Remarkable Foursome is a Mathematical Wonder. It presents quite a take on the Fibonacci number series. It develops into what is called the Golden Ratio. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. The Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics. What sequence defines this series? Eventually the second of two consecutive numbers divided by the 1st = the Golden ratio: φ is the symbol for this ratio.
In mathematics, the Fibonacci numbers are the numbers in a specific integer sequence. Their defining feature is every number after the first two is the sum of the two preceding ones:}
At 1st glance the “foursome” number square and Fibonacci seem in-congruent. But the remarkable foursome fuses the numbers on the 4 x 4 square as follows: Examine it numbers vertically left to right:
First row: 4 + 9 = 13. Then 5 + 16 = 21.
Second row: 14 + 7 = 21. Then 11 + 2 = 13.
Third row 15 + 6 =21. Then 10 + 3 = 13.
Fourth row: 1 + 12 = 13. Then 7 + 13 = 21.
All total are either 13 or 21. Of course, 13 = 21 = 34. This is just the tip of the iceberg. Fibonacci numbers on the square go further. Again look at the numbers vertically. Consider the four vertical rows again. This time add every other number as follows:
Row one: 4 + 5 = 9. Then 9 + 16 = 25.
Row two: 14 + 11 = 25. Then 7 + 2 = 9.
Row three: 15 + 10 = 25. Then 6 + 3 = 9.
Row four. 1 + 8 = 9. Then 12 + 13 = 25.
I know what my reader is thinking: 25 and 9 are not in the Fibonacci series. But, yes they are. Three and five are both Fibonacci numbers:
3² = 9.
5² = 25.
Mathematician Mark Barr proposed using the first letter in the name of Greek sculptor Phidias, phi, to symbolize the golden ratio. Usually, the lowercase form (φ or φ) is used.
Michael Maestlin, first to publish a decimal approximation of the golden ratio, in 1597.
The golden ratio has been claimed to have held a special fascination for at least 2,400 years, although without reliable evidence. According to Mario Livio.
Number Square of the Remarkable Foursome
Number squares were once the backbone of a lost civilization. This time marked a Golden Age of peace and plenty. Tradition associates the 4 x 4 number square with Jupiter. Each planet had its own set of numbers. Jupiter was the leader of the Olympian Gods; Jupiter means “Jovial King” and/or “Father of Thunder.” Jupiter is associated with luck and good fortune. It is the mentor/Guru /teacher of gods. More on internal link below.
Enhancing Jupiter Creates Harmony. With this blog I again try to delve into the destroyed past. So much has been ruined. For one, the Library at Alexandria was burned down during Roman times. It was the jewel par excellence of ancient knowledge. In general, conquerors made it a habit to destroy even traces of their subdued civilizations. Another example was ancient Carthage. It also was subdued by the Romans. About 50,000 Carthaginians were sold into slavery. The city was set ablaze and razed to the ground. Only ruins and rubble remain (feature picture). How did philosophers of the past attempt to prevent such occurrences?
Jupiter was thought to the great benefactor of mankind. This is symbolized in the woodcarving of the listless angel pictured below. It displays the classic 4 x 4 number square in the background. Ancient civilizations used this number code to call on the beneficial effects of Jupiter. In the carving, this square is mounted underneath the bell. The bell meant to draw her attention to it. When it does, she will cheer up. Being a musician, I have blogged extensively about harmony. Reading the 3 internal links below will offer background on this little known topic.
Enhancing Jupiter – This planet was associated with luck, fortune and wealth.
Plato refers to the 272 as the number of harmony in his Canon. Harmonia was the wife of Cadmus. Her name in Greek, spelled with the letters add up to 272. This is by the rules of gematria. Here is the connection between the 4 x 4 number square and harmony. Total all the numbers from 1 – 16 on this square. The sum is 136. Multiply 136 x 2 = 272. Harmony is therefore the twice enhanced value square of Jupiter. That poses a question: Is a person who finds harmony in his is life twice as happy as one who has only found wealth?
