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.
Artists Help Multitudes on their Life’s Journey. Those who read my posts know the importance of a particular spiritual presence. I call it the Oquaga Spirit. Its haunt is Oquaga Lake. However, sometimes it visits other lakes in upstate New York. The rugged and beautiful terrain of this area has inspired many artists. Among the most colorful was Washington Irving. Here is an internal link. I wrote many books on this lake. The poetry seems to have been dictated by a spirit. I call her the Oquaga Spirit. I sense she was from the Lennie Lenape. Their dwelling was throughout the area including New Jersey. Below, I offer some poetry dictated by the Oquaga spirit. That particular year, summer of 1985, the spirit spoke in quatrains using the rhythm of iambic pentameter.
The Lenape (English: /ləˈnɑːpi/ or /ˈlɛnəpi/), also called the Leni Lenape, Lenni Lenape and Delaware people, are an indigenous people of the Northeastern Woodlands. Theylive in Canada and the United States. Historical territory included present-day New Jersey and eastern Pennsylvania along the Delaware River watershed, New York City, western Long Island, and the Lower Hudson Valley.[notes 1]
Artists Help Multitudes Thanks to a Spiritual Presence
Laughing and Crying
(written with inspiration offered by the Oquaga Spirit)
A narrow wall separates laughing from crying.
Laughing and crying both create tears.
At times it’s difficult to decide which is there.
Certainly, they may both exist side by side.
Tears enable their creator to release tensions.
Tears then become the liquid to cleanse the mind.
It can enhance a mood that is already joyful
Or release the sadness that burdens its holder.
Kings were well aware of the worth of laughter.
Jesters were given a place of honor in the court.
Musicians were once honored for the same reason:
Beautiful playing can create tearful happiness.
Comedy and music are necessary arts for mankind.
The Greeks even personified these arts as Muses.
We would be wise to carefully nurture our artists.
Artists help multitudes purge away problems.
Reversing Polarities in Math and Music. First, let us define polarity:
- the relative orientation of poles; the direction of a magnetic or electric field.plural noun: polarities“the magnetic field peaks in strength immediately after switching polarity”
|synonyms:||difference, dichotomy, separation, opposition, contradiction, antithesis, antagonism.|
Reversing Polarities in the Number Square
Many blogs on DSOworks are about this basic 3 x 3 number square. They are easy to access. I’ll use the bar figure of the numbers 9-5-1 for purposes of explanation. Taken as a straight read, any three numbers that cross the central 5 in a straight line is its own number backwards. It is just like a bar magnet. The number that always occurs is 1,110. Here, 951 + 159 = 1,110.
Next, let’s cut these numbers down the middle. We now have 95 and 15. This still has its North and South poles. This is like the split bar magnet on the left. Note: 95 + 15 =110. Reversed- 59 and 51 =110. These numbers are smaller than the initial 159 and 951. However, they still have their poles. A theme on DSOworks.com is how this number square sets the cosmos in motion.
Reversing Polarities in Triads or Key Signature Relationships
The subdominant and dominant relationship mark the extremes in the poles of the keys. The tonic draws these two opposite keys together. Here’s how:
- The highest note of subdominant “F” chord is “C”. That is also the lowest note of the tonic triad.
- The highest note in the tonic triad example here is “G”. That now becomes the lowest note of the dominant “G” triad. This central “C” triad bonds the extremes together.
- Finally let’s cut the three letter names so “G” now becomes the central note. “C” is now set to the left. “D” is now to the right. This becomes like cutting the bar pole magnet in two new parts.
Conclusion: Polarity refers back to the 3 x 3 number square. I would like to conclude a picture of an emblem of the Lennie Lenape. They have a wonderful motto: “we are all family”. The Lenape (English: /ləˈnɑːpi/ or /ˈlɛnəpi/), also called the Leni Lenape, Lenni Lenape and Delaware people. They are an indigenous people of the Northeastern Woodlands. They live in Canada and the United States.
