginning student of chemistry knows these numbers define the most stable isotope of iron: (1) 30 neutrons. (2) atomic number 56 (3) Finally 56 – 30 = 26. That is the atomic number of iron. Why is this important? Iron is the ash of nuclear fusion on stars. When enough iron is at the star’s core, it explodes. This creates all the heavier elements than iron.

Here’s the big question: Does Stonehenge represent the cosmic stellar process of creation? Was this known in the distant past? Or, is this just another numerical co-incidence?

Plus one factor shared by Geometry and Math. This post applies to all of the prominent ancient number squares. For various reasons, they are also called magic squares. What characterizes these squares of numbers? In recreational mathematics and combinatorial design, a magic square^{[1]} is a {\displaystyle n\times n} square grid (where n is the number of cells on each side) filled with distinct positive integers in the range {\displaystyle 1,2,…,n^{2}}.

Each cell contains a different integer.

The sum of the integers in each row, column and diagonal is equal.^{[2]}

So Where is the Plus One Factor?

The plus one in number squares is one thing above and beyond obvious definition on the number square. Let’s look at the application in geometry first. The 3 by 3 number square is the smallest that can be constructed. It has 2 parallel lines that intersect two more parallel lines. Thus, 3 x 3 columns of vertical and horizontal numbers, are set on a 2 x 2 set of horizontal and vertical lines. Note: By custom, these parallel lines are not encased by a square. Surrounding these nine numbers by a square would then create 4 x 4 parallel lines. In a way, this hides the true nature of the number square in consideration. Number square perimeters should be left open ended as in the featured picture. I must confess, some of my earlier number square pictures are encased.

Here is the mathematical plus one factor: This number square contains the numbers 1 to 9. Any straight row of three totals 15. Opposite numbers total ten. Hence, the following sets of numbers total 10: 4 + 6; 3 + 7; 8 + 2; and 9 + 1. The plus one factor becomes the total of the opposite numbers- 10. Ten is above and beyond the nine. It is not even notated on the prime number square; being invisible, like the Deity. So how does this apply in religious antiquity?

The 1st of the 10 Commandments is the Plus One Factor

The 10 Commandments are thus modeled on the 3 x 3 number square. The 1st commandment is actually not a commandment. It is a statement of the presence of the Deity who is above and beyond everything. He is invisible, like the number 10. Compare it to the “colel” in numbers. That’s why in the 10 Commandments it becomes a statement as opposed the apparent nature of the other nine numbers.

Graphic Polarity Activation on the 3 x 3 square. The prime number square of every higher number square is the 3 x 3. The complete, traditional, square is pictured at the bottom of the featured picture. There are a number of possible arrangements, possibly seven. However, the understanding of the distant past begins with this traditional. Many blogs on DSOworks are about this number square. Check them out by key word. They are free to view. I currently have some 570 posts about two primary subjects: (1) Music (2) Number squares. Most of the posts on number squares about the 3 x 3. It is the simplest, yet the most complex. Both of these subjects were the backbone of a former and lost Golden Age.

The full set of rings, imaged as Saturn eclipsed the Sun from the vantage of the Cassini orbiter. It was 1.2 million km distant, on 19 July 2013. The brightness is exaggerated. Earth appears as a dot at 4 o’clock. Our planet can be seen between the G and E rings. Most important for this blog: The rings of Saturn are the most extensive ring system of any planet in the Solar System. Why is the important? There are three obvious perimeters around this number square. However, the number of possible rings goes to infinity.

Graphic Polarity Activation Instructions

Reference the traditional arrangement at the bottom as I point our a few of the possibilities. Also a have a number of internal links on infinity and this number square. Also, “perfect numbers” favor this number square. Ancients knew this. Today, our civilization does not. Of course, there once was a Golden Age. Today peace and plenty seem be elusive. Here are a couple of such links on DSOworks.com:

Graphic Polarity Activation on Isaiah 45:2-3New International Version (NIV)

^{2 }I will go before you and will level the mountains^{[a]}; I will break down gates of bronze and cut through bars of iron. ^{3 }I will give you hidden treasures, riches stored in secret places, so that you may know that I am the Lord, the God of Israel, who summons you by name.

