Triangles Everywhere

Triangles Everywhere

I was recently exploring the idea of the triangle – its form, function, stability, and meanings. In Freemasonry, as in many traditions, the triangle holds significant influence in symbolic meanings.

A triangle is a polygon with three sides and three vertices. There are many forms of triangles – right, equilateral, obtuse, acute, isosceles, and scalene. There are also oblique and degenerate triangles. Triangles may be multiple types. Triangles are generally believed to be two-dimensional objects whose interior angles, at least in Euclidean space, equal 180 degrees. They can be various shapes but the ones most often seen are right triangles and equilateral triangles.

Of the triangle knowledge from history, the famous philosophers Pythagoras, Plato, and Euclid are known best for theorems, ideas, and esoteric supposition surrounding the form. The form is so basic that it’s most likely older than written history. Ancient petroglyphs, such as those from Columbia, the Sierras in North America, and Mexico, show humans with bodies and heads in the form of triangles. This is a basic shape that mimicked the human form, with wide shoulders and narrow waist, or a wide head crown and narrow chin. There isn’t anything to indicate, in-depth, the symbolic meaning of the triangle other than it being incorporated into the human form.

The Egyptians used the triangle quite often, generally in the realignment of land plots after the Nile floods but also in architecture. In a 2000 thesis article regarding the “sacred triangle,” the author asserts that Egyptians knew and used, even in the Old Kingdom, the “sacred triangle” of 3:4:5. Indeed, the author goes on to state that using straight vertices, or a “simple, straight vertical pole,” to find location or identify specific time of day or days of the year. While this is a heavy-mathematics article, the reader might find some deeper, symbolic meanings in the geometry.

During the 6th C. B.C.E., the School of Pythagoras became known for its theorem regarding the formation of the ‘sacred triangle.’ Pythagoras left no mathematical writings of his own, while Euclid and Plato did. Thales of Miletus is really the creator of basic mathematics and geometry, and probably the first to give us theorems about the triangle. Pythagoras, who created the words philosophy and mathematics, is more well-known and did much to bring the form of the triangle into deeper meaning.

To Pythagoras, the number 10 was the holiest of numbers; the tetractys is a triangle form of 10 dots, created by interlinking the dots into nine triangles forming the 10th, larger triangle. It is used to symbolize the creative forces of the universe. From ancient-symbol.com, “In the figure, the first row has a single point that is representative of the Creator, the active principle, the divine power behind all creation and is associated with wisdom. The second row contains two points that represent the passive principle and are associated with friction, movement, impulse, strength, and courage. The third row with three points signifies the world coming out of the union of the above two, a union of physical and mental balance and is associated with harmony. The fourth row has four points that represent the four liberal arts & sciences that complete the world. These four points symbolize the four elements of earth, fire, air, and water.” This was, generally speaking, the first time that the philosophical meaning of a number, its holiness and perfection, being derived from pure mathematical reasoning rather than from inductive reasoning. It was more than the total of our fingers on our hands. Another interesting article on the triangle and tetractys, among other things, can be found here: http://www.projectawe.org/blog/2015/12/21/up-and-down-the-monochord-part-iii-triangle-trinity-unity. The author of this blog does a very good and thorough job of digging into these ideas, and I would highly encourage everyone interested in these subjects to read it.

In the alchemical writings of the Middle Ages, the classical elements of hermeticism were based off the form of the triangle, turned upward or down, with a line to denote the opposite or without to indicate the base elements. The conjoining of fire and water is indicative of balance and achieving perfection. The triangle is also seen in the “triangle of art” also known as Solomon’s Triangle. The circle in that triangle represents the space where spirits are called, with the triangle representative of the safe space from which the magician worked.

Triangles in astrology are seen as very positive, and a grand trine, or golden triangle, is seen as a creative, harmonious flow of energy in a person’s life; they generally are composed of the objects being in the same elements, in the form of an equilateral triangle.

Triangles are a form of stability, where two extremes are balanced by a third point. Triangles are everywhere in Freemasonry, overt and subtle, and have different stories surrounding each. These different stories speak to individuals differently even if the core remains the same; depending on the degree being worked and studied, the aspirant may find different aspects of the same truth. These truths are not much different than the ancient Egyptians and Greeks found and used in their daily lives. There are always extremes and balance is achieved by that third, divine point. One might also see that all emanates from the Divine, the single point, which may also turn into that point within a circle which is perfect balance. The perfect man may be the one who finds equilibrium during whatever storm shakes him. Taking this symbolism into our daily lives and applying it to our relationships with people is really the value of the study of symbol. We can work toward being the middle point between extremes, able to see both sides in equal measure. A more holistic view of those things that permeate our lives creates a better person.