Faith Comments in poetry by the Oquaga Spirit. What is faith? Nature speaks. On Oquaga Lake she speak a lot. She talks on cloudy days. She talks sunny days. I was fortunate to make the acquaintance of the Oquaga Spirit on hikes in the Catskill mountains. Oquaga Lake in surrounded by forests. My spirit on the lake was a female. She was of the Lennie Lenape tribe, The internal link explains how the women were in charge of the community. The spirit spoke in the 1st poem in 1985. Ten years later, 1995, she spoke once more of faith. This poem also will be the subject of a 2nd blog. Faith and knowledge help spiritual growth.
|Religion was primarily an individual matter for Woodland Indian people. It permeated everyday life. The world of the Great Lakes Indians was filled with a host of spirits (manido; plural manidog). They inhabited trees, plants, birds, and animals. I have one internal link. For a span of over 15 years, I was their house piano player.|
Cosmic phenomena were considered spirits. These included the sun, the moon, thunder, lightning, the four winds, and the thunderbirds. The Great Lakes Indians gave offerings of tobacco. These offerings were constantly given. They had many purposes. Among them:
Faith Comments on “Faith” – Different takes. Here is the earlier one of 1985
The wise know that the Sun shines behind the clouds.
Though the day be dark, they believe in light.
Knowing that clouds, no matter how thick, will disperse;
And clouds are only temporal; while the Sun endures.
Those without faith falter when the skies darken.
Seeing the heavens overcast, they forget the source.
And become despondent, thinking the day is done.
Their sight is stopped short by mere fluffy veils.
Those unfortunates scoff at the utopian belief in faith.
For them the vapor of clouds is more real than the divine.
And if there is no overcast, they’ll sow the seeds of rain;
Making reality confirm to the clouds in their heads.
Clouds are but thin impostors above us.
A mask to fool those of little faith.
For even in the thick of a full-fledged storm.
The eternal source of happiness is somewhere shining.
Faith requires the patience to out wait the darkness.
The fury of winds, rain and hail combined
Often come to test the tenacity of man.
But in the face of faith, the storm will fade.
Faith Comments Also Apparent in Pictures
Aquarian Number Square of Saturn is Being Activated. Each planet has its own number square. This parallels each astrological sign being ruled by its own planet(s). Here is the traditional association:
- 3 x 3 rules Saturn.
- 4 x 4 is Jupiter.
- 5 x 5 is Mars.
- 6 x 6 rules the Sun.
- 7 x 7 rules Venus.
- 8 x 8 is Mercury.
- 9 x 9 is the Moon.
The planet Uranus was discovered by William Herschel, Date was March 13, 1781. Before then, Saturn was the sole ruler of Aquarius.
Nicholas Campion wrote a book,The Book of World Horoscopes. It lists various references. These are about astrological sources for the start of the Age of Aquarius. Based on Campion’s research 29 “experts” claim it arrived in the 20th century. The 24th century in second place with twelve claimants.
My conclusion as to the Aquarian beginning sides with the 20th century. Why? I was privileged to gain insights of the ancients into the 3 x 3 number square. It was of Saturn. The numbers interact in an infinite number of ways. It looks like the smallest number square. But, it is the largest due to interaction by polar opposites. Interaction is an integral part of love and brotherhood.
Aquarian Number Square of Saturn is to the Left
The musical Aquarius discusses the essence of this age:
And Jupiter aligns with Mars
Then peace will guide the planets
And love will steer the stars
This is the dawning of the age of Aquarius
Age of Aquarius
Sympathy and trust abounding
No more falsehoods or derisions
Golden living dreams of visions
Mystic crystal revelation
And the mind’s true liberation
Weather Also Points to the Arrival of the Aquarian Age
Professionally I am a piano player. Many summers were spent with my family on Oquaga Lake. It is located by Deposit, New York, Location is just over the Delaware river. I was the piano player at Scott’s Oquaga Lake House. The area was the former dwelling place of the Lennie Lenape tribe. I led many hikes through the Catskill Mountains. There, I sensed a female spirit’s presence. It communicated its knowledge of this number square. Perhaps the 3 x 3 number square is merely the icing on an already served delicious, Aquarian cake?
