Pythagoras and the Magic Square

Pythagorean numerology strongly suggests that Pythagoras was greatly influenced by magic squares. 



THE MAGIC SQUARE OF THREE

 

The ancient Chinese had made the connection of the Luo Shu, the right angle, and the calendar for almost 1,500 years prior to Pythagoras being born.

This knowledge of mathematics and the Luo Shu most likely was acquired by the Indian society via the ancient Chinese and is the basis for the mandala. Pythagoras could have been exposed to ancient Chinese math and philosophy of the Luo Shu any number of ways.

Pythagoras was a great traveler and was known to have studied in India and therefore could have been exposed to the Magic Square through his Indian experiences. Pythagoras also lived on the island of Samos, one mile from present day Asia Minor, Turkey.

Although this part of the world was controlled by the Greeks in the time of Pythagoras, there is a Muslim connection with the near East (Assyria, Iran, Babylonia) and Western China.  The Turkic speaking Muslim Uighurs settled in what is now Dunhuang, (Xinjiang) in Western China over four thousand years ago. This is the part of China where Indian Buddhism merged with the Muslim world and the Chinese world. Many different cultures co-existed here during the heyday of the Silk Road and travelers on the Silk Road could easily have imported exciting ideas as well as precious commodities between Asia Minor, India, and China.  

Map of Silk Road2"

MAP OF SILK ROAD

Though the Pythagoreans never left any record of using Magic Squares, this is not conclusive evidence that they were unfamiliar with them. It is possible, and it is likely as Pythagorean numerology has much in common with Chinese numerology. It is the Luo Shu that aids in understanding the language of numbers and the mysteries of Nature. It is the Luo Shu that is the basis of Chinese and Pythagorean numerology.

Pythagoras would certainly agree that numbers are a language with great wisdom to impart to the student as he proved the world of sound and vision are governed by number. This author believes that Pythagoras was influenced by ancient Chinese mathematics and most likely knew about the Magic Square or Luo Shu. Here are some facts to consider:

  1. A Pythagorean triad of numbers appears in every Magic Square in the Luo Shu format.
  2. Any Magic Square in the Luo Shu format is a relationship between the squares of two consecutive numbers (see chart) just as the octave can be expressed the same way, that is, as a ratio of 2 to 1, (the other known musical intervals as ratios of 3 to 2 and 4 to 3) . This relationship of consecutive numbers is present in both Magic Squares and music.
  3. Sir Isaac Newton was fairly certain that the Pythagoreans were well informed of the law of inverse squares . (Brownowski, Jacob Ascent of Man DVD series). This note is rather interesting as Isaac Newton must have known that the Pythagoreans were adept at applying the squares of numbers (in the form of Magic Squares and the gnomon) to make astronomical and calendrical measurements.
  4. Pythagorean numerology is similar to Chinese numerology as both cultures believed that number was the key to understanding the harmony of the Universe.
  5. The Pythagoreans believed that everything emanates from the Monad, or the number One. Magic Squares also emanate from the number one as any Magic Square can be constructed by knowing where to place the number one and using the Hindu or Persian Continuous Method.
  6. Odd numbers had greater relevance to the Pythagoreans and the ancient Chinese than even numbers. Only the magic squares of odd numbers can be arranged in a Luo Shu pattern and therefore only odd numbers can generate magic squares with a Pythagorean triad of numbers as well as contain calendrical information.
  7. Only odd numbers can be created by taking the difference between two consecutive numbers (squared), beginning with zero and one, (this is the only pair of consecutive numbers that does not generate a magic square).

Example


Order of Square     Magic Square No.       Center Cell            Pythagorean Triad 

 

12 - 02  =  1                0                  12  +   02  =   1                      0

22 - 12  =  3                1                  22  +  12  =   5                  3, 4, 5

32 - 22  =  5                2                  32  +  22  =  13                5, 12, 13

42 - 32  =  7                3                  42  +  32   =  25                7, 24, 25

52 - 42  =  9                4                  52  +  42  =  41                9,  40, 41

62  - 52  =  11               5                  62  +  52   =  61               11, 60, 61

72  - 62 =  13               6                  72  +  62   =  85               13, 84, 85

Magic squares (in the Luo Shu format) are a relationship between two consecutive numbers, squared 

Odd numbers can be created by the subtraction of two consecutrive numbers, squared. 

Cycles of seven (the 13x13 and 27x27 Magic Squares) will lead to revelatory information about Time and Space.