Astronomy and the Quadrivium

Astronomy and the Quadrivium

Perhaps your first thought, as was mine, is: “How can Astronomy be an ‘art?'” Furthermore, how can Astronomy be called a ‘liberal’ art? From a very interesting (and worth exploring) website called “Arts of Liberty,” we have a snippet for explanation:

“To call astronomy an ‘art’ can come as a shock to a modern reader… Perhaps without thinking much about it, we think of “science” as being a genuine and exact knowledge, whereas ‘art’ is more expressive, or touchy-feely.  But, that is not quite adequate, since medicine is also an ‘art,’ and it is anything but touchy-feely… And while ‘science’ and ‘art’ do not appear to be synonyms, it could very well be that the same discipline can be called both a ‘science’ and an ‘art,’ although for different reasons.

To understand this properly requires us to consider a sense of the word ‘science’ not in common use today.  The word ‘science’ comes from the Latin word scientia, which meant a very exact knowledge, a rigorous and sure knowledge of things deduced from self-evident truths.  The ancient Greeks would have called such knowledge epistémé...  

In the vocabulary of the ancients, an ‘art,’ like a science, meant a carefully reasoned-out knowledge, but more than that, it meant a knowledge of how to produce something.  Where there is no ‘product,’ there is no ‘art.’  So it is possible for a form of knowledge to be a ‘science’ but not an ‘art.’  For example, Aristotle considered the study of god to be a ‘science,’ a body of knowledge rigorously reasoned out from self-evident principles, but not an ‘art,’ because it did not teach us how to make gods, or how to do anything about god.”

Ptolemaicsystem-smallClaudius Ptolemy (100-170 CE) was a Greek mathematician living in Alexandria. His work The Amalgest was one of the most influential astronomical works until Galileo’s discoveries in the 17th C. The Amalgest documents many mathematical and astronomical treatises, including works by other mathematicians – works thought to be lost. The most significant piece of this Amalgest (total of 13 books), is the documentation of the geocentric model of the universe. Ptolemy’s work became the accepted theory of the structure of the planets and stars, with the Earth central to all.

This influenced not only astronomy and mathematics but also theology, philosophy, and fine art. Three centuries after it was written, Hypatia and her father Theon, genius mathematicians, added to the work with their own commentary, throwing in their thoughts of elliptical orbits, the procession of the equinoxes, revising Ptolemy’s Handy Tables, and introducing the sexigesimal calculation systems. It’s believed that this rendering of the Amalgest, with the Hypatia/Theon commentary, is the one that was used for the majority of the Middle Ages although no direct reference to Theon survives and Hypatia is mentioned only in a passing 10th C. reference.


And thus, the Quadrivium ends. I hope you’ve enjoyed my answer to the Bro.’s challenge of finding a significant event, work, or person who influenced each specific liberal art. The question was posed, should Freemason’s really learn the liberal arts? The answer, to me, should be obvious. Not only should we learn the liberal arts individually, but understand their context in the whole of being educated about the natural world. Human beings can be taught easily to survive; we cannot just “pick up” how to thrive, generate ideas, and create a better world.

An example of this “Freemasonic mindset” is James Madison, even though he was not a Freemason. In his early twenties, when the United States was in its infancy, he gave up much of his career and life to studying the histories and government of world cultures. He was relentless in his pursuit of the histories and knowledge of government administration, what worked, what didn’t; he studied philosophy, history, theology, art, classical literature, geography – the liberal arts and more. By the time he finished, and began his work in the new nation’s government, he was arguably the single biggest influencer in shaping the United States Constitution and the framework of our Democracy. By learning the past deeply, he was able to innovate and create a new world. To me, that is a main goal of the Service of Freemasons.

Grammar and the Trivium

Grammar and the Trivium

Previously, I posted about the Seven Liberal Arts in general and the Trivium in particular. Recently, a challenge was given to me about providing examples of how the liberal arts are part of our everyday life, and why the human seeking to enlighten their mind might care about them. The challenge was to provide short essays on each. Three-hundred word essays are always a challenge but the gauntlet has been picked up. We’ll call these Liberal Arts: petit fours.

Therefore, for today, I give you Grammar.grammar


Grammar is the skill of knowing language. In order to form sound reasoning, one must be able to learn the words, sentence structure, and forms that make up their language and thereby, communicate clearly and with confidence. In classical training, Grammar is the “who, what, why, when, and how” of understanding and knowledge. Grammar is taught more mechanically in the modern age, which does a disservice:  humans need more than nuts and bolts to create clear ideas and communicate them. Much of what we need to learn goes beyond the adverb or adjective.