How does Isaiah allude to graphic polarity activation with the above? Look at the chapter number. It is 45. Total the numbers 1 to 9 in the grid. The order does not matter. Sum = 45.

Next, look at the two verse numbers of the Scripture. They they are verses 2 and 3. The sum of the verse numbers define the central number of the number square. 2 + 3 = 5. “Five” activates the entire system of all number squares. This is the smallest and prototype of all number squares.

Breaking the gates of brass and cutting through the bars of iron allude to reading the numbers without the grid. See the internal links above.

Specific applications will be covered in future blogs.

Please credit an Indian spirit from the Lennie Lenape tribe for my knowledge of this number square. Her haunt is Oquaga Lake at Scott’s Oquaga Lake House. I was Scott’s piano player for some 15 summer seasons. There, I encountered the spirit on hikes in the Catskill Mountains.

Catskill Resort Celebration- my Home Away from Home. The Catskill Mountain Resorts are coming back. It’s possibly starting with Scott’s Oquaga Lake House. I was the Scott’s piano player for some 15 years. Oh boy, are the Catskills coming back! They have just been the background for a wagon load full of prestigious top entertainment industry awards. Some of the list is below, in blue. Immediately below is the Catskill Mountain movie trail from The Marvelous Mrs. Maisel.

Catskill Resort Celebration at Scott’s Oquaga Lake House

Als0, below the picture is link to a special interview with one of the stars: Rachel Brosnahan chats with Jimmy Fallon about the latest season of The Marvelous Mrs. Maisel. She talks about years ago Scott’s turned down the filming of Dirty Dancing. The clip at Scotts, relatively new posts, have 75,00 views.

Above, Rachel is speaking in the press room at the 23rd annual Critics’ Choice Awards. It is at the Barker Hangar. Date is Thursday, Jan. 11, 2018. Location is Santa Monica, Calif. (Jordan Strauss | Invision/AP)

Yes miracles still happen. Just when everybody is ready to give the resort up, this happens. Scott’s will be featured in quite a number of episodes this coming year. I have been the piano player at Scott’s Oquaga Lake House over a span of some 15 years. Hard times hit the resort. Bus loads of people from Ontario, Canada stopped coming. This was due to higher taxes and added health insurance costs on group bus tours. A high percentage of their business was Canadian. In addition to to regular fair, Canadians loved the wilderness and seemingly magical feeling of this pristine, clear lake.

More Catskill Resort Celebration

Here is one of my my contributions to Scott’s Oquaga Lake House: As Rubinoff and His Violin’s arranger and accompanist for over 15 years, I brought Rubinoff to the resort. This was in 1984. At age 86 David Rubinoff also performed miracles. This youtube video is the only complete 44 minute+ concert of his in existence.He took America by storm in the 1930’s. Please also enjoy this rare Scott’s video as I (David Ohrenstein) accompany this “legendary” violinist. He plays his Strad. It belonged to the Czars of Russia.

Lost Concert “Rubinoff and His Violin” on Oquaga Lake, 1984 – YouTube

Last, but not least for my wife, Sharon, and myself. We wrote an opera comique entitled Patra. It will be showcased on Schroon lake in New York state this coming September of2019. The American Center for New Works Development is sponsoring it under the auspices of the Seagle Music Colony. More details on our website. DSOworks.com. Patra has a banner heading. Exact date to be announced shortly. Don’t miss this event!