Quadripartite Division of Time as an Ancient Tool.The Vikings were fierce warriors and pirates. They built magnificent fortresses,” Søren Sindbæk, a professor of medieval archaeology at Aarhus University in Denmark, said in a statement .
I (David) blog a lot about quadripartite division- 1.e. division into four parts. This goes back to Biblical Paradise. This ideal state was at the crossing of the Tigris and Euphrates rivers.
Why division into four? Ancient to prehistoric civilizations were all about number squares. At the heart of all evenly numbered squares are four squares. In the illustration below they numbers 10, 11, 6, and 7. This is the ancient 4 x 4 square of Jupiter. It was thought to invoke the influence of that planet. Jupiter represented success in action. That action could be military or, simply, business. Or, the Jupiter effect could even apply to interpersonal relationships. Odd number squares, by contrast, have only one square at the center. Many blogs about number squares are on DSOworks.com. The blogs are easy to access. Press all posts. They will lead the way back to a lost and forgotten Golden Age,
Why is Understanding the Quadripartite Division of Time Beneficial?
The following analyzes just one aspect of fourfold cyclic time. Many factors cause cyclic activity. The Moon is a great factor. The Sun is another. Obviously, from the graph below, sunspot activity is low. Eventually I will explore through future blogs many of the cycles that can affect us. Key- understanding time can help us to control the effects of cyclic activity. Prof. A.L. Tchijevsky wrote a treatise on sunspot and human activity. It is called: Investigation into the Relationship Between the Sunspot Activity and the Course of Universal Historical Process from V Century B.C. to the Present Day. His chart had the following:
Statistics from 72 countries.
Time span was 500 B.C. to 1922 A.D.
Mass excitement occurs in cycles of 11 years. This corresponds with sunspot activity. His mass excitement statistics included wars, revolutions, riots, expeditions, and mass migrations. A simple spiral can help us understand the cycle’s four states.
The cycle is low. The spiral is unwound. Everything is relaxed.
The cycle winds up. Things begin to tighten
The cyclic peak is reached. That equates with maximum trouble and chaos.
The cycle unwinds. Things go back to relaxed.
What does the quadripartite circle accomplish?
We can transfer the fourfold effect of the cycle onto something physical: A circle, spiral or even a maze. The spiral can be a winding ascending road. The circle can be a Viking fortress. The maze can be shaped from bushes in a garden. In other words, physical models take on the psychological effect of cycles. That gives the possibility of live our lives calmly and peacefully. We can actually rebuild a lost Golden Age of Peace and Plenty.
Fourfold Orientation Comes from a Number Square. Even numbered squares of antiquity have 4 central numbers. The 4 x 4 number square is key. It is the first even numbered square. The compass also orients by fourfold. It is an instrument used for navigation and orientation that shows direction relative to the geographic cardinal directions (or points). Usually, a diagram called a compass rose shows the directions north, south, east, and west. On the compass it is as abbreviated initials N,S,E,W:
The number square balances and orients by numbers.
The compass balances and orients direct or geography.
Fourfold Orientation and How the Central Numbers Hold All Potential
The four numbers at the center of the 4 x 4 number square are are: 6, 11, 7 and 10. Do the following operations:
Draw a diagonal so that 6 and 11 are crossed by a diagonal line.
Then cross 7 and 10 by another. Multiply these two sets of central numbers. We get 66 and 70.
Then add both sets together. Thus, (6 x 11) + (7 x 10) = 136.
Next, add all the numbers from one to sixteen. Their total is also 136.
This means the center of the 4 x 4 number square computed in such a fashion, holds the entire sum of numbers of that square. This is also true for all even numbered squares. It is a mathematical law.
Creation in Genesis draws on the featured picture. Our Creator describes his work on each day as “good.” In Hebrew letters doubled as numbers. They shared the same symbol. “Good” in Hebrew is Tov (טוב). Viewed as numbers, these letters total 17. Hebrew words are read from right to left. The first letter is 9. The second is 6. The third symbol is for #2. Thus, 9 + 6 + 2 = 17. Next, look at the featured picture. Any two opposite numbers around the perimeter total 17. Examples: (1 + 16) or (12 + 5) or (8 + 9). This was God’s favored number square for Genesis. Thus, having a “good day” is having a productive day. Is that good for business or what?