An example of this is figures of speech.Cornelis Cort 1565 Grammar Figures of speech are the use of any of a variety of techniques to give an auxiliary meaning, idea, or feeling. An example of this is dysphemism. This is the use of a harsh, more offensive word instead of one considered less harsh. Dysphemism is often contrasted with Euphemism. Dysphemisms are generally used to shock or offend.

Examples of dysphemism are “cancer stick” for cigarette,  “belly bomb” for doughnut, and “treeware” for books. Examples of Euphemisms are lighter, such as “between jobs” for unemployed, or “passed away” for death. Knowing the difference of these two figures of speech allows the audience to be placed in a certain frame of mind and creates a scene for the next stages of what is to be communicated.grandpa

As our use of grammar grows, we need tounderstand how figures of speech like this work and use them effectively when we will eventually make our case (rhetoric) via the tool of language organized into thought (logic). Thus, the well-rounded thinking man should understand not only the technical grammar of his own language, but also how the tools of grammar may be applied to the body of human knowledge for further study.

In order to communicate his own interpretation of the symbolism of any topic of organized learning, as well as what he learns from the natSocratic Methodural world around him, the study of grammar, regardless of the age of the individual, is pivotal.  Grammar is foundational to all problem-solving methods.

What would the Socratic Method be without proper grammar by which to understand and debate the ethical questions of nature?

As Socrates knew: to be able to instruct, to learn deference, and to be able to speak with authority, the enlightened human must concern himself with the very basic study of communication. That is, the study of the grammar of one’s language.

 

 

The Seven Liberal Arts – The Trivium

The Seven Liberal Arts – The Trivium

There is a real affinity for the goals of Freemasonry and the Seven Liberal Arts. From earliest teachings, we see that they are the foundation of many degree rites, the first of which is the FellowCraft Degree. To understand why this is, I think we must first understand the structure of the Seven Liberal Arts and what their history is.

The Liberal Arts have been, from antiquity, been the foundation stone upon which knowledge of the natural world rests. The seven liberal arts have been utilized since ancient Greece. Plato and Pythagoras were first in codifying their importance; the flowering of our western understanding of the liberal arts took place in medieval education systems, where they were categorized into the Trivium and the Quadrivium. Grammar, Logic, Rhetoric are the Trivium, and Arithmetic, Geometry, Music, and Astronomy are the Quadrivium. The Trivium combines the use of the senses with knowledge to lay the foundation for further study. The Quadrivium was considered to be the higher level education for the philosopher, and employed the use of the Trivium to be able to compose higher ideas and thereby, expand the knowledge of the human condition.

Freemasons the world over have expounded on the Seven Liberal Arts ad infinitum. All you need to do is search Freemasonry and Seven Liberal Arts, and you get a great deal of regurgitated drivel. That is not what I am striving to do in this next series. Here, my goal is to simply explain why the Seven Liberal Arts seem to have a kinship with Freemasonry, and perhaps provide small examples of each – withsevenliberalarts and without a Freemasonic connection. It’s up to you, the reader, to decide what you’d like to do with the information.

Plato’s Dialogues explain the curriculum outlined in detail and for any serious student of liberal arts, Plato is required reading. I, therefore, will not relate these concepts here. Suffice to say that the study of the Liberal Arts is more of a study of knowledge than it is of any specific actual data and information. As we may have learned by now, knowledge without application is dead and useless. Knowledge in the pursuit of higher ideals and higher ideas is more valuable than… than… well, you get the idea. Remember, one of the goals of Freemasonry is to better the human condition while standing up in defiance of falsehood, ignorance, and hatred. How do we do that if we are not searching to better our communication and knowledge, and the ways to bring both to life?

The Trivium is, as I said above, the foundation stone of the Seven Liberal Arts and really provides us the method and ability to communicate. It is composed of Grammar, Logic, and Rhetoric.

  • Grammar: Knowledge and Learning of Language
  • Logic: Reasoning, Questioning, and Thinking with Language
  • Rhetoric: Directing, moving, and Persuading using Language

While these all seem to be in relation to language, they are much more than language. They are the skills involved in achieving these ends. Therefore, the study of Grammar is also the study of history, geography, reading, and writing. It is basic, absolutely, but more encompassing than simply learning one’s ABCs and how to put pen on paper and write. Logic is about how we learn – we use our senses to experience, put our minds to thought, question, and experiment. We learn to ask the correct questions to achieve the answers we seek. They are not provided to us – we must seek them out and test for ourselves. Finally, rhetoric is the ability to take what we have learned with grammar and dialectic and put them firmly into the hands of an audience we are attempting to persuade. Rhetoric uses emotional discourse, thoughtfully created and properly applied, to communicate new ideas.