Hollywood Nineteen Thirties under Rubinoff’s Baton. I frequently blog about David Rubinoff and His Violin. That’s because I worked with him for over 15 years. My capacity was as his arranger and piano accompanist. The years spanned 1971 to 1986. In 1986 Dave passed away at age 89. He was the very model of musical success. This was especially true in Hollywood during the nineteen thirties. I’ll never forget the spontaneity of his reply when I said to him: “Mr Rubinoff, music has been good to you.” He immediately replied as a matter of factly, “Why, that’s because I’ve been good to music.”

You can now listen to a recent concert that I was honored to perform at with maestro Steven Greenman. Steve performs the Fiddler just as Rubinoff intended it. The Ted Lewis Big Band museum curator and conductor extraordinaire, Joseph Rubin, invited me in from Sarasota to play the concert honoring my friend and mentor, David Rubinoff.

Dave’s wife, Darlene Rubinoff, wrote a book about his life. Dave personally dictated it to her as she tape recorded his voice. Eloquence, sophistication, technical prowess, passion and perfection marked his playing. But most of all he openly conveyed the love he had for his audience. In return his audiences loved loved him. This was to the tune of hundreds of thousands annually in the 1930’s. In this regard I must quote Mr. Rubinoff’s words through his angel of a wife, Darlene Azar Rubinoff:

“I worked every hour of the day and night, driving everyone with no conception of time, being only interested in my music and pleasing the public. My audiences screamed and applauded. They were after me night and day, waiting for me outside the stage door for a glimpse or for an autograph. I seldom refused them. They were the reason for my success. That is why I drove the orchestra and the arrangers so hard. I screamed, I cajoled. I even, on occasion, threw things in order to win my way. The amazing thing was, I was always right when it came to my music.”

Please enjoy the internal link below of the concert I gave with Rubinoff in the Catskills at Scott’s Oquaga Lake House. The youtube link is at the end of the blog. It was over 30 years ago. Also, my wife Sharon and I have written a new opera entitled “Patra”. The featured artwork is used by permission from the “From Cairo With Love” art gallery in Cairo, Egypt. It will be premiered in New York on Schroon Lake this coming September. Please read about the details under the “stage”on our front page of DSOworks.com.

Measurement Interchange on the Great Pyramid. The Great Pyramid uses different units of measure. British Antiquarian John Frederick Carden Michell (9 February 1933 – 24 April 2009) was an English author and esotericist who was a prominent figure in the development of the Earth mysteries movement. He discusses how the Great Pyramid was conceived by three primary measurement units: They were (1) the 12″ foot. (2) The 1.71818…foot long, shorter Egyptian cubit. (3) The 2.7272… foot long megalithic yard. In his View over Atlantis, he states that:

“The important discoveries about the past have been made not so much through the present refined techniques of treasure hunting and grave robbery, but through the intuition of those whose faith in poetry led them to scientific truth.”

This is the Measurement Interchange for the Great Pyramid- It Spearheaded a Former Golden Age

I credit the Lennie Lenape NE American Indians for my discovery for my discovery the hidden engineering capabilities of the 3 x 3 number square. An Indian spirit guide accompanied me on walks around Oquaga Lake. I was the house piano player at Scott’s Oquaga Lake House over some 15 summer seasons. She instructed me on the infinite codes hidden in this number square. Read the internal link if you wish to understand the math:

Go around the perimeter overlapping two number at the time: 49 + 92 + 27 + 76 + 61 + 18 + 83 + 34 = 440. The square base of the Great Pyramid measures 440 cubits on each side.

Go around the perimeter again by single numbers and add them: 4 + 9 + 2 + 7 + 6 + 1 + 8 + 3 = 40. Add the numbers of the two perimeters thus far” as 440 + 40 = 480. The height of the un untruncated Great Pyramid is 480 feet.

Add opposite numbers around the perimeter three at the time as 438 + 672 = 1110. This number-1,110- can be found in 7 more ways. The perimeter around the Great Pyramid is also 1,110 megalithic yards.

