The Sun, Moon, and Stars

The Sun, Moon, and Stars

WE have more right to be astonished that the astronomical references are so few, rather than to be surprised that there are so many!  We are taught that geometry and Masonry were originally synonymous terms and geometry, fifth of the Seven Liberal Arts and Sciences, is given more prominence in our Fellowcraft degree than the seventh, Astronomy. Yet, the beginnings of astronomy far antedate the earliest geometrician. Indeed, geometry came into existence to answer the ceaseless questionings of man as to the “why” of celestial phenomena. 

In these modern days, it is difficult to visualize the vital importance of the heavens generally, to early man. We can hardly conceive of their terror of the eclipse and the comet or sense their veneration for the Sun and his bride, the Moon. We are too well educated. We know too much about “the proportions which connect this vast machine.”  

ANCIENT IMPORT OF THE HEAVENS

THE astronomer has pushed back the frontiers of his science beyond the inquiries of most of us; the questions which occur as a result of unaided visual observations have all been answered.  We have substituted facts for fancies regarding the sun, the moon, the solar system, the comet, and the eclipse.  

Albert Pike, the great Masonic student “who found Masonry in a hovel and left her in a palace” says:

WE cannot, even in the remotest degree, feel, though we may partially and imperfectly imagine, how those great, primitive, simple-hearted children of Nature, felt in regard to the Starry Hosts, thereupon the slopes of the Himalayas, on the Chaldean plains, in the Persian and Median deserts, and upon the banks of the great, strange River, the Nile. To them the universe was alive – instinct with forces and powers, mysterious and beyond their comprehension. To them it was no machine, no great system of clockwork; but a great live creature, in sympathy with or inimical to man. To them, all was a mystery and a miracle, and the stars flashing overhead spoke to their hearts almost in an audible language. Jupiter, with its kingly splendors, was the Emperor of the starry legions. Venus looked lovingly on the earth and blessed it; Mars with his crimson fires threatened war and misfortune; and Saturn, cold and grave, chilled and repelled them. The ever-changing moon, faithful companion of the sun, was a constant miracle and wonder; the Sun himself the visible emblem of the creative and generative power. To them, the earth was a great plain, over which the sun, the moon, and the planets revolved, its servants, framed to give it light.

Of the stars, some were beneficent existences that brought with them Spring-time and fruits and flowers – some, faithful, sentinels, advising them of coming inundations, of the season of storm and of deadly winds some heralds of evil, which, steadily foretelling. they seemed to cause. To them, the eclipses were portents of evil, and their causes hidden in mystery, and supernatural.  The regular returns of the stars, the comings of Arcturus, Orion, Sirius, the Pleides, and Aldebaran; and the journeyings of the Sun, were voluntary and not mechanical to them. What wonder that astronomy became to them the most important of sciences; that those who learned it became rulers; and that vast edifices, the pyramids, the tower or Temple of Bel, and other like erections elsewhere in the East, were builded for astronomical purposes? – and what wonder that, in their great childlike simplicity, they worshipped the Light, the Sun, the Planets, and the stars; and personified them, and eagerly believed in the histories invented for them; in that age when the capacity for belief was infinite; as indeed, if we but reflect, it still is and ever will be?

– Bro. Albert Pike

Anglo-Saxons usually consider history as their history; science as their science; religion as their religion. This somewhat naive viewpoint is hardly substantiated by a less egoistic survey of knowledge. Columbus’s sailors believed they would “fall off the edge” of a flat world, yet Pythagoras knew the earth to be a ball.  The ecliptic was known before Solomon’s Temple was built.  The Chinese predicted eclipses long, long before the Europeans of the middle age quit regarding them as portents of doom!

FREEMASONRY’S ANCIENT ASTRONOMICAL LORE

THE Astronomical lore of Freemasonry is very old. The foundations of our degrees are far more ancient than we can prove by documentary evidence. It is surely not stretching credulity to believe that the study which antedates “Geometry, the first and noblest of sciences,” must have been impressed on our Order, its ceremonies and its symbols, long before Preston and Webb worked their ingenious revolutions in our rituals and gave us the system of degrees we use – in one form or another – today.

The astronomical references in our degrees begin with the points of the compass; East, West, and South; and the place of darkness, the North.  We are taught the reason why the North is a place of darkness by the position of Solomon’s Temple with reference to the ecliptic, a most important astronomical conception.  The Sun is the Past Master’s own symbol; our Masters rule their lodges – or are supposed to! – with the same regularity with the Sun rules the day and the Moon governs the night.  Our explanation of our Lesser Lights is obviously an adaption of a concept which dates back to the earliest of religions; specifically, to the Egyptian Isis, Osiris, and Horus; represented by the Sun, Moon, and Venus.

Circumambulation about the Altar is in imitation of the course of the Sun.  We traverse our lodges from East to West by way of the South, as did the Sun Worshipers who thus imitated the daily passage of their deity through the heavens. Measures of time are wholly a matter of astronomy. Days and nights were before man, and consequently before astronomy, but hours and minutes, high twelve and low twelve, are inventions of the mind, depending upon the astronomical observation of the Sun at Meridian to determine noon, and consequently all other periods of time.  Indeed, we are taught this in the Middle Chamber work, in which we give to Geometry the premier place as a means by which the astronomer may “fix the duration of time and seasons, years and cycles.”

PILLARS AND GLOBES OF THE LODGE

Porch of King Solomon’s Temple

ATOP the Pillars, representing those in the porch of King Solomon’s Temple, appear the terrestrial and celestial globes. In the Fellowcraft degree, we are told in beautiful and poetic language that “numberless worlds are around us, all framed by the same Divine Artist, which roll through the vast expanse and are all conducted by the same unerring law of nature.”

Our Ancient Brethren, observing that the sun rose and set, easily determining East and West in a general way. As the rises and sets through a variation of 47 degrees north and south during a six-month period the determination were not exact. The earliest Chaldean stargazers, progenitors of the astronomers of later ages, saw that the apparently revolving heavens pivoted on a point nearly coincident with a certain star.  We know that the true north diverges about from the North Star one and one-half degrees, but their observations were sufficiently accurate to determine a North – and consequently East, West, and South. The reference to the ecliptic in the Sublime Degree has puzzled many a brother who has not studied the elements of astronomy. The earliest astronomers defined the ecliptic as the hypothetical “circular” plane of the earth’s path about the sun, with the sun in the “center.”