Interrelationships of the Past Crossed Disciplines. Numbers were an ancient reasoning tool. Ancient philosophers and priests used common numbers to emphasize similarities. This blog simply illustrates one example: How Great Pyramid and the Platonic solids use the same numbers. I’ll walk my reader through the meaning of two diagrams.
First: The dimensions of the Great Pyramid. Its essential dimensions are: Square base is 8 x 8 great cubits. The four triangulated faces peak together at 5 great cubits: Note-
- The base is square. It measures 440 shorter Egyptian cubits of 1.71818.. feet on each side.
- One Great Cubit is 55 of such smaller cubits.
- The Great Pyramid measures 440 cubits or 8 such great cubits on each side.
- The truncated height is 275 of these smaller cubits.
- By great cubits this becomes 5.
Next we turn our attention to the 5 solids. First, 5 is the key number for both: The Great Pyramid has 5 faces. There are 5 Platonic solids.What is the source of five? It is not an arbitrary number. Look at the 3 x 3 number square. Five is at its core. Very important: Interrelationships are deeper than they appear on this number square. Through opposite polarities they go to infinity! One example is in the next paragraph.
I mentioned each side of the Pyramid is 440 cubits. Where is 440 n this number square? For this I must credit an Indian spirit I believe to be from the Lennie Lenape tribe. I spent many summers on Oquaga Lake.
Take the numbers around the perimeter. Add them two at the time as follows: 49 + 92 + 27 + 76 + 61 + 18 + 83 + 34 = 440. It is the same forwards or backwards. Each side of the square-based Great Pyramid is 440 cubits. It’s the numbers that are important: Ancients of varied civilizations attached their own units of measure to these key numbers. What was the primary reason the Great Pyramid was built?
- To illustrate every way the 3 x 3 square can function.
- With this knowledge, a new Golden Age of Peace and Plenty can be implemented
Next, look at the illustrations of the Platonic solids. Vertical column one (on the left) totals the features each solid. Each of the five has its own horizontal column. This shows the added horizontal values. Here is the total number of faces, corners and edges for each solid. In other words, the topology.
- The tetrahedron has 14.
- The cube has 26.
- The octahedron has 26.
- The icosahedron has 62.
- The dodecahedron has 62.
This information can be found in standard textbooks on geometry. Next the chart reduces these topology numbers as follows:
- Fourteen: 1 +4 = 5. This is for the tetrahedron.
- Twenty-six: 2 + 6 = 8. This applies to the cube and octahedron.
- The third different number is sixty-two. 6 + 2 = 8. This applies to the dodecahedron and icosahedron.
We thus see four eights and one five. That duplicates the four-square base of 8 Great Cubits on each side and the pyramid’s height of 5 Great Cubits.
Ancient Computing Utilized the Platonic Solids. First: What are the Platonic solids? In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size) regular (all angles equal and all sides equal) polygonal faces. They have the same number of faces meeting at each vertex. Five solids meet those criteria. That’s it. A 6th cannot be constructed.
|Four faces||Six faces||Eight faces||Twelve faces||Twenty faces|
The tetrahedron is the basis of the other four solids. Look at the 1st five numbers. With that knowledge, here is some mathematical fun. 1² x 2² x 3² x 4² x 5² = 14,400. Where is 14,400 significant as an ancient number?
The tetrahedron is the basic unit of the five.
By vertices, its 4 triangles total 720º (4 x 180° per triangle). Then 7 + 2 + 0 = 9.
The solid whose faces contain the most degrees of the 5 is the dodecahedron
With 9 x 720° = 6,480°. (This is exactly 9 x the tetrahedron’with 720° degrees). (9 x 720 = 6480). Its second way is, 6 + 4 + 8 + 0 = 18. Reducing the number by horizontal adding of the smaller numbers, 1 + 8 = 9.
With the remaining three solids: Cube has 2,160°. Each of its 6 squares has 360°. Thus, 6 x 360 = 2160. That is 3 times the 720° of the tetrahedron. Reduce 2160 and we have: 2 + 1 + 6 + 0 = 9.