Thus, we have found the functioning of the three primary units of antiquity demonstrated at the Great Pyramid through this simple number square. Speaking of Michell’s mention of poetry, I have a book of poetry called The Oquaga Spirit Speaks. Here is a sample.

Mexican Pyramid Squares the Circle. First. What is “square the circle?” Squaring the circle is a problem proposed by ancientgeometers. It is the challenge of constructing a square with the same area as a given circle. You may only use a finite number of steps with compass and straightedge. In 1882, the task was proven to be impossible. This was a consequence of the Lindemann–Weierstrass theorem. But wait a minute. Lindemann and Weierstrass did not consider R. Buckminister Fuller’s theories in conjunction with the Mexican Pyramid of the Sun.

Mexican Pyramid Really Spheres the Circle

So who was R. Buckminster Fuller?

R. BUCKMINSTER FULLER, 1895 – 1983

The Estate of R. Buckminster Fuller:

Hailed as “one of the greatest minds of our times,” R. Buckminster Fuller was renowned for his comprehensive perspective on the world’s problems. For more than five decades, he developed pioneering solutions that reflected his commitment to the potential of innovative design to create technology that does “more with less”. Born in Milton, Massachusetts, on July 12, 1895, Richard Buckminster Fuller belonged to a family noted for producing strong individualists. They were inclined toward activism and public service. Fuller developed an early understanding of nature during family excursions to Bear Island, Maine. He also became familiar with the principles of boat maintenance and construction. Below are a couple of internal links for further information.

Comparing the Mexican Pyramid of the Sun and Fuller’s Formula for Packing of Spheres

Packing of spheres in successive layers falls under a formula. It was discovered by R. Buckminster Fuller. It’s the number of the particular layer being considered, squared x 10 + 2. You can pinpoint how many spheres successivelyen circle a central sphere. Here are the 1st five examples.

For the 1st layer, 1² x 10 + 2 = 12 spheres.

The 2nd layer we have 2² x 10 + 2 = 42.

For the 3rd layer, 3² x 10 + 2 = 92.

The 4th layer is 4² x 10 + 2 = 162.

The 5th layer is 5² x 10 + 2 = 252.

Ancients looked at what things had in common by common numbers. This was regardless of unit of measure used. We can thus equate the packing of the 5th layer of spheres with the measure of the Mexican Sun Pyramid. Also, Plato’s Ideal City, in his Republic, had 2520 rings. Is this line of thought just fun? Perhaps. But also, perhaps there is no such thing as mere co-incidence?

Mayan Egyptian Connection Spans Atlantic Ocean. Who were the Mayans? The Maya developed their first civilization in the Preclassic period.^{[9]} Scholars continue to discuss when this era of Maya civilization began. Discoveries of Maya occupation at Cuello, Belize have been carbon dated to around 2600 BC.^{[10]} The civilization still had great endurance. Look back some 3,000 years. Mayan Tikal was around from 250 to 700 AD. At its height during the Late Classic, the Tikal city polity had expanded to have a population of well over 100,000.^{[37]}

Egyptian Mayan Connection

We have no written evidence of connection between the two cultures and their countries. But, we do have similarity by measurement. Many are too fixated on proof by written record. They forget that numbers and letters once shared the same symbol. This practice of using the same symbol for both is called gematria- a Greek word. Only our modern languages (except Hebrew) have separate symbols for both. In effect, when you made a measurement, you also could imply a (1) A word. (2) A phrase. (3) An entire sentence. (4) Even a larger unit of writing translated into numbers.

Great Court at Tikal

A surviving Mayan great court is at Tikal. It outlines a rectangle. East to West is 400 feet in length. North to South is 250 feet in width. The courtyard is flanked by platforms, large temples and pyramids. The ratio of the length to the width of the Tikal courtyard is 8:5. Note 400/250 = 8/5 = 1.6. Compare this to the Great Pyramid of Egypt. One side of the square base is smaller Egyptian 440 cubits of 1.71818…feet. Its truncated height is 275 of the same sized cubits. 440÷275 = 8/5 = 1.6.