Fourfold Orientation is also Basic to Mankind
A fourfold compass regarding the psyche is basic according to Carl G. Jung. It explains the means through which the conscious orients to experience. Below, the seasons, is another.
Sensation is sense perception. It tells you something exists.
Thinking tells you what it is.
Feeling determines whether or not it is agreeable.
Intuition tells you where it came from and where it’s going.
Many blogs will appear about the fourfold orientation.
Jupiter Offers Square Deal and Then Some. The word Jupiter translates to Jovial King. Jovial, according to Webster, is characterized by hearty, joyous humor. We all need this influence in our lives. The question becomes, how did Jupiter acquire this meaning? And, what can we do to become more hearty and joyous in this trying day and age?
Leader of the Olympian Gods; Jupiter means “Jovial King” and/or “Father of Thunder”.
Answer to Jupiter Offers Square Deal lies in its magnificent number square of antiquity
Every planet had its own number square. This squares were used to invoke the influence of their particular planet. Jupiter’s was 4 x 4. Below is the traditional arrangement. It hides a special code of numbers. This was called the Fibonacci series. Numbers are pictured and described below.
Jupiter Offers – so where are 13 and 21 in the 4 x 4 number square?
The 4 x 4 number square hides the numbers of a special group of numbers. It is called the Fibonacci series. The numbers are set. The graph above starts the series. Numbers grow by successive addition. In the Fibonacci series we have 1,1,2,3,5,8,13,34…Of course the series continues to infinity. Life favors the ratio of any two consecutive numbers. As the series develops, the ratio gets closer and closer to 1.618… That number is called by the Greek word, phi, or the Golden Section. A definitive phi number can never be exactly reached. It is an irrational number that extends to infinity. Could that be why man will always fall short of immortality?
Back to the 4 x 4 Number Square
Look at the numbers vertically two at the time: 16 + 5 = 21. Underneath, 9 + 4 = 13. Next, 3 + 10 = 13. Then, 13 + 8 = 21. Next 12 + 1 =13 etc,.The entire square is filled with Fibonacci numbers 13 and 21. . Be assured that our Neolithic ancestors knew everything that you are now reading about.
They also knew that: (1) The potentiality of the entire number square is dormant in the central four numbers. Here’s how: Cross multiply the central four numbers. Then add the two products as follows: (10 x 7) + (6 x 11) = 136. (2) The 4 x 4 number square uses the numbers 1 through 16. Add these numbers. Their sum is 136. That is the same as the cross multiplication products and their sums just given. Not only does this number square of Jupiter evoke infinite potential for growth, but it also harbors within its central four numbers the potentiality for that growth. Our ancestors tapped into this knowledge.
The square was understood at least 11,000 years ago. Number squares played a large part in lost and forgotten civilizations right here on planet Earth. That’s one of the major themes of our DSOworks.com website. Music is its main theme. I believe that a peaceful civilization can be restored by the study of music and by revitalizing lost knowledge.
Jupiter Number Square Sets Legal Ages. Each planet was once connected to a number square. Here is the Saturn list. Saturn is 3 x 3. Jupiter is 4 x 4. Mars is 5 x 5. Sun is 6 x 6. Venus is 7 x 7. Mercury is 8 x 8. Moon is 9 x9.
Next, what are some primary legal ages? Of course, there can be quite a few depending on the culture. The two I pick belong to the 4 x 4 number square. They are of significance in our western civilization. These ages are 13 and 21. This is when a person takes reponsibility for their own actions. In Judaism 13 it is the year of the Bat and Bar Mitzvahs. Then the legal age in many western cultures is 21. People are considered to be grown up or adults.
By Jupiter, so where are 13 and 21 in the 4 x 4 number square?
