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Suit Yourself™ International Magazine #37: Archetype - Much Ado About Nothing (Zero and Polarity)

  

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Suit Yourself™ International Magazine  #37: Archetype - Much Ado About Nothing: Zero and Polarity

 

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ARCHETYPE - MUCH ADO ABOUT NOTHING: Zero and Polarity

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This is the 37th in our articles series and I hope this information is helpful.

All previous articles in the series can be found in our Library:
https://suityourself.international/libraryindex.html
and in the Magazine Archives:
https://suityourself.international/appanage/index.php?_a=newsletter
If you are experiencing problems viewing this newsletter in email, please use one of these links.

Upon request, reprint permission and an addendum of substantiating resources are available for all magazine articles. When requesting reprint permission or addenda, please include the issue date and full issue title. All magazine articles are copyright © Debra Spencer, Suit Yourself ™ International. All rights reserved. ISSN 2474-820X.
 

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     The Argo approaching the Symplegades, the crushing rocks, on the way to Colchis, at The End Of The World, where lies The Golden Fleece.

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In Archetype #36 - The "T" Intersection, I discussed our habit of framing our choices as dichotomies, opposites at a "T" intersection, and presented some arguments for why we might want to consider a different "frame".  I suggested reasons for pursuing a quest to overcome polarity-thinking, and how obtaining a larger context would give us a method for resolving what at first appear to be insurmountable difficulties, inherent dichotomies going in entirely different directions with very different results. Nature apparently hedges her bets, and so can we.  As Carl Jung said, "The greatest and most important problems of life are all fundamentally insoluble. They can never be solved but only outgrown."

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"The greatest and most important problems of life are all fundamentally insoluble. They can never be solved but only outgrown." - Carl Jung.

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The mythic story of the Search For The Golden Fleece depicts the search to find a "cure" for this polarity, to understand and "bridge" inherent opposites. The Golden Fleece represents the third alternative; the myths tell us that the Argonauts searched for the Golden Fleece "at the ends of the world", in other words, it lies beyond our current understanding. Gold is the ancient alchemical symbol for transmutation, i.e."turning lead into gold". Fleece is pelt, the warm surface covering and coating the skin, protection from "the elements".

The various versions of this myth also tell us that we can bring the Golden Fleece back to our world, but to do so is not sufficient, because the myths also detail the consequences should we bring back the Fleece but fail to integrate it.  

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Jason finds the Golden Fleece in Colchis, beyond the ends of the world, and now must bring it back. Movie still from the 1963 movie Jason and the Argonauts.

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BEGIN WITH NOTHING

Why bother understanding archetypes? How can something so abstract control energy? How do archetypes even begin manifesting? Why do they manifest?  What started them in the first place? Why do some show up in force only at certain pivotal times, on certain occasions?  What about "free will"?

For answers to any of these questions, we must begin at the beginning, when there was nothing. Belief is not required.

 

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        Zero: Is "Nothing" sacred around here? Cartoon by Jiji-Math.

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What's a symbol of "nothing"? It's when you do nothing.  Leave the paper blank; don't draw anything at all. Because the moment you so much as make a point on the paper, you've indicated "something"; you've given embodiment to a "something".  And you can't draw a line without imagining it as between two "points" -- the point you just made, and some other point somewhere else, even if you haven't yet drawn that 2nd point and it's still in your "imagination".  To draw a line, you have to start somewhere, and that somewhere is a point.

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     All manifestation begins with the point.

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That  "point" is the start of all out-picturing.  And the composite, of point, line, and circle, as a sequence, becomes the symbol of emanation, of manifestation. The circle symbolizes both perfection and completion.  It is perfectly symmetrical: a continuous, perfectly controlled, "flow" from a given point.

Likewise, the numerical symbol for Zero is not a symbol of "nothing"; it is a circle. Zero's appearance as a numerical place indicator is a relatively recent development in mathematics.  We use the circle Zero to symbolize a "state change".   This  numerical circular symbol for Zero represents the "point of origin", "the point of departure", the "source of radiation". 

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       Circle radians tau.

