I teach SAT preparation courses and as part of the instruction teach basic math and geometric concepts. Not too long ago I had a student who was not grasping the Pythagorean Theorem, so I made a drawing for him to explain it and prove that it worked. I chose the 3-4-5 right triangle for my example and went about making my useful, yet ugly artwork. The kids always like hearing me berate my own artistic skills. I just never had a hand for it and pointing this out always adds a bit of levity to the lesson. The drawing shows what a mathematical square is and why the theorem works.
a2 + b2 = c2, where a and b are the legs and c is the hypotenuse
32 + 42 = 52
9 + 16 = 25
Sure enough, the hypotenuse side has 25 squares. Eureka!
If you have not seen it – and I have encountered many Masons who have not – this symbol (albeit better designed than my own toddler-like artwork), when suspended from a square, is the symbol of a past master in some jurisdictions. I understand this to be mostly an English emblem, not used much in the States, except in one of the Masonic lectures.
I have read that the meaning of it hanging from the square is to denote that the wearer of the jewel has served as master and thus has had to solve many advanced or complex problems. We do not today regard the Pythagorean Theorem as a particularly advanced geometric concept, but until just a hundred years ago or maybe a little more, literacy was nowhere near the levels we see today, and as such, many of the rather simple geometric tricks like this were not widely taught. They were taught to those who could afford to go to schools, and masters of the building trades knew such secrets, but the common person on the street would not have known about them. Before he could learn this type of thing, a workman would have to prove himself worthy of being taught it.
This starts to sound familiar to those of us who are merely speculative workmen.
This sort of secrecy surrounding information is important for quality control. You can’t have someone walking onto a job site, claiming to a master of his craft, and perhaps having an idea about calculating lengths with this theorem, but not knowing how and when to use it. You can’t have a journeyman or fellow of the craft show up for work without a solid knowledge of how to use a square or level. All this would make for bad quality. This is why secrets of the building trades are necessary – so that the information is not misused or misunderstood. Errors in a building can be disastrous. Knowing how and when to use the tools is key.
That is what we strive to do in our lodges. We try to teach the secrets, and then have the candidates demonstrate their understanding of what has been inculcated before we begin to build on that knowledge. If we do it right, the edifice we construct is built from friendship and its foundation is faith, hope, and charity. If we do it wrong, and rush through the education to get to a perceived end goal, the learning is little and we end up spending our strength for naught.