The 4 x 4 number square hides the numbers of a special group of numbers. It is called the Fibonacci series. The numbers are set and always the same. The graph above starts the series. Numbers grow by successive addition. We have 1,1,2,3,5,8,13,34…Of course the series contnues to infinity. Life favors the ratio of any two consequtive numbers as it develops. The ratio gets closer and closer to 1.618… The true number of phi can never be exactly reached. It is an irrational number. Could that be why man falls short of immortality? This ratio has a special name, “phi”. It is also called the Golden Section of Golden ratio.
Back to the 4 x 4 Number Square
Look at the numbers vertically two at the time: 16 + 5 = 21. Underneath, 9 + 4 = 13. Next, 3 + 10 = 13. Then, 13 + 8 = 21. The entire square is filled with Fibonacci numbers. Success is action, by tradtion, comes by this number series. Our Neolithic ancestors knew everything that you are reading about here. This was atleast 11,000 years ago. Number squares played a large part in lost civilizations. I believe that a peaceful civilization can be restored by revitalizing such lost knowledge.
Black Elk of the Sioux. Black Elk was a medicine man for the Oglala Sioux Indians. He verbally related his story to John Neihardt who published a book in 1932 with Black Elk’s words called :Black Elk Speaks. If you think that the Book of Revelations of John in the New Testament can be confusing, Black Elk Speaks is definitely on a par. It definitely has many similarities. His vision has both the wisdom and analogies used by the Bible which further leads me to believe the possibility that the American Indians branched out from a lost tribe of Israel.
“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) Of course, two intersecting rivers have always been the location of concepts of Paradise. What do the 4 quarters refer to? The answer: even numbered, number squares, in particular the 4 x 4 number square of which I have written numerous blogs. Please review these on DSOworks.com
The “horses took their places in their quarters, looking inward, four by four” (also chapter 3 of Black Elk Speaks). These 4 central numbers of this first and therefore prime even-numbered number square are 10,11,6, and 7. They represent the four corners of the Earth. Here is the key:
THE FORMULA OF BLACK ELK’S VISION
In the majority of middle eastern civilization and elsewhere, the 4 x 4 number square represented the symbolic potential of the planet Jupiter for success is action, business, and creating opportunities. Each of the 7 planets were assigned its own number square.
All potential lies in the central four numbers of even numbered squares for a totality of creation explained as follows: Here is the formula: The upper left central number (10) I call UL. The upper right number I call UR. The lower left I call LL and the lower right I call LR. The sum of all the numbers in any even numbered number square can be represented by “S”. The formula becomes (UL X LR) + (LL + UR) = S. The prototype example above becomes (10 x 7) + (6 x 11) = 136 (sum of the numbers from 1 to 16)
This number square was called upon on by God in Genesis on each day of creation. I’ve already blogged about this; but to summarize – on each day God called his work, “Good,” In Hebrew “good” has a numerical equivalent of 17, On the above number square, any opposite numbers total 17 as- 16 + 1; 10 + 7; 4 + 13 etc.
Here is the clincher: As all life as we know it develops by a mathematical ratio called “phi”, 1.618… to 1; this square holds are series of numbers called the Fibonacci that develops in that ratio. The first Fibonacci numbers are: 1,1,2,3,5,8,13,21,34,55…Now look at the above square: 16 + 5 = 21; 3 + 10 = 13; 2 + 11 + 13; 13 + 8 = 31 etc. Their totals are always the Fibonacci numbers of life.
Conclusion: A find a strong parallel between the vision of Black Elk, medicine man for the Oglala Sioux, and Genesis of the Bible or Revelations of the New Testament. I can only conclude that if we but know it, all mankind is one with our Creator and that we should all reclaim our natural birthright in this wonderful upcoming age to be filled with peace and plenty. Finally, please keep watching for my book of poetry dictated to me by an old Indian spirit, female of the matriarchal, Lennie Lenape tribe. It is called The Oquaga Spirit Speaks- 89 pages of poetry and pictures dictated to me by this spirit around Oquaga Lake. It will be listed for on the products page of DSOworks,com very reasonably.