The 47th Problem Of Euclid - Why?

Guest Post by Worshipful Brother Brian C. Thomas

For those new to Emeth, welcome, it is great to have you with us. For those new to Emeth, I write about Freemasonry regularly, with a focus on improving the Masonic experience for Masons everywhere. To do so, I draw upon my own experiences as a Worshipful Master, District Deputy to the Grand Master, and as Grand Master. Emeth also hosts daily discussion threads, with superb contributions from very diverse voices. I hope that you find Emeth valuable to your own Masonic journey.

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This week I am honored to publish a guest post from a friend and superb Mason, W. Brother Brian C. Thomas. So, without further delay…

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The 47th Problem of Euclid - Why?

I have been puzzled by many things, not the least of which is; “Why does Freemasonry use the 47th Problem of Euclid – more commonly known as the Pythagorean Theorem – with such reverence and importance?” Having been in Freemasonry for over 50 years I have more questions than answers but this singular notion has captured my attention. Perhaps, I have recently stumbled upon an explanation. First some background.

Geometry

“Geometry, the first and noblest of sciences, is the basis upon which the superstructure of Freemasonry is erected” Most Masons, having taken geometry in High School, would rather forget that experience. Yet Geometry was the keystone of knowledge in the ancient world. Geometry (Geo =earth, metry= measurement) defined most of the intellectual tools needed to build a structure, define a field, travel to a distant location, contemplate the heavens and define the world.

Recall, the Fellowcraft degree teaches us that Geometry allows us to trace nature and discover the power, wisdom and goodness of the Great Architect of the Universe. An attentive Mason leaves the degree with a notion that through Geometry he will come to better know the Deity through nature. Yet in the Master Mason degree the only mention of Geometry is the 47th Proposition of Euclid with the notion that it merely teaches us to love art and science.

Pythagorean Theorem

Pythagoras (580 - 490 BCE), a philosopher, mathematician, teacher and mystic, preceded Euclid in describing that, given any right triangle, the sum of the squares of the sides equals the square of the hypotenuse, and he, in turn, received that knowledge from the Egyptians who used ropes knotted in segments to redefine property lines and corners after the Nile River flooded each year. But the rule was not unique to Egypt. It was known by the Sumerians, Celts, and Chinese as well.

Pythagoras established a mystery school. Pythagoras and his students believed was the universe is ordered according to laws and mathematics of the Deity. The main focus of Pythagorean thought was ethics; reality is mathematical, the soul is divine and certain symbols possess mystical significance. Keep that in mind as we journey on.

“Greatest among the rules laid down by the Supreme Architect of the Universe, in His great book of nature, is this of the 47th problem…”. “With it he reduces the chaos of ignorance to the law and order of intelligent appreciation of the cosmos. With it he instructs his fellow-Masons that God is always geometrizing and that the great book of Nature is to be read through a square.”

The question remains, “Why did this commonly known geometrical rule become distorted as to its origin and used so ubiquitously in Freemasonry?” Why does Freemasonry attribute the theorem to Euclid rather than Pythagoras? Is the absurdity of describing Pythagoras as exclaiming “Eureka’, an obvious fiction, ”

(Archimedes exclaimed “Eureka” after having discovered that he could determine the volume of any object by the displacement of water) used as a pointer to say that there is a deeper meaning here? How does that deeper meaning connect to geometry?

Euclid’s Contribution

Euclid (300 BCE) taught in Alexandria, Egypt and was a student of the great Plato. He wrote 13 books, collectively called “The Elements” attempting to logically prove all of the mathematical and geometric constructs of the day. He was so successful that “Euclidean Geometry” was one of the cornerstones of a classic liberal education for over 2000 years. The Geometry you learned in High School and College consisted of the proofs contained in “The Elements”.

Euclidean Geometry is really pure logic. Starting from 10 unquestionable axioms, Euclid built a series of proofs based on theorems and derivations. His first book contained the proof of the Pythagorean Theorem which he calls the 47th Proposition. The actual proof is not as important as the way he approached it. Euclid was one of the first to apply pure logic to both practical and abstract notions, which, in turn, was the basis for the scientific method developed in the Enlightenment. Parenthetically, President James Garfield, a Mason, offered a proof of the Pythagorean Theorem using the point in a circle bounded by two tangent parallel lines. Does that sound familiar?

The 47th Proposition in Masonry

This is all well and good, but Euclid proved many theorems. Why is the 47th Proposition more important than the all the others unmentioned propositions?

