May's
Masonic Minute

Masonic Minute – May 2011

To be elected the Master of a Lodge is the highest honor the Lodge has in its power to confer on any of its members. When the Master’s period of office is completed he is presented with a Past Masters’ Jewel by the members of the Lodge, in appreciation of his dedication and service and to symbolise that he has passed through the Craft degrees to a new level of seniority.

In the Ahiman Rezon the Jewel is prescribed as “A Square and the diagram of the 47th Proposition of the 1st Book of Euclid pendant within it.” And “is of silver”. “The sides of the square to be 2 1/8 and 2 1/2 inches respectively and may have raised borders and be embellished with appropriate Masonic emblems, either engraved or raised upon the square. The jewel shall be suspended from a blue ribbon or from a hanger or cross bars, the entire jewel, hanger or cross bars to be made of silver only and no gold, precious or imitation stones shall be used in any part of its construction.”

The 47th proposition of Euclid features prominently in many Masonic Jurisdiction’s Past Masters jewels. Selecting this symbol out of the many used in Freemasonry to represent one of its highest honors must mean that it is a very significant and central symbol of the Craft. Yet, many Freemasons do not know why it is so centrally featured in the Past Masters jewel. Clearly the 47th proposition is based on Geometry, and all Freemasons know that Geometry and Freemasonry are synonymous terms.

What is the importance of the 47th Proposition that it has been selected to symbolize our past masters? Putting aside the issue of the 47th Proposition as a symbol we turn to its practical application in the process of building. This proposition teaches one of the most important principles of geometry, known to us as the Pythagorean Theorem, which is communicated by the formula “A” squared + “B” squared = “C” squared when working with a Right Triangle where “C” represents the hypotenuse. Builders use the theorem to square the corners of rooms by using the ratio of the numbers three, four and five. Three squared plus four squared = five squared. Also of interest to note is the use of the 3, 4, 5 length ratio of a Right Triangle in some jurisdictions. In those ritual traditions, a candidate will traverse the lodge three times as an Entered Apprentice, four times as a Fellow Craft, and five times as a Master Mason, thus “forming a Square” by the time he is Raised.

To put it simply, this theorem demonstrates a discovery which is the foundation of Geometry, and of architecture. It occupies a vital place in the history of human knowledge, and, it can be argued, is the starting point of all science.

First, who was Euclid? Euclid was a Greek mathematician, living in Alexandria, Egypt around 300 BC. His contribution to Geometry was not by originating, so much as cataloging ideas. Euclid, literally, wrote the book on Geometry. He compiled everything that was known at his time about Geometry into a book, which he called “Elements of Geometry”. That book stood as the authority on Geometry for more than 2000 years. Over the centuries it became the most published book in the world after the Bible. Page by page, Euclid presents each principle of Geometry with detailed explanations, beginning by defining a point, then a line, and moving on to gradually more complex demonstrations. Accordingly, the order in which the problems are discussed has become the system for cataloging and naming them, much as we know to quote the Bible by chapter and verse. The idea we are interested in was Proposition number 47 of Book 1.

It is important to note that Euclid was the collector and cataloger of geometrical propositions. The person credited with the actual discovery of the 47th Proposition was another Greek philosopher of an even earlier age. Pythagoras was born on the island of Samos, in the Aegean Sea in about 580 BC. It is said says he traveled widely, and was initiated into various mysteries, in Tyre, Babylon, and Egypt before settling in Crotona, a Greek colony in southern Italy, where a school of his disciples, a sort of early secret society, grew up. Both Euclid and Pythagoras are mentioned in Old Charges and manuscripts of Freemasonry as far back as the 1400's.

Mathematics and numbers were central to the philosophy Pythagoras taught, but unfortunately, as in the cases of other Greek thinkers, like Socrates, nothing of his own writings remain, but only those of his students.

I'm going to take you even further back in time, to Ancient Egypt. Obviously, the Egyptians who built the pyramids and other monuments that have survived the millennia were superb operative masons, and even then, geometry was central to their craft. If you wanted to make a right angle, you would take your mason's square, and use it to square the angle you were working on. However, what if you didn't have a square to use as a tool, or a protractor to measure ninety degrees or another right angle to compare it to? The Egyptian masons knew the answer. They knew that if you took a rod 3 cubits long, another rod 4 cubits long, and another rod 5 cubits long, laid them end to end in a triangle, the angle where the 3- and 4-cubit rods met was always a right angle. To the Egyptians, this was a wonderful and powerful tool, almost bordering on the magical. Their chief architects carried a set of rods to use whenever a square corner was needed. Another method was to take a string with twelve cubits marked out on it, and stake it out in a triangle with three cubits on one side, four on another, and five on the other. Of course the unit of measurement could be anything...a cubit, a foot, a meter, an inch, a yard...it was the relative lengths of 3 by 4 by 5 that resulted in a right triangle.

Pythagoras found that this held, not just for the 3 by 4 by 5 triangle, but for any right triangle. He started with what was just a useful tool and discovered a fundamental rule of nature. What the Pythagorean Theorem, also called the 47th Proposition of Euclid, says, is that for any right triangle, that is, any triangle containing a 90-degree angle, the square of the "hypotenuse," the longer side, equals the sum of the squares of the two shorter sides.

Today over a hundred ways have been found to prove this proposition. To explain any of them requires drawing diagrams, which I can't do in this setting, but all these proofs arrive at that moment of epiphany when the pieces come together like a jigsaw puzzle. Pythagoras had peeked under the veneer of the universe, and found that space had a kind of architecture, and that architecture was made of numbers. To us, looking at this from the vantage point of a couple of thousand years later, the 47th proposition might seem a little less dramatic. It is, after all, just another one of the laws of nature. We have to remember that to the Pythagoreans, it was a new and wonderful thing to find that there were mathematical laws of nature. Even now, we can't explain why space fits together this way we are just so used to seeing it that we tend to overlook the implications of a world ruled by numbers.

Now, it was possible to use Geometry to make predictions, not just on paper, but in the field. You could indirectly tell the length of something it was impossible to measure directly. If you knew the lengths of two sides of a right triangle, you could predict the length of the third, and always be right. The world obeyed numbers, not at random times, but always. Armed with this insight, Pythagoras taught that numbers were even more real than the world they described. To the Pythagoreans, they were discovering a divine language of pure mathematics. To us, they were discovering that the universe could be described, predicted, and understood.

Our Past Master’s through their experience, knowledge and skill have further squared themselves and this symbol is suspended from a Square, to show that the Past Master has learned how to make complex constructions from the simple angle of ninety degrees. Therefore the 47th Proposition has become a fitting symbol to represent this achievement.

May's Masonic Minute

May's
Masonic Minute