If it is not clear to the Freemason now why at least the Trivium is not important, one might want to question what they have actually learned while being a Freemason. Many may think that Freemasonry is all about enlightenment, walking in squares, or religious meanings. It might be those things to some but I think the true goals of Freemasonry are to provide a framework of how to be in the world, to make that world better for those that follow us but more importantly, for our own betterment. We cannot communicate lofty ideals via ritual alone – we need to be able to express what we have learned to a wider audience, to bring new thoughts to a wider world. To me, when we talk about service to the world, there is no greater service than being a hand-up to the betterment of the human condition and we do that by “teaching a man how to fish.” Study of the Liberal Arts is by one means to catch that “fish.”

Hortus_Deliciarum,_Die_Philosophie_mit_den_sieben_freien_Künsten

Freakonomics and Freemasonry

Freakonomics and Freemasonry

In 2005, a University of Chicago economist and a New York Times journalist revolutionized economic thinking in popular culture with their non-fiction book, “Freakonomics: A Rogue Economist Explores the Hidden Side of Everything.”  The authors put forward a fresh perspective as to how the world works through an exploratory lens they refer to as “the hidden side.”  The authors argue that this exploration can be accomplished by “stripping away a layer or two from modern life and seeing what is happening underneath.” The book is formatted by postulating a series of thought-provoking questions. What do school teachers and sumo wrestlers have in common? Which is more dangerous, a gun or a swimming pool? What kind of impact did Roe v. Wade have on violent crime? Since the original work was pubFreakonomics Authorslished in 2005, the Freakonomics authors have capitalized on their success by creating a Freakonomics brand through additional books, lectures, blogs, and a weekly podcast.

According to Steven Levitt, economics was a science with excellent tools for gaining answers but a serious shortage of interesting questions to direct the application of those tools.  He provided an original set of  thought-provoking questions and then applied the tools of his economic training. The result was statistically significant, rational explanations to explain perplexing phenomenon in the modern world. Often eschewing conventional wisdom, Levitt and Dubner created controversy by demonstrating empirical evidence for events, including their theory that the legalization of abortion in the 1970s reduced violent crime in the United States two decades later. Unconcerned with shocking the mainstream population, the authors argue that morality is how individuals would like the world to work, and economics is the way the world actually operates. The book outlines a number of basic principles related to economics: 1) Incentives are the cornerstone of life; 2) conventional wisdom is often wrong; 3) Dramatic events or effects often have distant, subtle causes; 4) Experts use their informational advantage to serve their own agenda; and 5) knowing what to measure and how to measure makes the world less complicated. 

Incentives

Freakonomics postulates that economics is the study of human behavior, explained through the investigation of incentives. Thus, to understand human behavior, one must understand the incentives which motivate him into action.  Levitt and Dubner write, “Economists love incentives. The typical economist believes the world has not yet invented a problem that he cannot fix if given a free hand to design the proper incentive scheme.” According to the authors, incentives come in three varieties: moral, social, and economic. Moral incentives motivate an individual to act out of conscienceincentiveseconomic or conviction. Social incentives inspire individuals to act in order to avoid shame or achieve glory. Finally, economic incentives direct people to act in their financial interest.  

To explain how these incentives work in the real world, Levitt and Dubner utilized an example of a day care center in Haifa, Israel.  In this example, the center’s management faced a recurring problem: parents were late to pick up their children and staff had to be paid extra wages to watch the children past the agreed upon schedule. Management decided to enact a fee for the late pickup of a child, which they believed would discourage parental tardiness. Instead, they was shocked to discover that parents showed up late more often after the fee was instituted. According to the authors, the fee had the reverse impact on parental arrival times because the parents traded a moral incentive, a sense of guilt for being late, for an economic incentive, a small fee for a late pickup. These parents changed their behavior by assessing the benefits of the extra time in their schedule and decided that the price was worth the added cost. 