As a matter of fact, the sun is not in the center and the earth’s path about the sun is not circular. The earth travels once about the sun in three hundred and sixty-five days, and a fraction, on an “elliptic” path; the sun is at one of the foci of that ellipse. The axis of the earth, about which it turns once in twenty-four hours, thus making a night and a day, is inclined to this hypothetical plane by 23 and one-half degrees.  At one point in its yearly path, the north pole of the earth is inclined towards the sun by this amount. Halfway further around in its path the north pole is inclined away from the sun by this angle. The longest day in the northern hemisphere – June 21st – occurs when the north pole is most inclined toward the sun.

Ant building situated between latitudes 23 and one-half north and 23 and one-half south of the equator, will receive the rays of the sun at meridian (high twelve, or noon) from the north at some time during the year.  King Solomon’s Temple at Jerusalem, being in latitude 31 degrees 47 seconds north, lay beyond this limit.  At no time in the year, therefore, did the sun or moon at meridian “darts its rays into the northerly portion thereof.”

As astronomy in Europe is comparatively modern, some have argued that this reason for considering the North, Masonically, as a place of darkness, must also be comparatively modern. This is wholly mistaken – Pythagoras (to go further back) recognized the obliquity of the world’s axis to the ecliptic, as well as that the earth was a sphere suspended in space.  While Pythagoras (510 B.C.) is much younger than Solomon’s Temple, he is almost two thousand years older than the beginnings of astronomy in Europe.

UNIVERSALITY AND SYMBOLISM

THE “world celestial and terrestrial” on the brazen pillars were added by modern ritual makers.  Solomon knew them not, but contemporaries of Solomon believed the heavens to be a sphere revolving around the earth.  To them the earth stood still; a hollow sphere with its inner surface dotted with stars.  The slowly turning “celestial sphere” is as old as mankind’s observations of the “starry decked heavens.”

It is to be noted that terrestrial and celestial spheres are both used as emblems of universality.  They are not mere duplications for emphasis; they teach their own individual part of “universality.”  What is “universal” on the earth – as for instance, the necessity of mankind to breathe, drink water, and eat in order to live – is not necessarily “universal” in all the universe.  We have no knowledge that any other planet in our solar system is inhabited – what evidence there is, is rather to the contrary.  

We have no knowledge that any other sun has any inhabited planets in its system.  Neither have we any knowledge that they have not.  If life does exist in some other, to us unknown world, it may be entirely different from life on this planet. Hence, a symbol of universality, which applied only to earth would be a self-contradiction.

Real Universality means what it says. It appertains to the whole universe. While a Mason’s Charity, considered as giving relief to the poor and distressed, must obviously be confined to this particular planet, his charity of thought may, so we are taught, extend “through the boundless realms of eternity.” Hence “the world terrestrial” and “the world celestial” on our representations of the pillars, in denoting universality means that the principles of our Order are not founded upon mere earthly conditions and transient truths, but rest upon Divine and limitless foundations, coexistent with the whole cosmos and its creator.

We are taught of the “All-Seeing Eye whom the Sun, Moon, and Stars obey and under whose watchful care even comets perform their stupendous revolutions.” In this astronomical reference is, oddly enough, a potent argument, both for the extreme care in the transmission of ritual unchanged from mouth to ear, and the urgent necessity of curbing well-intentioned brethren who wish to “improve” the ritual.

The word “revolution” in this paragraph (it is so printed in the earliest Webb monitors) fixes it as a comparatively modern conception.  Tycho Brahe, progenitor of the modern maker and user of fine instruments among astronomers, whose discoveries have left an indelible impression on astronomy, made no attempt to consider comets as orbital bodies.  Galileo thought them “emanations of the atmosphere.”  Not until the seventeenth century was well underway did a few daring spirits suggest that these celestial portents of evil, these terribly heavenly demons which had inspired terror in the hearts of men for uncounted generations, were actually parts of the solar system and that many if not most of them were periodic, actually returning again and again; in other words, that they revolved about the sun.

Obviously, then, this passage of our ritual cannot have come down to us by a “word of mouth” transmission from an epoch earlier than that in which men first commenced to believe that a comet was not an augury of evil but a part of the solar system.  The so-called “lunar lodges” have far more a practical than an astronomical basis.  

The Milky Way Credit: 9NewsDenver

In the early days of Masonry, both in England and in this country, many if not most lodges, met on dates fixed in advance, but according to the time when the moon was full; not because the moon “Governed” the night, but because it illuminated the traveler’s path! In days when roads were but muddy paths between town and hamlet, when any journey was hazardous and on black nights dangerous in the extreme, the natural illumination of the moon, making the road easy to find and the depredations of highwaymen the more difficult, was a matter of some moment!  One final curious derivation of a Masonic symbol from the heavens and we are through.  The symbol universally associated with the Stewards of a Masonic lodge is the cornucopia.

According to the mythology of the Greeks, which goes back to the very dawn of civilization, the God Zeus was nourished in infancy from the milk of a goat, Amalthea. In gratitude, the God placed Amalthea forever in the heavens as a constellation, but first gave one of Amalthea’s horns to his nurses with the assurance that it would forever pour for them whatever they desired!  The “horn of plenty,” or the cornucopia, is thus a symbol of abundance.  The goat from which it came may be found by the curious among the constellations under the name of Capricorn.  The “Tropic of Capricorn” of our school days is the southern limit of the swing of the sun on the path which marks the ecliptic, on which it inclines first its north and then its south pole towards our luminary.  Hence there is a connection, not the less direct for being tenuous, between out Stewards, their symbol, the lights in the lodge, the “place of darkness” and Solomon’s Temple.

Of such curious links and interesting bypaths is the study of astronomy and its connection with Freemasonry, the more beautiful when we see eye to eye with the Psalmist in the Great Light:

“The Heavens Declare the Glory of God and the Firmament Sheweth His Handiwork.”


