Parallel lines are a common visual theme throughout Freemasonry. Whether they are represented by two pillars, our patron Saints John standing side by side, or a portion of one of the first symbols introduced to new Masons; there are many overt, exoteric references to this geometric ideal.
Mathematically, parallel lines are two vectors traveling on the same plane that never intersect. In many ways this construct esoterically alludes to something deeper; a concept of perfection that can not actually exist in this world. It is impossible for man to create two actual parallel lines, but yet the concept somehow can exist in our minds or in the elegance of an equation. Truly parallel lines are not only an impossible pursuit of man, but they do not even occur in nature itself.
I personally identified with the concept of parallel lines long before I was a Mason. I considered parallel lines evidence of how two people can travel together in life, providing each other with strength and support, moving towards the same goal and destination without colliding or becoming hopelessly intertwined, I felt this was the ultimate expression of a successful relationship.
Esoterically speaking, these impossible parallels have a profoundly deeper meaning that reminds us that the perfection of the universe can not be obtained by mankind, only pursued. However, I feel that there is still something missing from that explanation. I propose that the real underlying meaning of the symbol of parallel lines is not only its reference to the perfection of a geometric and mathematical ideal. Symbolically, parallel lines also represent the only true parallel in nature that surrounds us all. Time. Time is the only constant that progresses forward, unwavering, without change of speed, angle or persistence. To paraphrase Shakespeare's Hamlet; “we are all traveling on the level of time, towards that undiscovered country, whose bourne no man returns.” Indeed, mankind is traveling on a constant course in parallel towards the same inevitable end. Time and it’s relation to humanity is the 4th dimensional expression of a two and three dimensional concept.
In Masonry, we have a concept of “being on the level” or “meeting as equals.” The parallel course of time and its inevitable conclusion is the hidden message secreted between parallel lines that should endeavor us to pursue the perfection of their ideal.