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In chemistry, a state change is a change from one state (such as solid or liquid or gas) to another state (such as solid to liquid, or liquid to gas) without a change in chemical composition. This is the process whereby heat changes something from a solid to a liquid. For example, it takes a long time to thaw out a frozen turkey. 

By contrast, a "phase transition" is a fundamental change in some feature, aspect, or characteristic of a physical system, often involving the absorption or emission of energy from the system, and results in a transition of that system to another state. It becomes another "system". The melting of ice is a phase transition of water from a solid phase to a liquid phase, requiring energy in the form of heat.

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  This raccoon goes to wash off his block of ice in the warm water of a stone bird bath, but finds to his surprise, as he tries to wash it, that it has dissolved instead!
The ice block was NOT dry ice.

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HISTORY OF "O"

Why do we use Zero to indicate a state change? The answer is because this is precisely what Zero represents. Despite Zero's relatively recent appearance as a numerical place indicator and even more recent development in abstract mathematics, Zero has represented this aspect of begetting from its' inceptions.

The concept for Zero has been traced back to the Babylonians, although they did not use it alone or at the end of a number. Mayan culture used it as a digit, in their vigesimal (base-20) positional numeral system, as an arithmetic numerical placeholder for counting and tracking numbers; the earliest example of this has a date of 36 BC ( https://en.wikipedia.org/wiki/0).

In India, beginning in the 7th century, the concept of Zero evolved, and progressed beyond being used to alter numbers, moving into geometry, extrapolating groups of numbers as actual space.  Eventually, Zero was used to represent Nature's continuums in general, showing up as various algebras and abstract mathematical calculations.

In Sanskrit, the word for Zero is SUNYA.  Sunya is a specific container; and while this is often translated into English as "emptiness" or "vacant" or some such silliness; Sunya does not mean "empty" or "vacant" nor does it imply this. Precisely what kind of container Sunya actually is, is indicated by the root of the word Sunya, which is VI.  Vi means to swell, as in a womb which is waiting and receptive, with the potential to give birth.  Sunya is the Center, the Beginning, the Dynamic capable of receiving and then radiating, replete with the potential to give birth to all things. This is not "empty" any more than a "potential" is empty.  Sunya represents the dynamic energy that is the source of all; the begetter, of, among many things, the first point.  Sunya is the radiative generative source, begetter of all subsequent action, movement, change, and thus of course the number lines, all the axis, the diameters and the circle, the configurations of atoms  into the Elements of the Periodic Table, and the subsequent elemental configurations into molecules. Sunya is the source of the first point, the second point, the line joining them=radii x time=circle.  From India, Zero entered the Arabic-speaking world, where it was called SIFR. The word Sifr is the root of both our word Zero and our word Cipher.  

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A simple early circular Circle cipher SIFR.

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Zero was known in Europe by 1000 AD but the West found the concept problematic. The ancient Greeks had no symbol for zero nor a specific digit placeholder for it. Perhaps the earliest documented use in the Hellenistic World of something close to the Zero concept is in Ptolemy's Almagest, the Syntaxis Mathematica of approximately 130 AD,  which is his work on mathematical astronomy; this is an application where the concept of zero is a huge help in describing things too far away to see that none the less are affecting what is seen. Ptolemy uses a small circle with a long overbar alone and not as a place holder, to show fractional positions, arcs, but not integrals. Ptolemy, influenced by Hipparchus and the Babylonians, used this within a sexagesimal numeral system that concurrently also used alphabetical Greek numerals. Ouch. He clearly had the idea and needed it, and did the best he could with what he had, but I don't know if this really "counts" as "Zero" or not. The Romans used Roman Numerals without a Zero, from the founding of the city of Rome in the 8th century BC. I guess they weren't worrying about too much going "over the hill and far away". 

 

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     Western Mathematical concepts are not the only Mathematics there is.

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The innuendos inherent in the concept of Zero seemed to be profoundly unsettling to the West. The West really resisted using Zero for another 650 years, after which time the concept finally appears definitively in perspective drawing. As I've discussed elsewhere in this series in detail, Eastern and Western concepts are inherent opposites; thus concepts developed by either always face inherent challenges being integrated into the other on the opposite side of their One Radii Number Line. The European Middle Ages believed Zero introduced a horror of "nothingness" into the fullness of God's Creation; this is enormously ironic because Sunya depicts exactly the opposite albeit guaranteeing "nothingness" can never happen. However, by the European Renaissance, the concept of perspective in Art had developed and matured. Art was an area where the concept of Zero as infinity in portraits and landscapes was considerably less threatening than the same in Astronomy. 