* Originally Published: SHORT TALK BULLETIN – Vol.VIII, March 1930, No.3.

What is the Truth behind the 47th Problem of Euclid?

What is the Truth behind the 47th Problem of Euclid?

Containing more real food for thought, and impressing on the receptive mind a greater truth than any other of the emblems in the lecture of the Sublime Degree, the 47th problem of Euclid generally gets less attention, and certainly less than all the rest. Just why this grand exception should receive so little explanation in our lecture; just how it has happened, that, although the Fellowcraft’s degree makes so much of Geometry, Geometry’s right hand should be so cavalierly treated, is not for the present inquiry to settle. We all know that the single paragraph of our lecture devoted to Pythagoras and his work is passed over with no more emphasis than that given to the Bee Hive of the Book of Constitutions. More’s the pity; you may ask many a Mason to explain the 47th problem, or even the meaning of the word “hecatomb,” and receive only an evasive answer, or a frank “I don’t know – why don’t you ask the Deputy?”

The Masonic legend of Euclid is very old – just how old we do not know, but it long antedates our present Master Mason’s Degree.  The paragraph relating to Pythagoras in our lecture we take wholly from Thomas Smith Webb, whose first Monitor appeared at the close of the eighteenth century. It is repeated here to refresh the memory of those many brethren who usually leave before the lecture:

The 47th problem of Euclid was an invention of our ancient friend and brother, the great Pythagoras, who, in his travels through Asia, Africa and Europe was initiated into several orders of Priesthood, and was also Raised to the Sublime Degree of Master Mason. This wise philosopher enriched his mind abundantly in a general knowledge of things, and more especially in Geometry. On this subject he drew out many problems and theorems, and, among the most distinguished, he erected this, when, in the joy of his heart, he exclaimed Eureka, in the Greek Language signifying “I have found it,” and upon the discovery of which he is said to have sacrificed a hecatomb. It teaches Masons to be general lovers of the arts and sciences.

Some of facts here stated are historically true; those which are only fanciful at least bear out the symbolism of the conception. In the sense that Pythagoras was a learned man, a leader, a teacher, a founder of a school, a wise man who saw God in nature and in number; and he was a “friend and brother.” That he was “initiated into several orders of Priesthood” is a matter of history.  

That he was “Raised to the Sublime Degree of Master Mason” is of course poetic license and an impossibility, as the “Sublime Degree” as we know it is only a few hundred years old – not more than three at the very outside. Pythagoras is known to have traveled, but the probabilities are that his wanderings were confined to the countries bordering the Mediterranean. He did go to Egypt, but it is at least problematical that he got much further into Asia than Asia Minor.

He did indeed “enrich his mind abundantly” in many matters, and particularly in mathematics. That he was the first to “erect” the 47th problem is possible, but not proved; at least he worked with it so much that it is sometimes called “The Pythagorean problem.” If he did discover it he might have exclaimed “Eureka” but he sacrificed a hecatomb – a hundred head of cattle – is entirely out of character, since the Pythagoreans were vegetarians and reverenced all animal life.

Pythagoras was probably born on the island of Samos, and from contemporary Grecian accounts was a studious lad whose manhood was spent in the emphasis of mind as opposed to the body, although he was trained as an athlete. He was antipathetic to the licentiousness of the aristocratic life of his time and he and his followers were persecuted by those who did not understand them. Aristotle wrote of him: “The Pythagoreans first applied themselves to mathematics, a science which they improved; and penetrated with it, they fancied that the principles of mathematics were the principles of all things.”

It was written by Eudemus that:  “Pythagoreans changed geometry into the form of a liberal science, regarding its principles in a purely abstract manner and investigated its theorems from the immaterial and intellectual point of view,” a statement which rings with familiar music in the ears of Masons.

Diogenes said “It was Pythagoras who carried Geometry to perfection,” also “He discovered the numerical relations of the musical scale.” Proclus states: “The word Mathematics originated with the Pythagoreans!”

The sacrifice of the hecatomb apparently rests on a statement of Plutarch, who probably took it from Apollodorus, that “Pythagoras sacrificed an ox on finding a geometrical diagram.”  As the Pythagoreans originated the doctrine of Metempsychosis which predicates that all souls live first in animals and then in man – the same doctrine of reincarnation held so generally in the East from whence Pythagoras might have heard it – the philosopher and his followers were vegetarians and reverenced all animal life, so the “sacrifice” is probably mythical.

Certainly, there is nothing in contemporary accounts of Pythagoras to lead us to think that he was either sufficiently wealthy or silly enough to slaughter a hundred valuable cattle to express his delight at learning to prove what was later to be the 47th problem of Euclid.

In Pythagoras’ day (582 B.C.), of course, the “47th problem” was not called that.

It remained for Euclid, of Alexandria, several hundred years later, to write his books of Geometry, of which the 47th and 48th problems form the end of the first book. It is generally conceded either that Pythagoras did indeed discover the Pythagorean problem, or that it was known prior to his time, and used by him; and that Euclid, recording in writing the science of Geometry as it was known then, merely availed himself of the mathematical knowledge of his era.

It is probably the most extraordinary of all scientific matters that the books of Euclid, written three hundred years or more before the Christian era, should still be used in schools. While a hundred different geometries have been invented or discovered since his day, Euclid’s “Elements” are still the foundation of that science which is the first step beyond the common mathematics of every day. In spite of the emphasis placed upon geometry in our Fellowcrafts degree our insistence that it is of a divine and moral nature, and that by its study we are enabled not only to prove the wonderful properties of nature but to demonstrate the more important truths of morality, it is common knowledge that most men know nothing of the science which they studied – and most despised – in their school days.

If one man in ten in any lodge can demonstrate the 47th problem of Euclid, the lodge is above the common run in educational standards!

And yet the 47th problem is at the root not only of geometry, but of most applied mathematics; certainly, of all which are essential in engineering, in astronomy, in surveying, and in that wide expanse of problems concerned with finding one unknown from two known factors.  At the close of the first book Euclid states the 47th problem – and its correlative 48th – as follows:

47th – In every right angle triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

48th – If the square described of one of the sides of a triangle be equal to the squares described of the other two sides, then the angle contained by these two is a right angle.