Reverend Anderson felt the 47th Proposition so important that he included an illustration of it on the front cover of his “Constitutions,” the code of Freemasonry. His “Constitutions” states; “The Greater Pythagoras, provided the author of the 47th Proposition of Euclid’s first Book; which, if duly observed, is the Foundation of all Masonry, sacred, civil, military.” The 47th Proposition is the “Foundation of all Masonry!”

As we progress through the years the Preston-Webb Lectures muddle the issue by saying that; “This discovery (47th Proposition) was accepted by our ancient brethren as a key to the nature of the Divine Being. It inspires Masons to be lovers of the arts and sciences.” So we learn in the Master Mason degree that the ancients thought the Proposition was a “key to the divine nature” but we now feel it only teaches us to be a lover of art and science. I side with the ancients.

Perhaps, Albert Pike put it best in when he said; “If the great symbol of Pythagoras, known as the 47th Problem of Euclid, means only… that Masons are great lovers of the Arts and Sciences in general, it should at once disappear from the charts or tracing-boards of our Lodges; for the explanation explains nothing, and makes the symbol no symbol at all of anything.” Yet he hints at the real meaning in his book on the symbolism of the 32nd˚ mentioning the name of the philosopher, Benidictus Spinoza – more on him later.

Age of Enlightenment

We will now take a leap from 300 BCE to the Enlightenment in Europe which occurred in the mid and late 17th century in an attempt to explain why the 47th Proposition of Euclid became so revered by intellectuals and eventually Freemasons. The Age of Enlightenment, sometimes referred to as the Age of Reason, describes a period in the mid to late 1600s where the culture dramatically changed from one of superstition, intolerance, hierarchy and authoritarianism to reason, tolerance and individualism.

Recall that for over 1200 years the church was dictatorial and pedantic. The church controlled culture, society, politics and life in general. Any deviation could be punished by physical and/or social punishment. The Catholic Church declared that no one could reach heaven without the blessing of the church hierarchy. The church controlled the government in most European countries and kingdoms.

Kings and Potentates warred and plundered. Life for most was controlled and fatalistic. Yet a few hardy intellectual souls looked to the East and found more freedom of thought and action. The Orient held knowledge that was forbidden in the West because it was not in accord with scripture. Though books were burned and intellectuals were killed a determined underground culture existed.

The oral tradition persisted because books were scarce and education tightly controlled. Strangely, many monasteries possessed books and manuscripts with this secret knowledge unknown to the church hierarchy. New ideas were passed orally and in secret among the intellectual class so that they did not literally lose their heads.

The writings of Francis Bacon (1562-1626), Johnathan Kepler (1571-1630) Rene Descartes (1596-1650), Baruch (Benidictus) Spinoza (1632-1677), John Locke (1632-1704), Voltaire (1694-1778) and others sparked a desire for freedom of action and thought, challenging the church and stirring the people. At first slowly and later at a furious pace new ideas were dispersed and accepted. Reason and freedom became an accepted goal to the dismay of the church and princes.

Enlightenment thinkers did not necessarily agree on methods but there was a consensus as to results. Immanuel Kant summed it up in his 1784 essay “What is Enlightenment” by describing it as, “Enlightenment is man’s emergence from self-incurred immaturity.” The Enlightenment was egalitarian, addressed the common concern and was founded on reason.

Many countries and kingdoms sought to suppress Enlightenment thought but these heretical ideas circulated freely in secret organizations and venues until the early 1700s when the threat of harm from the church and government authorities receded.

The predominate means of education was “associationism”, which is just another word for memorization. Books were in short supply and many were censored, yet a thriving underground allowed those that did exist to circulate widely. Natural history was the vogue. Revealed Deity gave way to experienced Deity. The concept of nature demonstrating God’s work became vogue and the study of nature exploded.

Dorinda Outram says, “Enlightenment was a desire for human affairs to be guided by rationality rather than by faith, superstition, or revelation; a belief in the power of human reason to change society and liberate the individual from the restraints of custom or arbitrary authority; all backed up by a world view increasingly validated by science rather than religion or tradition.”

This was the environment that spawned Freemasonry and from which Masonry took its values of an oral tradition, secrecy, direct interaction with Deity, a culture of trust and respect and egalitarianism. The German historian Reinhart Koselleck claimed that, “On the Continent there were two social structures that left a decisive imprint on the Age of Enlightenment: the Republic of Letters and the Masonic lodges.