Conventional Wisdom

Freakonomics is a persuasive read, in part, because of the authors’ innovative way of employing powerful quantitative tools of economic inquiry to refute conventional wisdom. The problem with conventional wisdom is not that is it always incorrect, rather that such explanations are simply accepted by the general population without questioning or examination.  To many, human social behavior is complex and requires too much effort to understand. In an effort to avoid mental analysis, we accept conventional wisdom delivered  in short phrases which comfort us with their simplicity and familiarity. Taught as children, we hear the same phrase repeatedly until we start parroting it back as an explanation. Such aphorisms include “an apple a day keeps the doctor away,” “the early bird gets the worm,” and “what doesn’t kill you makes you stronger.” Conventional wisdom is often first created by experts in a field, i.e. physicians advised patients to avoid eating eggs to maintain a healthy level of cholesterol. These conclusions get repeated in the media and by other experts who further establish credibility. Repeated often enough, a false attribution of causality becomes accepted by society as conventional wisdom to explain a problem. 

Levitt and Dubner cite several examples of conventional wisdom, which is demonstrably in error including the positive societal connotations of allowing your child to attend a play date where the family owns a swimming pool versus the negative associations of allowing your child to visit a home where guns are kept. According to the U.S. Center for Disease Control (CDC), there is one drowning of a child for every 11,000 residential pools in the United States.  There are approximately 6 million pools in the United States, which equates to  550 children under the age of ten who drown each year. Comparatively, there is 1 child killed by a gun for every 1 million guns. There are an estimated 200 million guns in the United States, which means that roughly 175 children under ten die each year from guns. Thus, the likelihood of death by pool equates to 1 in 11,000 versus death by gun to 1 in 1 million. The authors write, “If you both own a gun and a swimming pool in your backyard, the swimming pool is about 100 times more likely to kill a child than the gun is.”

Dramatic Events 

Freakonomics postulates that economic inquiry, the gathering and interpreting of data, is time intensive and complex. When considering the causes that precipitated a dramatic event, the answer is often outside the realm of attributed factors. The book carefully analyses the dramatic rise in crime reported in the early 1990s and the predictions that the violence would increase dramatically in the decade. President Clinton spoke to the fears abounding from the increase in deaths by gunfire, carjackings, robbery, and rape. He stated, “We know we’ve got about six years to turn this juvenile crime thing around or our country is going to be living with chaos.” In a drastic turn of events, crime began to fall in 1995 and continued in thjacket_freakonomics_lge subsequent years. The teenage murder rate did not rise to the levels predicted, rather it fell more than fifty percent within five years. By 2000, the U.S. murder rate had dropped to the lowest levels in thirty-five years. Experts then theorized a number of logical reasons for the drop in crime: the booming economy. the proliferation of gun control laws, and innovative policing techniques. Levitt and Dubner’s analysis concluded that the real underlying cause was attributable to the legalization of abortion in 1973 and the related decrease of children born into poverty. 

Experts and Informational Advantage 

Freakonomics explores how specific individuals can capitalize on their informational advantage to serve their own goals. The authors examine the informational advantage held by a real estate agent, including the current condition of local housing markets. They can combine this superior knowledge to expedite a home sale which may be at a price less than what the seller could have obtained by a longer listing period. The real estate agent’s commission is structured in such a way that what may be a significant increase in profit for the sellers equates to negligible increase in the fees they receive for the sale of the home. Moreover, the real estate agent’s credibility is often linked to how fast a home is sold, i.e. days on the market. The authors cite evidence of real estate agents using their informational advantage to scare sellers into accepting a lower offer to achieve a deal which is in the agent’s best interest. 

Measuring the World

Freakonomics provides new insights by applying the scientific process to address economic and social issues. The authors formulated testable hypotheses and then gathered the relevant data, often from what was previously considered unconventional sources to test those hypotheses. Freakonomics provides concrete illustrations of how unconventional methods of data gathering and innovate means of interpreWorkingtoolsting said data provides new insights into how our world works. The book argues that knowing what to measure and how to measure it makes a complicated world easier to understand.

The Freakonomics of Freemasonry

Popular culture often relays a mistaken point of view of Freemasonry as being an elite organization, where individual members possess and yield undue power in our society. This is an example of the principle that conventional wisdom is often wrong and should be examined by the individual. Stereotypes about Freemasonry have been exacerbated and enforced by the media, i.e. attention to sensationalized books such as “The Lost Symbol” by Dan Brown.

In reality, Freemasonry is an educational and self-improvement system that requires hard work and dedication. Not unlike a school, members are taught how to behave as upright members of society and instructed on how to improve their lives through greater control of their bodies and minds. Many freemasons are very successful individuals who reap the benefits of education in the seven liberal arts and sciences, including grammar, logic, rhetoric, music, arithmetic, geometry and astronomy.  Repetition is a recipe for success as the more time an individual takes to perfect his skills, related to writing, public speaking, debate, and logical reasoning, the greater the probability he will have in being successful in the business world and in society in general.