This sounds more complicated than it is. Of all people, Masons should know what a square is!  As our ritual teaches us, a square is a right angle or the fourth part of a circle, or an angle of ninety degrees.  For the benefit of those who have forgotten their school days, the “hypotenuse” is the line which makes a right angle (a square) into a triangle, by connecting the ends of the two lines which from the right angle.

For illustrative purposes let us consider that the familiar Masonic square has one arm six inches long and one arm eight inches long.  If a square be erected on the six-inch arm, that square will contain square inches to the number of six times six, or thirty-six square inches.  The square erected on the eight-inch arm will contain square inches to the number of eight times eight, or sixty-four square inches. The sum of sixty-four and thirty-six square inches is one hundred square inches.

According to the 47th problem the square which can be erected upon the hypotenuse, or line adjoining the six and eight-inch arms of the square should contain one hundred square inches. The only square which can contain one hundred square inches has ten-inch sides, since ten, and no other number is the square root of one hundred. This is provable mathematically, but it is also demonstrable with an actual square. The curious only need lay off a line six inches long, at right angles to a line eight inches long; connect the free ends by a line (the Hypotenuse) and measure the length of that line to be convinced – it is, indeed, ten inches long.

This simple matter then is the famous 47th problem.  But while it is simple in conception it is complicated with innumerable ramifications in use.

It is the root of all geometry. It is behind the discovery of every unknown from two known factors. It is the very cornerstone of mathematics. The engineer who tunnels from either side through a mountain uses it to get his two shafts to meet in the center. The surveyor who wants to know how high a mountain may be ascertains the answer through the 47th problem.

The astronomer who calculates the distance of the sun, the moon, the planets, and who fixes “the duration of time and seasons, years and cycles,” depends upon the 47th problem for his results.  The navigator traveling the trackless seas uses the 47th problem in determining his latitude, his longitude, and his true time.  Eclipses are predicted; tides are specified as to height and time of occurrence, land is surveyed, roads run, shafts dug, and bridges built because of the 47th problem of Euclid – probably discovered by Pythagoras – shows the way.

It is difficult to show “why” it is true; easy to demonstrate that it is true. If you ask why the reason for its truth is difficult to demonstrate, let us reduce the search for “why” to a fundamental and ask “why” is two added to two always four, and never five or three?” We answer “because we call the product of two added to two by the name of four.” If we express the conception of “fourness” by some other name, then two plus two would be that other name. But the truth would be the same, regardless of the name.  So it is with the 47th problem of Euclid. The sum of the squares of the sides of any right-angled triangle – no matter what their dimensions – always exactly equals the square of the line connecting their ends (the hypotenuse). One line may be a few 10’s of an inch long – the other several miles long; the problem invariably works out, both by actual measurement upon the earth and by mathematical demonstration. [Image Credit: 47th Problem of Euclid by Peter Savant]

It is impossible for us to conceive of a place in the universe where two added to two produces five, and not four (in our language). We cannot conceive of a world, no matter how far distant among the stars, where the 47th problem is not true. For “true” means absolute – not dependent upon time, or space, or place, or world or even universe. Truth, we are taught, is a divine attribute and as such is coincident with Divinity, omnipresent.

It is in this sense that the 47th problem “teaches Masons to be general lovers of the art and sciences.” The universality of this strange and important mathematical principle must impress the thoughtful with the immutability of the laws of nature. The third of the movable jewels of the Entered Apprentice Degree reminds us that “so should we, both operative and speculative, endeavor to erect our spiritual building (house) in accordance with the rules laid down by the Supreme Architect of the Universe, in the great books of nature and revelation, which are our spiritual, moral and Masonic Trestleboard.”

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; this rule that, given a right angle triangle, we may find the length of any side if we know the other two; or, given the squares of all three, we may learn whether the angle is a “Right” angle, or not. With the 47th problem, man reaches out into the universe and produces the science of astronomy.  

With it, he measures the most infinite of distances.  With it, he describes the whole framework and the handiwork of nature.  With it, he calculates the orbits and the positions of those “numberless worlds about us.” 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.

Considered thus, the “invention of our ancient friend and brother, the great Pythagoras,” becomes one of the most impressive, as it is one of the most important, of the emblems of all Freemasonry, since to the initiate it is a symbol of the power, the wisdom and the goodness of the Great Artificer of the Universe.  It is the plainer for its mystery – the more mysterious because it is so easy to comprehend.

Not for nothing does the Fellowcraft’s degree beg our attention to the study of the seven liberal arts and sciences, especially the science of geometry, or Masonry. Here, in the Third Degree, is the very heart of Geometry, and a close and vital connection between it and the greatest of all Freemasonry’s teachings – the knowledge of the “All-Seeing Eye.”

He that hath ears to hear – let him hear – and he that hath eyes to see – let him look!  When he has both listened and looked, and understood the truth behind the 47th problem he will see a new meaning to the reception of a Fellowcraft, understand better that a square teaches morality, and comprehend why the “angle of 90 degrees, or the fourth part of a circle” is dedicated to the Master!


~  From, SHORT TALK BULLETIN – Vol.VIII, October 1930, No.10.

Combating Ignorance

Combating Ignorance

It is only necessary to make war with five things; with the maladies of the body, the ignorances of the mind, with the passions of the body, with the seditions of the city and the discords of families.” – Pythagoras

Science is not a philosophy or a spiritual path; it’s a way of behaving in the world. It is a way of thinking that encourages logic, reason, information and communication in such a way as to explore the world in wonder and discovery.

It is unfortunate that polarization and nationalism, tribalism if you will, have made “fake news” and “alternative facts” part of our everyday life now. It is a reality with which we must learn how to navigate. It is not only learning to dig through facts and figures, research and media hype, but it is learning that we must, sometimes, unlearn. It begin with the idea of “we must know” is a fallacy. What we must do is begin to swim in our own ignorance and be cognizant of what we do not know.