Perspective is a method to represent more accurately the relative distance of three-dimensional objects when reproduced on two dimensional flat surfaces. Prior to this "revelation", artists and map makers, using flat surfaces to render reality, did not indicate relative positions of things in time and space; paintings, drawings, maps, and wall carvings were all flat, they didn't look at all "real life" and their practical use was limited.  Any object distant from you looks smaller in size relative to you.  Using the concept of perspective, objects distant from you in space can be drawn as smaller objects relative to their distance from you, and by "you" I mean you as the viewer of the work. Now this sounds obvious, but nobody had ever done it before.

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     Perspective drawing with the imaginary vanishing point.

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Perspective "overlays" an imaginary ruler onto infinite space, with the viewer and surrounding objects sitting somewhere along, and on, this ruler, at a specific distance relative to each other. This "infinite ruler" measures, and indicates, the apparent relative distance of any objects seen by the viewer, even when something is so far away, it vanishes to a point in the distance, meaning that from the viewer's point of view, it's so far away, they can't see it anymore.  This imaginary abstract "vanishing point" is a concept representing relative time and space; this became the established Western method for representing relative 3D on flat two dimensional surfaces.

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     "Perspective", cartoon by Sidney Harris, www.sciencecartoonsplus.com.

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Modern Western names for the number Zero (0) in English include zero, nought (UK), naught (US), nil, or—in contexts where at least one adjacent digit distinguishes it from the letter "O"—it is pronounced as a long vowel oh or o. 

Wikipedia (https://en.wikipedia.org/wiki/0) tells us this: "The word zero came into the English language via French zéro from Italian zero, Italian contraction of Venetian zevero form of 'Italian zefiro via ṣafira or ṣifr.
In pre-Islamic time the word ṣifr (Arabic) had the meaning "empty". Sifr evolved to mean zero when it was used to translate śūnya (Sanskrit) from India.The first known English use of zero was in 1598. The Italian mathematician Fibonacci (c. 1170–1250), who grew up in North Africa and is credited with introducing the decimal system to Europe, used the term zephyrum. This became zefiro in Italian, and was then contracted to zero in Venetian. The Italian word zefiro was already in existence (meaning "west wind" from Latin and Greek zephyrus) and may have influenced the spelling when transcribing Arabic ṣifr. There are different words used for the number or concept of zero depending on the context. For the simple notion of lacking, the words nothing and none are often used. Sometimes the words nought, naught and aught are used. Several sports have specific words for zero, such as nil in association football (soccer), love in tennis and a duck in cricket. It is often called oh in the context of telephone numbers. Slang words for zero include zip, zilch, nada, and scratch. Duck egg and goose egg are also slang for zero."   (https://en.wikipedia.org/wiki/0)

"The pinyin character líng means "zero" in Chinese, although O is also common. Etymologically, this is an onomatopoeic word for "light rain". The upper part of the character means "rain", and the lower part is lìng, for the sound." ( https://en.wikipedia.org/wiki/Names_for_the_number_0 )


 

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     Snoopy and Woodstock sing Oh-OOH-Oh-O Jazz Band. Peanuts cartoon by Charles Shultz.

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Zero is used to indicate that numbers change. Our culture uses the same sequence set of nine numbers (1, 2, 3, 4, 5, 6, 7, 8, 9) to represent all sorts of different things, including different quantities, different directions, different combinations, different states, and different phases. 

Numbers never just "sit still".

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        Toutes les nombres. An antique engraving showing numbers drawn as human acrobats in varoius positions.

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It's confusing to use the same symbols to represent so many different things.  We had to come up with more symbols to clarify more specific indications. 

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        Groucho Marx offering Margaret Dumont a card, saying "You can keep it; I've got 51 left" from the movie Duck Soup.