Icosahedron has 20 triangles. Every triangle has 180°. Thus, 20 x 180 = 360o. That is five times the 720 ° of the basic tetrahedron. Reduce 3600 and we have: 3 + 6 + 0 + 0 = 9
Finally, there’s the octahedron with 8 triangles. 8 x 180° = 1440. That is 2 x the 720° of the tetrahedron. Then 1 + 4 + 4 + 0 = 9.
In content and quality number 9 imbues the regular solids.
Ancient Computing had a Source
- Why was number 9 the limiting number of the Platonic solids in the manner described above? I like to call the nine-boxed digits in the number square below the “stamping mill of the Universe.” Nine is the highest number of the traditional arrangement of the pictured numbers.
- A second mystery: Why are there only 5 possible regular polyhedrons? Because 5 is the core number of the 3 x 3 number square. The infinitely complex Universe is stamped out from this simplest of number squares.
- A third mystery to solve:: Why was a megalithic mile 14,400 feet? How did it relate to King Arthur’s Palace? The answer is simple. Total the number of degrees in the 5 solids. They are listed above. We have, 720 + 1440 + 2160 + 3600 + 6480 = 14,400. Now read the internal link below.
Mesolithic cultures worked with the 3 x 3 number square for ancient computing. Roses hold a primary ancient secret. Again, read this internal link. The high priests of various cultures and countries knew its secrets. Another known entity was how this tiny number square can become infinite. Link is also below. I’m attempting to restore this lost knowledge. My insights all took place on Oquaga Lake. I was the house piano player at Scott’s Oquaga Lake House for years. I communed with a female Indian spirit from the Lennie Lenape. This numerical square could offer a common vision based on balance. That, in turn, could initiate another Golden Age.
Joyful -When Radiated By Anyone- Elevates Stature. This is to the highest levels. This blog will attempt to answer how and why. It ties into an ancient Middle Eastern concept called gematria. It refers to the sharing of a letter and number by the same symbol. Once there was no separate notation for letters and numbers. That is foreign to our current day thinking. In the Middle East it was common. Hebrew still illustrates this in the calendar:
Some words had the same numerical value. This is true with the two key Hebrew words: joy and Redeemer. Also, within a phrase, one (1) could be added without changing the essential numerical meaning. This was called the colel. This blog makes the point: Any happy person helps all mankind. This is true regardless of religion or nationality.
The two Hebrew words, joy and Messiah, both have a value of 353. The words are given below.
Original Word: מָשִׁ֫יחַ. This translates to the Redeemer, Messiah.
A Joyful Gematria
In addition to this 353 co-incidence, we’ll examine two more correspondences: In Greek gematria it specified Hermes. Key numbers were once shared by even different cultures. Read my 353rd blog. The link is given below.
Now for the ancient source of 353: It is hidden in a well known number code. Read the internal link below called 3 x 3 number square Archives.The code hides 1110: When 1110 becomes a circumference, then 353… becomes its diameter. At one time number squares structured civilization. They formulated a peaceful era.
Finally, 352 is the gematria of the two words that immediately precede Judaism’s most important prayer- Hear O Israel. Milk and honey are the last two words of Deut: 6:3. Hear O Israel are the first words of Deut. 6:4. These words in Deut. 6:3 are translated into as “milk and honey.” Read another internal link below. What does this mean? When the lost codes hidden in the 3 x 3 number square are activated, the lands will flow will “milk and honey.”
Open Mind in my Book of Poetry-The Oquaga Spirit Speaks. Who or what is the Oquaga Spirit? She is an essence that dwells around Oquaga Lake. I believe the spirit is that of an American Indian. She was of the Lennie Lenape tribe. Lenape kinship system has matrilineal clans. Children belong to their mother’s clan. From the mother’s clan, children gained social status and identity.
I (David) was the house piano player at Scott’s Oquaga lake House. My employment covered a span of about 25 years. In the mornings I’d stroll and the spirit would be afloat. “So much she needed an ear, she ignored my tranquility.” Some years we did not go to the lake. That was primarily when our children were in school. Over the decades the spirit changed her mode of communication. She primarily used two forms of poetry. Also, she instructed me on the hidden codes in number squares. I have been sharing her wisdom through this website.