To be blunt, if we want to fight ignorance, we must start with our own.

project_open-scienceWe listen every day to people who, by virtue of their self-appointed “knowledge,” without the science or experience to back it up, discard the rigorous work that scientists have done to establish or debunk our knowledge of nature. Chemists, astrophysicists, climatologists, oceanographers, biologists, geneticists, and nutritionists have all been sidelined when their messages did not fit the narrative of corporate interests or media hype. Those that seem to have the most money, most market share, or most “brand” have the last say. We separate the educated as elitists and the corporate interests as “the common man.” Who would have our best interests at heart?

To be very clear, expertise is not the same thing as elitism. A real expert and scientist knows where their knowledge boundaries lie. They know that they know less than they have researched, and are on a quest to explore. They are developing theories and testing them, asking what didn’t work and what did. They know that the fruits of their labors may take years, decades, to bear truth, and most likely lead to more questions.

Elitism, on the other hand, is “the belief or attitude that individuals who form an elite—a select group of people with an intrinsic quality, high intellect, wealth, special skills, or experience—are more likely to be constructive to society as a whole, and therefore deserve influence or authority greater than that of others.” They are the self-appointed leaders or gurus that have the answers. A scientist may be an elitist, but that is not a reflection on science but on the character of the individual. Or lack thereof.

Having just finished the documentary, “Behind the Curve,” on Netflix, I found it extremely interesting to listen to both sides of the debate on “flat earth theory.” There are those in the Flat Earth community who truly believe what science has let them down, that they have the truth and the science to back it up. What was extremely interesting was to hear the scientist’s remarks about this group of contrary thinkers. There was no condescension or elitism of any of the scientists interviewed. There was no pity or condemnation. It was a true desire to not ignore or sideline the discussion but to engage in it; it was about bringing people together rather than considering it an “us” and “them” situation. This was not about belief and fact; it was about education. Knowledge. Combating ignorance.

Freemasonry has an interesting take on the ideas of nature and science as they are combined with philosophy and a search for Truth. It is one of the few places that it seems both can come together, to discuss and debate with a very open narrative. Science is valued as much as the experiential; physics and metaphysics co-exist in conversation and thought. Nothing is off limits. These conversations, whether in a Lodge meeting or in social gatherings, at study groups or philosophical study centers are the ways we fight ignorance, if we are willing to listen.

top-10-books-every-college-student-read-e1464023124869I recently attended a study group where the topic was considering whether or not humanity had an influence on climate change. I was dead certain that humans influenced nature’s cycles; how could it not? There are seven billion people in the world, occupying space, consuming resources, and polluting the world around them. It was a belief and I knew it. However, I challenged myself to come with an open mind and not not make a judgment before entering the room. I am not, by training, a climatologist, meteorologist, geologist, or any other kind of -ologist. I know high-school level geology, and freshman college science. Let’s face it, I know nothing. What I did was bring in my own attitude and readings from media and pseudo-science journals, aimed at producing a message swinging one way or another. Being out of school for many years, I also felt the pride of age – I knew something of the world, darn it. I really felt like “know thyself” was part of my vernacular.

I admit to the conversation bringing my opinion around to a more moderate view rather than to a specific “side” of the debate.  The presenter discussed scientific findings I had not considered, and geologic facts of which I had absolutely no knowledge. I learned about ice ages, findings in the melting of current glaciers, ice core samples, geologic time scales, and historical facts of global significance. I won’t say that my mind was changed; I will say that I walked out with a broader idea of questioning what I have been told, and learning the truth for myself. I learned that what I had was a belief, not evidence. If I was going to change my ignorance, I needed to do the work. Myself.

This is where, to me, the collision of science and Freemasonry are at their best. Freemasonry is a mystery school – an initiatory rite that brings about the idea that the human being is nature and the best way to understand nature and the mysteries of life and death, is to study nature. How to study nature? Ancient Greek mystery schools according to Blavatsky are “not a unique system but, based on the spiritual structure of the universe,” of which it is important to understand Nature. They are inextricably linked, the Spirit and Nature, perhaps even one in the same. Freemasonry, as a modern descendant of these mystery schools seeks to take the core of nature and spirit, and propel the human into learning that both reside within humanity, and it is the Freemason’s job to not only continue to seek truth but to also seek Truth. It is to always ask questions, from knowing yourself to knowing the world, and doubt everything. It is a respect for the scientific process as much as it is for our own process. We are seven billion experiences and all are equally valid. Else, why are we having them?

pythagorasFor the ancient philosophers, ignorance was the opposite of good. To both Aristotle and Plato, no one does wrong willingly but only out of ignorance. Socrates had his own methods for combating ignorance, and many of these principles can be found in Freemasonic ritual and education. From continuous learning and making a daily advancement in education to providing education rather than criticism, the Freemason becomes a scientist of the world. Freemasons build on Socrates idea that one should “know thyself” in that they are lacking in knowledge, and that we have no idea what is best for others. The center point is the key to balance in all things but especially to combating ignorance. A measured approach, curious yet mindful. Lastly, I think Socrates was most right when he said that ignorance is inevitable. When Socrates said “I know nothing except the fact of my ignorance,” what he was saying was that he was not ignorant of all things but that he was aware that he was ignorant of all things. He knew that he would be forever ignorant and it was only through perseverance that he could become “good.”

Freemasonry and Geometry: What are the Symbolic Meanings of the Most Basic Geometric Forms?

Freemasonry and Geometry: What are the Symbolic Meanings of the Most Basic Geometric Forms?

The more abstract a concept is, the more meaning that we can find in it. Is this because the meaning is all projected from within our minds, or because there is something objectively real there to be found? Plato or Pythagoras certainly believed the latter, as did Jung with his archetypes, and certainly the abstraction of mathematics has enabled much of our modern scientific grasp of the workings of the world around us.

In Freemasonry, we deal in symbols constantly. The Temple itself is a symbol, as are all the rituals which take place within, and there are layers of meaning which are only revealed as one progresses through the degrees. Geometry, in particular, is very significant to Freemasonry. This stems not only from the practical geometrical knowledge that was required to build grand cathedrals and other structures by operative masonry, but also from the Western wisdom teachings stemming from Pythagoras, Plato, and others, often referred to as Sacred Geometry, which sees a greater symbolic significance in geometrical forms.