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When Zero is used as the "decimal point",  this changes the representation of the numbers so they instead represent parts or fractions of some whole, i.e. fractions, whose denominator is usually some power of 10 (ten). This is usually indicated by a dot (decimal point or point or "period") written before the numerator: 1.0,  0.10,  0.010,  0.001, etc. corresponding to 1.0 or 1/0 or 1,  0.10 or 10/100 or 1/10th, etc.

 

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"I ordered a ten gallon hat but they put the decimal in the wrong place." Cartoon by Bedtime Math.

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To indicate a change in direction, i.e. polarity,  we use a minus sign (dash line, thus -) or a plus sign (pair of crossed dashes, thus +).  

Despite what modern textbooks tell you, a negative sign in front of a number does NOT mean that the number is less than Zero in amount, volume, or anything else -- it only, repeat, only indicates that the number is going in a different direction from numbers that have plus signs in front of them, and you have to take its' direction into account when merging it with anything.

 

 

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The "positive" or "negative" polarity of a magnet depends on the current field flow directions: clockwise or counterclockwise.

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To create an electromagnet, you need energy to move as an electromagnetic current flow between two opposite poles.

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Number sequences proceed from the Zero point in one of two opposite directions, and these directions are indicated by their signs..

 

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Number line with -4 and +4 marked as "OPPOSITES"  and integers.

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Their signs are a polarity, a pair of opposites: they move as a group, in sequence, either in a direction indicated by a "minus" sign (dash or line thus -) or in a direction indicated by a "plus" sign (a cross of two lines, thus: +).

 

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Number line with  arrows.

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There is only one radius of any circle, only one center, and consequently, two diameters. Using the "plus" and "minus" signs, motion along the diameters can be indicated as for example, longitude, latitude, and international date and time lines.

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Sphere showing equator, prime meridian, and longitude as horizontal angle with latitude as vertical angle.

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What do I mean when I say "There is only one radius of any circle"?  A circle exists as the result of a moving fixed distance between two points.  That distance is created first by making a first point, and we call that first point the "center".  Then we make a second point somewhere else.  Then, starting at the center "point" , we draw a line "outwards' i.e. radiating, from that center point until it reaches the second point; this line now connects, joins, the two points, and this line is called the "radii"; it establishes the radiating outwards distance relationship between the first center point to the second "outer" point, a.k.a. a "ratio". These two points, in this radii ratio fixed relationship "distance", create what we call the "circle" as we rotate them around with the first point fixed at the center -- "circle" is our name for that ratio-fixed rotation movement. Thus there is only one "radius". The rotation around the fixed center to create the 'circle' can be clockwise or counterclockwise, in any orientation.

 

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There is one radius, and two diameters, to a circle.

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A change in direction, of polarity, can thus be indicated by a change of sign. And a change of sign can indicate a change in direction, of polarity. The numbers can also move out or in from the Zero point. Numbers can move inwards, towards the Zero point as convex, "moving towards" or converging, at some "source", central point, point of origin, indicated by Zero. Or numbers can move outward from the zero point as concave, "moving away", radiating out,  or "emanating" from some "source", central point, point of origin, indicated again by Zero, like a flashlight. 

 

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Electromagnetism: energy flows between two poles.

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Another example: think of your heart beating as diastolic - systolic action.  Again, and more obviously, you have to take a number's direction into account when combining  it with anything. Two diastolic beats aren't equivalent to diastolic - systolic! Two wrongs don't make a right, however three rights will make a left.

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"If two negatives make a positive, how come two wrongs don't make a right? Cartoon by Mark Anderson

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On an axis, or "number line",  Zero indicates the point where the number sequence changes orientation, direction of emanation, polarity. Combining numbers along this line or axis thus depends on their relative locations, their location in relation to this Zero point, and this relationship defines their "rules" when they are combined, i.e. +2, +1, 0, -1, -2, etc. correspond to combinations such as [(+2) minus (-1)] = +1, etc.

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This "Number Line" shows how to get "there" in "two" ways, pun intended.

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Any number of axis can be combined, joined together, and when configured thus, all share a common point, or "location", or "joint", indicated by Zero. 

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Any number of axis can be combined; an example of continuous surface Gyroid star.