Spinoza

It’s difficult to say if 16th and 17th century philosophers spawned the Enlightenment or if the Enlightenment generated many great philosophers. Either way, the Enlightenment and the philosophers who lived and wrote in it dramatically changed the world. Two eminent philosophers deserve the attention of Freemasons; Rene Descartes and Benidictus Spinoza. Both used Euclidian based proofs to demonstrate their concepts. Just as Euclid started from several self evident axioms and definitions to create propositions that led to geometric proofs, Descartes and Spinoza used the exact same method to demonstrate and justify their concepts of God, spirituality, being and thinking.

Descartes preceded Spinoza and it is reasonable to believe influenced him though Spinoza disagreed with Descartes on several important concepts of God’s nature and the interaction of the human mind and body.

Spinoza’s Jewish family fled Portugal to avoid the Inquisition and settled in Holland, the most intellectually tolerant of all European countries. Spinoza’s early writings got him excommunicated by the Jewish community. He was reduced to wandering about as an itinerant lens grinder. While doing so he worked on his opus, Ethica Ordine Geometric Demonstrata or “Ethics, Demonstrated in Geometrical Order” which was published after his death and is now known as just “Ethics.”

Ethics is ingenious not only by what it says but how it says it. Spinoza mimics Euclid in his systematic proof that God is the universe, the single substance in which all natural phenomena exists. Such a concept of God could be universally accepted in all religions. He is clear that we can know God without intersession of the church and that a spark of the divine is within us to be discovered. These notions were horrifying to Jewish, Protestant and Catholic theologians because such a God would not be an anthropomorphic father figure known only through priests or rabbis. Every person could find God in nature because God is nature. He uses the word “nature” in a broader and deeper sense than we use it today.

So Spinoza and Euclid, though certainly not contemporaries, used the same exact method of arriving at their conclusion. Euclid rose on the shoulders of Pythagoras and Spinoza rose on the shoulders of Descartes but both proved the theories of their mentor.

Ethics is not an easy read. A student would have to slog through over 250 lemmas, propositions and corollaries but the result is astounding, a definitive proof that God exists and is the universe. Because God exists and is the universe the ethical laws of God are fixed and unyielding throughout the cosmos.

Why should Masons care?

Be reminded that Freemasonry is based on a belief in a Supreme Being and is built on the foundation of Geometry. Masons use symbols as pointers and reminders in our lifelong journey. We are taught that Geometry is the first and noblest of sciences and is the basis upon which the superstructure of Freemasonry is erected. In a careful reading of the Fellowcraft “Geometry Lecture” will yield many of the important points proven in Spinoza’s Ethics.

Albert Pike said “…hence it follows, that the human mind is a part of the infinite intellect of God…” In fact, Pike mentions Spinoza several times in his writings.

I was flummoxed by all this Masonic talk about Geometry, Pythagoras, and the 47th Problem (Proposition) of Euclid until I stumbled over a short 2006 paper by Bro. Jeff Peace in a blog called The Burning Taper. While Bro. Jeff merely speculated on the connection between the 47th Proposition of Euclid, Spinoza and Freemasonry it was enough to get my attention and cause me to follow his lead. The connection between the 47th Proposition and Spinoza is also mentioned in a paper by Theron Dunn on beaconofmasoniclight.blogspot.com.

The Lesson

Perhaps the notion that Geometry and the 47th Problem of Euclid, as the foundation of Masonry, is a pointer to something else because that “something else” was heresy during the Enlightenment. Perhaps, just perhaps, early Masons read, understood and agreed with Spinoza’s concept of God and our relation to him. Perhaps, just perhaps, the 47th Problem of Euclid is pointing to a specific Proposition in Spinoza’s Ethics that describes an important, or maybe the most important, concept of Freemasonry.

I submit to you Benedictus Spinoza’s 47th Proposition:

Prop. XLVII “The human mind has an adequate knowledge of the eternal and infinite essence of God”

I propose that the 47th Proposition of Euclid as used in Freemasonry points to the 47th Proposition of Spinoza which, in turn describes the root of our journey in Masonry; to discover within ourselves the eternal and infinite essence of God.

WB Brian C Thomas

Myrtle Lodge #108 – WA

Seattle Valley, Scottish Rite, 33˚

SRICF VIII˚

Note: An edited version of this paper was published in the Journal of the Masonic Society, Issue 27, Winter 2015 (www.themasonicsociety.com). We are proud to publish it in full here.

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Just in case you missed it:

Freemasonry Is A Sacred Institution