While its common to find interpretations of more complex forms like the Flower of Life, or Metatron’s Cube, some of the geometric forms I find most fascinating are the simplest. This is because the simpler a form is, the more universal it is. In the simplest forms, I see the very foundations of all creation. So, what is the symbolic significance of a few of these simple geometric forms?

What follows are not in any sense “official” masonic interpretations of these forms, but merely one mason’s reflections on them. Books can and have been written to interpret these and other geometric forms, so here we will just be sampling a few.

The Point

pointThe point is the beginning of all forms, and all finite things. In that sense, it is the most abstract representation of finity, of a finite form. It does not even have definitions, specific boundaries, size, or dimensions, and therefore is the most abstract finite thing that can emerge from the formless infinity. It is also the beginning of duality, because in the point, you have one thing which is separated from everything else, the thing and its surrounding context, self and world. Yet, without a clear boundary, it still contains an element of infinity within it. The point can be viewed as infinitely small, or infinitely large. Without boundaries and other objects to be compared to, it has no reference.

In the point, we can see the fundamental essence of all finite entities, including each person: the Self, consciousness, existence.

The Line

HorizThe line is the first movement of the point, the first dimension of form. As such, it represents the most basic possible expression of time and motion. In the line, we can see the progression from moment to moment of what was first seen in the point. While the point is motionless and still, the line implies a trajectory, and a continuity. It is also the first impression of a space in which motion and change can take place. Yet, the line is only the simplest, most primal of forms with a boundary, and does not yet demonstrate a space in which objects may exist, although it begins to imply them.

In the line, we can see the fundamental essence of all motion and change, linearity, past progressing into future, and memory.

The Cross

sacred geometryThe cross is where two lines meet at a perfect right angle, and the simplest indication of the second dimension. In the cross, we can see the implied 2-dimensional plane stretching out in four directions. Also within the cross, we can see both the singular point, and the line doubled. Like every new form, it is the expansion of what came before it. The cross is where two intersect to become one; two planes, two people, two forces, and the point at which they meet is also their origin.

In the cross, we can see the fundamental essence of all duality, multiplicity, and complexity. It is the simplest possible mandala, and also represents the multiple dimensions of self, whether masculine/feminine, thinking/feeling, or ordered/chaotic, intersecting at the central point of consciousness or spirit.

The Circle

infinity circleThe circle is the perfect return of the trajectory of the point traveling in a line back to its origin. Simultaneously, it is an enlarged and expanded representation of the point, being equidistant in all directions from the center point. In the circle, the completeness and perfection of the process of the formless point expanding into form can be seen. Within the circle, we can fit any number of mandalic or sacred forms, such as the pantagram, the hexagram, the cross, or the equilateral triangle. It contains all of these in essence, and yet is beyond all of them.

In the circle, we can see the totality of form, the Ouroboros, the nearest form to infinity.

The Circumpunct

circumpunct freemasonryThe circumpunct is the completion of the journey from finite point to infinite circle. In the circumpunct, all of the dimensions of self which have progressed outward into form are in complete and total balance and alignment with their formless origin. In the mind, it is the personality in complete harmony with its essence and origin. It also represents the essential boundary of the self. While the point had a finite existence, it still had a certain infinite quality, in it’s lack of defined boundaries. In the circumpunct, we have both the boundary-less point of origin, and the boundary, with self on the inside, and world on the outside.

In the circumpunct, we can see the completion of all existence, the simultaneity of infinity and finite form, the perfection of self, world, and the relationship between the two.

Further Reflections

expanding dimensionsThe truth is that neither you nor I have ever really seen a point or a line, only things that are shaped like them, usually drawings on paper. But the truest sense in which a point and a line exist is in the abstract realm of ideas, yet they are clearly significant. We could not build anything without them, and this is true of mathematical abstractions, in general: they are ephemeral, yet essential. But can they be regarded as the true foundations of all creation, of reality itself?

What I am struck most by these simple forms is how each dimension, and the basic geometric form it represents, implies and transcends the next. The moment you create a point, it imples that that point could transcend the 0 dimension, and be a line, if only it moved beyond that 0 dimension. The moment you create a line, it implies that that line could move in a different direction, transcending that 1st dimensional existence, creating a plane. The moment you create a plane, it implies that that plane could be bent or folded, and that therefore a third dimension must exist. The moment you have a 3-dimensional object, it implies that that object can shift and change across time, thus implying a fourth dimension, transcendent from 3-dimensional space.

This seems to me to imply that the world in which we find ourselves is in fact a manifestation from the infinite 0 dimension, into the four dimensions where we currently find ourselves. Its almost as if a divine infinite mind, in similar manner to an architect, charted out and traced the fundamental principles of reality by which a creation could manifest.

But is that really where it ends? For us, the 4 dimensions are the extent of dimensionality we can see and understand, with even the 4th being somewhat mysterious to us. But what if this is merely because of our position along the spectrum of dimensions, and in actuality, this process of one dimension implying the next goes on infinitely, with the 4th implying and creating the 5th, the 5th the 6th, ad infinitum?

String theorists and various other kinds of physicists currently posit some number of dimensions, often 11 or higher, but what if there is no ceiling to the dimensional hierarchy extending into the unseen, unknown realms of possibility? In that case, we truly could be said to be dwelling in an infinite creation.

infinite dimensions

Eastern Sages, Western Secrets: What Has Vedanta to Do with Freemasonry?

Eastern Sages, Western Secrets: What Has Vedanta to Do with Freemasonry?

Like unto that of a man blindfolded and carried away by robbers from his own country is a man’s condition. The folds of cloth over his eyes being removed by a friend, he recovers the use of his eyes and slowly finds his way home, step by step, inquiring at each stage. So also, the good teacher instructs the seeker of Truth and helps him to unloose his bonds of desire. ~ From the Chandogya Upanishad 6:14:1/3

As a young seeker of Truth, I found the wisdom of the East long before I found the hidden wisdom of the West. After I had turned away from the exoteric religion of my upbringing, and briefly embraced the alternative orthodoxy of nihilistic materialist scientism, I began to seek truths beyond the tiresome antagonism of the “religion vs. science” debate, and it was not long before I discovered the Bhagavad Gita, Taoism, Buddhist teachings, and Western interpreters like Alan Watts and Ram Dass. Of all the Eastern traditions, Vedantic philosophy (rooted in the Vedas, Upanishads, and related texts) has influenced my worldview more than any other system of thought.