Rustle, Rustle, Rustle Goes the Wind – Mentions an Open Mind
Quote from the Spirit’s Poem, Rustle, Rustle, Rustle Goes the Wind:
Open the windows of you mind
To let the summer breezes through.
Then the scented summer wind
Will swoosh by to renew you.
- In the 1980’s she preferred iambic pentameter in quatrains.
- During the 1990’s she spoke in rhyming, triple meter. She also communicated her poetry in quatrains Here’s how quatrains are beneficial: . Quatrains of poetry invoke Jupiterian influences. Jupiter is the thinking-person’s planet. It is the guardian of the abstract mind. This planet rules higher learning. It bestows a yen for exploring ideas. This is both intellectually and spiritually. Number squares were once the guiding light of lost Golden Age. Also of key importance importance was the simplest number square. Ironically, it is also the most complex. It actually hides infinity. Check out my internal link below. You don’t even need an open mind for this blog. The math speaks for itself.
- Quatrains, in sets of four, invoke the 4 x 4 number square. Musical phrases also come in sets of 4 bars. They are called antecedent and consequent phrases. This same number square hides the pattern of the Fibonacci series. I believe we will enter a new Golden Age of Peace and Plenty. The wisdom of the American Indians can lead the way.
Below is an internal link to a poem entitled “Future Fog”.
$7.99 Oquaga Lake is located up the mountain from Deposit, NY in the foothills of the Catskill Mountains just across the border to Pennsylvania. This spring-fed lake is rated one of the cleanest in New York State. At points it’s over 150 feet deep. The lake’s diameter is about a mile across. Overall, its outline resembles a bear.
Number Square Standard Set by Sparta/Athens. There are two types of number squares. First are the odd numbered. Sparta puts forth the odd ideals. This is set in the 1st number square. It is the 3 x 3. The second type are the even. Athens was the prototype of the 4 x 4 number square. It is the 1st even number square. This blog will concern itself only with centers of these 1st two squares in this infinite series. As described by Hesiod, peace and plenty once marked a lost Golden Age. It was maintained by these number squares. Below are couple of internal links. They can offer an idea of how they were used.
Number Square Standard of Sparta/Athens Identified
Here is a quick review of some basic ideals of each of these two city-states and the number square standard.
- Athens was a center for the arts, learning and philosophy. It was the home of Plato‘s Academy and Aristotle‘s Lyceum, Athens is widely referred to as the cradle of Western civilization and the birthplace of democracy,
- Sparta was unique in ancient Greece for its social system and constitution. They configured their entire society to maximize military proficiency. It was completely focused on military training and excellence.
So What About the Number Square Centers for Sparta and Athens?
- In Sparta, military used rank, order, rigidity in a caste system. Thus the center of the 3 x 3 number square seemingly stands alone. It is marked by number “5”. It does have interconnections. However, they are there but lie hidden.They have been waiting for a Golden Age to be uncovered.
- In Athens both culture and philosophy, as is true everywhere, are based on interconnection. Here’s how this parallels the 4 x 4 square. : Note the 4 numbers at the center of the 4 x 4 square. Set one consists of 6 + 11 = 17. Set two has 10 + 7 = 17. Here we have a central equality by addition. The equality exists in a second manner way by multiplication: Take the same two pairs of numbers. This time, multiply them as ( 6 x 11) and (10 x 7). As 66 + 70, they total 136. Next, total the square’s individual numbers from 1 thru 16. They total also 136. This means the full numerical potential of the square exists in this cross multiplication and then addition of the four central numbers in the manner described. This sets the pattern for all even number squares.
Conclusion: These two city states were conceived to represent the two aspects of a lost number square order. They graphically illustrate the basic concepts behind both types of centers. The 1st chapter of Genesis accomplishes exactly the same. It has also preserved this lost order for the future. The time is here to revive this happy and even joyful, lost epoch. My education and understanding of number squares came from a female spirit belonging to the Lennie Lenape. The Oquaga Spirit Speaks is such a product on DSOworks.com. Click on the link below.