Last night was the long-awaited appearance of Bro. Steve Burkle at Atlas-Pythagoras Lodge, where he spoke on “The 47th Problem of Euclid and the Magic Squares,” an exploration of historic and esoteric aspects of the Pythagorean Theorem. Steve is a prolific writer and presenter of research work, keeping busy in a variety of venues, including the AMD. His lecture was the last in the lodge’s “Enlightening the Temple” series, that brought to the podium seven guest speakers during the year, including Rashied Bey, Trevor Stewart, and Tim Wallace-Murphy.
On the historical side, Steve explained the known origins – mathematical and historical – of the Theorem, and explained away the clumsy manner in which it is explained in the lecture of the Third Degree. In the process, he told us about John Dee and a curiosity named Plimpton 322. The former, of course, was the 16th century English esotericist and mathematician. The latter is an ancient Babylonian cuneiform, numbered 322 among the G.A. Plimpton Collection at Columbia University, and might be the best known artifact to show mathematics in archeological history. It dates to 1900-1600 BCE, and it reveals the most advanced mathematics known previous to ancient Greece because it teaches how to form right triangles akin to the Pythagorean way.
The 47th Problem of Euclid is key to Freemasonry because it is elemental to the design of the universe. In short:
In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
Often written as the equation:
a2 + b2 = c2
With the number 3 being a common denominator of deity, there are many ways the triad speaks to divinity. Plato’s three-fold principle has Thought (father/generative power), Primitive Matter (mother/passive principle), and Kosmos (offspring/product). Plutarch, writing of Isis and Osiris, continues along this thinking and explains that within this right triangle the perpendicular is the masculine; the base is the feminine; and their offspring (Horus) is the hypotenuse. (Read the Master Mason chapter in Albert Pike’s Morals and Dogma for a smarter rendering of this. Regardless of how much or how little one might meditate on geometrical theorems, this particular one can be appreciated as part of the “DNA” of the universe.)
Bro. Steve later explored numerology and gematria, linking the Pythagorean Theorem to what is called the Magic Square. A Magic Square is a matrix of rows and columns containing numbers that all agree on the same sum, no matter which direction is taken to add those numbers. To wit:
|I think what I like most about Powerpoint presentations is how I can|
photograph the images, instead of frantically taking notes!
|The Worshipful Master thanks Bro. Steve for the lecture.|