Now, as a newcomer to the Western wisdom tradition of Freemasonry, and to some extent also Theosophy, Alchemy, and Hermeticism, I am struck by the similarity in essence, but difference in expression between East and West. Although I still have much to learn, I sense that the one great Truth, described by Aldous Huxley as the Perennial Philosophy, is fundamentally the same in the Western traditions as in the East, but is clothed in secrecy and symbolism, and in some ways emphasizes certain values over others. The contrast between East and West is particularly interesting to me, as they are two halves of humanity’s collective mind, just as they represent two poles on our globe.

Torch Bearers from the East

eastern wisdomTo begin with, we can be fairly certain that the connection between East and West goes back at least as far as all of Western history, as we know it. The history of great Western philosophers is also in part a history of those who journeyed to the East, learned, and came back with new insights which had to be clothed and couched in the prevailing worldview of whatever Western culture they were returning to, in order to be understood and accepted; even then, they were often rejected, sometimes violently. Bearers of the torch carrying light from the East are notoriously persecuted upon their return to the West, and often meet a gruesome end.

Some think that none other than Jesus of Nazareth is one such example, although this is still a highly controversial theory, with inconclusive evidence that he visited the East during his “missing years.” Another is Pythagoras, who is thought to have traveled extensively in his youth, at least as far East as Persia, and who also was killed by the ignorant. One that is more recent, and therefore also more certain, is that of H. P. Blavatsky, one of the founders of Theosophy and originators of Victorian spiritualism, which also preceded and influenced much of what people consider to be “new age” or “new thought” ideas, today.

In general, I think that we underestimate the degree to which people traveled, and teachings were shared or spread via the Silk Road and other trade routes between East and West, throughout our history. It doesn’t help that our mainstream historians are hesitant to acknowledge Eastern influence on Western thought. So, with all this cross-pollination, why are the West and East not identical?

Wisdom in Contrast

east and westThe most striking difference to me between East and West, in terms of the mysteries, is that in the East they simply aren’t mysteries. There isn’t much secrecy in Vedantic, Buddhist, or Taoist traditions, teachers are prone to publicly say things like, “So long as God seems to be outside and far away, there is ignorance. But when God is realised within, that is true knowledge [Sri Ramakrishna].” The volumes of Vedantic and other Eastern teachings are filled with things like this, which in the West might be merely scoffed at today, but in the past, could have led to a burning at the stake or crucifixion, for speaking so blasphemously.

Here, we arrive at what seems to me to be the chief reason for the secrecy of the Western traditions, which is the millennium of history in which the desert religions of Abraham turned from their mystic origins to the darkness of fanaticism and ignorance, and dogma spread like a plague, reigning over the West with the fiery whip of religious persecution for roughly one thousand years. While our history lessons often breeze over this period as the “Dark Ages,” with some discussion of feudalism and monarchy, the harsh reality is that Western culture underwent an intellectual and religious cleansing, where all ideas that ran contrary to the dogmas of the church (or the mosque) were punished by torture, imprisonment, and gruesome death.

No wonder, then, that those who held the wisdom of the ancient traditions of the West were forced to seek shelter in organizations like operative freemasonry, which provided secrecy, as well as a highly effective organizational structure, and fertile ground for the symbolic coding of wisdom in the tools and principles of masonry. Meanwhile, our Eastern neighbors, safeguarded by distance, geographical features like the himalayas, and their own kingdoms and power structures, held the wisdom passed on from ancient times, and continued teaching it in a relatively open manner. This is an oversimplification, but is generally more accurate than not, I would say.

Aside from being hidden vs. open, what else separates West from East? Perhaps there is a more essential difference, due to differences in temperament and culture of the two peoples, shaped in part by their climates. I could make an argument that the harsh climates of Europe, mostly in the North, bred a spirituality more focused on action, intention, and the overcoming of obstacles, while mostly tropical Eastern environments, particularly in India, bred a spirituality with a more passive focus on meditation and surrender. This theory may have some merit, but ultimately we’ll never know for sure. It does seem to me that the West is more focused on building and actively working to perfect the human, while the East is more about dissolving, letting go, and becoming free from attachment.

At the risk being accused of over-simplifying neuroscience, the general dichotomy of the left and right sides of the brain could also be said to correspond to the same principle. In many ways, West and East are akin to the left and right. The West/Left is all about clearly defined logic, boundaries, and places a greater emphasis on intellect; the East/Right is more about direct perception, dissolving boundaries, and places greater emphasis on intuitive realizations. With all these differences, is there common ground? What is the corpus callosum of East and West?

The Bridge and the Stairway

philosophyI would say absolutely, and as the beginning of this post alludes to, there are striking similarities, at times, between the teachings of the Lodge or Western esotericism in general, and that of the Swamis. Both speak of the human condition as a state of darkness and ignorance striving for light; both design their sacred structures to resemble the human body; both tend towards idealism, or the belief that consciousness rather than matter is fundamental; both ultimately teach that God dwells within.

The commonalities are surely greater than the differences, and the essence, I believe, is one. In many ways, co-masonry in particular may be an excellent bridge between the two systems, with its close ties to theosophy, a much more Eastern tradition than many of the other Western systems, and its focus on adopting the feminine into the masculine lodge. Whatever the bridge we use, it seems clear to me that we must blend East and West, right and left, action and contemplation, intellect and intuition, if we are ever to rise above, and climb the stairway to a greater truth, some transcendent gnosis.

Ultimately, I believe that we are all approximating this same truth, like a middle point of a circle which both East and West circumambulate in their own ways. The classical human mystical experience, which all these traditions are ultimately based on, seems to be more-or-less universal across cultures, and to differ only in it’s interpretation post-experience, and the cultural context which either allows it to flourish, or forces it to hide and conceal itself. Either way, the truth will out, and the light will not be concealed for long, for it is what every human on this planet thirsts for, in the depths of their soul.