Comparing the Great Pyramid’s Dates to the Mayan first civilization in the Preclassic period.^{[9]}

Based on a mark in an interior chamber naming the work gang. and a reference to the fourth dynasty Egyptian Pharaoh Khufu, Egyptologists believe that the pyramid was built around 2560 BC. As stated above, Mayan carbon dating goes back to 2600 B.C. The dimensions of the Mayan courtyard and of the Great Pyramid had the same ratio of 8 to 5. These numbers are part of the Fibonacci series:

Leonardo Bonacci who was born 600 years before Beethoven. The Fibonacci series, named after him. is colored in red. Beethoven used the Fibonacci numbers in composing his fifth symphony. In the internal link underneath, I relate Fibonacci numbers to ancient number squares. I don’t know that Fibonacci ever made the connection?

BEETHOVEN’S DELIBERATE USE OF THE FIBONACCI NUMBERS

Behind Leonardo Bonacci’s back, the highest red number is 55. Each new number is the sum of the preceding two. Number 34 precedes 55. So, let’s continue the series: 34 + 55 = 89. Next, 55 + 89 = 144. Next 89 + 144 = 233 (the length of Beethoven’s opening section). Next 144 + 233 = 377 (which the length of Beethoven’s development section). Beethoven, being the brilliant genius that he was, knew exactly what he was doing. Note in red numbers. Number five is the 1st separated number. It is not consecutive. Almost every composer uses phrases in 4 bars. The genius of Beethoven made the opening phrase 5 bars long on purpose. He knew what he was doing!

The Best Architecture and Music are at Least Based on Tradition

The Egyptian Mayan connection of the 8 to five ratio is found with Beethoven. Of course, in this symphony Beethoven uses many phrases also use 8 bar phrases. When we listen to his 5th symphony it sounds natural. Can you imagine how he must have struggled to make the bar length come out right? Leonard Bernstein says of Beethoven and the 1st movement in The Joy of Music: “he will give away his life just to make sure that one note follows another inevitably.” In conclusion, I think that in addition to an even greater appreciation of Beethoven, we have graphic proof the relationship between music, numbers and architecture in this post: The Mayan Egyptian Connection and even more. This is why music lessons, theory and composition increase aptitude for mathematics.

Steady Eddie Had the Gift of Rhythm. I always seem to have had the best of luck in mentors. Maestro Edmund DeMattia was up there with the best. He recently passed away. I miss him. I’ve always excelled as a composer and am a fairly good pianist. Ed communicated how I could steady my rhythm in performance.

“Steady Eddie” was a Great Musical Innovator of the American Military

The idea for a “National Concert Band” began in 1973. Discussions were held among retired and former members of the four major military service bands in the Washington, DC area. The organization’s two main purposes were: (1) To provide a way for area military musicians to continue to play after retirement. (2) To preserve the concert band tradition of music in the United States. Ed also happened to be one of the founding members of the American Concert Band Association (ACB). The National Concert Band became a member of this professional organization. This was in no small part due to Ed. Because of him, those who retired from military service could continue their music in the National Concert Band .

One of Ed’s last concerts was with my wife and myself. Wife, mezzo soprano Sharon Ohrenstein, is also a composer, lyricist and arranger.

Sharon and I shared in co-composing. We worked together on a couple of military marches for Memorial Day. Link is below to our live performance of “Glory and Honor”. We even had Civil War Re-enactors firing their muskets during the concert on conductor’s cue!

Finally, what I am most proud of in the realm of the American military march. I worked with “Rubinoff and His Violin.” This was over a 15 year span. I was his arranger and accompanist. The American March King “-John Philip Sousa” gave Rubinoff’s career a big boost: He procured a continuous stipend from the State Department for bringing fine music to children in the public schools.

If you enjoyed this blog, please share it with friends. We can all be proud of our wonderful traditions!