The Sacred Tetractys: Why do Freemasons connect the dots?

The Sacred Tetractys: Why do Freemasons connect the dots?

If Pythagoras found himself transported to the modern world, he would have much to learn about technology, science, and human thought. But is there something Pythagoras can still teach us today in his symbol of the tetractys? What do the dots reveal? How is it significant to Freemasonry?

To start with, tetractys refers to a symbol of the Pythagoreans which consists of four rows of dots containing one, two, three, and four dots respectively which form an equilateral triangle. Many have found the tetractys full of sublime meaning.

When did the tetractys first come about? To answer this question may be more difficult. Very little is known about the real Pythagoras, or rather too much is “known” about him, but most of it is surely mistaken. The biographical trail is scattered with contradictions. It combines the sublime, the absurd, the inconceivable, and the just plain weird.

The teachings are elusive because he never wrote anything down. His treatises are only known to us through other Greek researchers. Consequently, it is up to present-day scholars (and there are many) to sift through these works in order to find a common thread that can be genuinely ascribed to Pythagoras. Jean Leblond I - 1605-1666

We do know that Pythagoras was born in Samos in the sixth century B.C.E. Pythagoras was both a mystic and a scientist, although some scholars tend to praise his mathematical prowess while looking away with embarrassment at his perceived “mysticism.” For Pythagoreans, they were one and the same.

The Science of Number was the cornerstone of the Pythagoreans. It describes, if not yet everything, at least something very important about physical reality, namely the sizes and shapes of the objects that inhabit it.

The Pythagoreans influenced the world by the simple expression:

“All is number.” – Pythagoras

What Did Pythagoras mean by this famous motto “All is Number?”

Is it possible to listen to this message today afresh, with Pythagorean ears? What teaching does the tetractys offer a Freemason?

The Tetractys: A Masonic Lecture by William Preston (1772)

FINAL Tetractys PrestonFreemasons in earlier times thought highly of Pythagorean philosophy. Brother Manly Palmer Hall, a 33° Mason dedicated an entire chapter in his work “The Secret Teachings of all Ages” to the both mystical and philosophical qualities of Pythagorean numbers.

Hall wrote:

“The ten dots, or Tetractys of Pythagoras, was a symbol of the greatest importance, for to the discerning mind it revealed the mystery of universal nature.”

Hall states that if one examines the tetractys symbolically a wealth of otherwise hidden wisdom begins to reveal itself.

The Prestonian Lectures (1772) give us further insight into some of the possible masonic thinking on the tetractys in the 1800’s.  It was the subject in one of the series of lectures written by Brother William Preston for instruction and education of the Lodge members.

An excerpt of the Lecture (1772) goes as follows:

“The Pythagorean philosophers and their ancestors considered a Tetractys or No. 4:

  • 1st as containing the decad;
  • 2nd as completing an entire and perfect triangle;
  • 3rd as comprising the 4 great principles of arithmetic and geometry;
  • 4th as representing in its several points the 4 elements of Air, Fire, Water and Earth, and collectively the whole system of the universe;
  • Lastly as separately typifying the 4 external principles of existence, generation, emanation, creation and preservation, thence collectively denoting the Great Architect of the Universe Wherefore to swear by the Tetractys was their most sacred and inviolate oath.”

In other words, it is taught to Freemasons that a four-fold pattern permeates the natural world, examples of which are the point, line, surface and solid and the four elements earth, water, air and fire. Musically they represent the perfect consonants: the unison, the octave, the fifth and the fourth.

The Divine Creator in Freemasonry is sometimes referred to as The Great “Architect” or Grand “Geometrician” always building the universe through the creative tools of the geometer. Tetractys itself can be interpreted as a divine blueprint of creation. Grand Geometrician

Some say that Pythagoras and his successors had two ways of teaching, one for the profane, and one for the initiated. The first was clear and unveiled, the second was symbolic and enigmatic. In order to achieve mastery of this universe, a person has to discover the veiled meaning of numbers hidden in all things.

I have often wondered if we could hypothetically peer into the mind of the Grand Geometrician, and the veil was lifted, what design would we see?

The Grand Design

Perhaps we would see how the Master Builder has ordered all things by measure and number and weight. Throughout the structure of the universe the properties of number are manifested. Geometry is fundamental to the work of the masonic builders. It is engaged with the first configurations of the Plan upon which the form is erected and the idea materialized.

Examining numbers symbolically, they represent more than quantities; they also have qualities. Brother H. P. Blavatsky in the “Secret Doctrine” tells us the numbers are entities. They are mysterious. They are essential to all forms. They are to be found in the realm of essential consciousness. They are clues to our evolution.

Blavatsky emphasizes that the study of numbers is not only a way of understanding nature, but it is also a means of turning the mind away from the physical world which Pythagoras held to be transitory and unreal, leading to the contemplation of the “real.”

Personally, I find that the masonic teachings in all their many symbolic forms a good way to study numbers. The reason I continually come back to Pythagorean philosophy is the tradition of music theory. In music, the Divine patterns of the Grand Geometrician are expressed in musical ratios. Harmony through sound, therefore, can be applied to all phenomena of nature, even going so far as to demonstrate the harmonic relationship of the planets, constellations, elements and everything, really. The reason being that all life vibrates, like the string. Tetractys Portal

Why do Freemasons connect the dots? Like many symbols, the tetractys can lead a craftsman down a rabbit hole of self-discovery. By rabbit hole, I mean a portal into a mysterious and infinite wonderland of formulas filled with beauty, confusion and intrigue – a place to encounter all sorts of adventures with concepts beyond our wildest dreams that keeps us coming back for more.

“The more deeply we study the processes of nature the greater in every direction becomes our admiration for the wonderful work of Him who made it all.”

– C.W. Leadbeader


Note: The full Prestonian Lecture on the Tetractys and Masonic Geometry can be referenced in Ars Quatuor Coronatorum, Volume 83.

Universal Freemasonry

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