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For example, three dimensions can be represented by 3 axis that point in 3 different directions:  left side/right side (conventionally indicated with the letter X), up/down (conventionally indicated with the letter Y) , and back/front (conventionally indicated with the letter Z).  When referring to vector quotients involving combinations of these axis, we use the lower case letters i. j, and k, respectively.

 

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Spins: Wheeeeee!!!

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All three axis, X, Y, Z, are the three different "directions" taken by one human body and that body is indicated by Zero.  Zero represents their common point, "location", or "joint" or "point of origin".   And since they all share the same center point of origin, anything happening  at one of these points along any one of these 3 axis affects the other 2. 

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Olympic Rhythm Gymnastics human pyramid.

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Gimbal lock is a phenomenon well known to airplane pilots. Gimbal lock is the loss of one degree of freedom in a three-dimensional three-gimbal mechanism; it occurs when the axes of two of the three gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate 2D space. A set of three gimbals can be mounted together to allow three degrees of freedom: roll, pitch, and yaw. When two of these gimbals rotate around the same axis, instead of separately rotating around their own separate axis, the system as a whole loses one degree of freedom.

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Gimbal lock.

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Cause and effect is made more evident. You can thus find the cause of any set of apparently unrelated symptoms, no matter on which combination of axis they are appearing. You can find the source of origin underlying any set of tales or stories. You can find the solution to a murder mystery. You can find the common denominator of anything repeating, and change it at the source. You can find a radiating electromagnetic wave.

 

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"There is one art, no more, no less, to do all things with artlessness." - Piet Hein.

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AN EXERCISE

Take a pencil and a piece of unlined paper in hand. The instant your pencil point touches that paper, you have established the point. By sequence of movement in time-space, draw a line to the left, from that point. The point, then, is the source of the line, as far as representation is concerned. 

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One radius, drawn from the center to the left.

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Polarity is represented here. Your will and mind impose themselves on the material substances of the pencil and paper. The thought of drawing the line is your subjective action. 

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One radius, drawn from the center to the right.

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The actual drawing is the objective action which results in the manifestation of the line. 

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An ancient Greek amphitheater in Sicily, Italy.

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Of the two instruments, the pencil is + (plus or masculine or yang) because its' substance is qualified to make the mark. The paper itself is - (minus, or feminine, or yin) because its' nature is to "receive" the impression of the pencil-point and to reflect back the picturing of your idea. 

The action of the pencil-point on the paper is analogous to the action of cosmic polarity on and through the material universe resulting in a specialized manifestation. By correspondence, you are also: the pencil and paper are matter, and the line is the specific result of the action of your will on the material substance. Creative will and imagination utilize the material universe to manifest archetypes, and those archetypes might be "humanity, ""cat," "oak tree," or "humming bird" (human, quadruped, vegetable, or bird). 

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 Harry Whittier Frees photograph, c1935,  bunny teaching kittens their math.

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Just as you, as an "emanation", are the source of your expressions, so the point you have drawn is the source of all lines, planes and (theoretically) solids, which can, or might, emanate from it.  As such, it is the abstract symbol of infinite subjectivity. From that point, lines can be drawn, in infinite space and infinite time. 

Because the line "lives", it is evidence that the point exists. Because we are sustained in manifestation, this is evidence that our source exists. The line, then, is specific effect from a specific cause. The drawing of it is a chemicalizing process, and the measurement of it is the exercise of your will to manifest perfectly the archetype in your mind. By "chemicalizing" and  "chemicalized" I mean changed by its' action or use.  An indefinite line is unfulfilled manifestation of the archetype. A measured line is specificity, definitely qualified as an archetypal out-picturing.

 

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Dessin par main, l'encre de Sumi, oiseaux. Birds drawn with Sumi ink.

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The point is, actually, a "filled-in dot".  Abstractly, and we're now dealing with abstractions, it symbolizes the pure composite of all dimensions. It's now the archetype of source, genesis, origin, beginning. The line, correspondingly, is the first emanation of the potential - source, because no other line is, as yet, drawn from the point. 

When the line is completed by specific measurement, it is fully "chemicalized", changed by its' action or use,  and it is qualified, by its' attributes, to then emanate planes and solids.  Just as a child, "emanated" by parents, possesses, when fully mature, the attributes of becoming a parent, so the child's maturity, of body and emotion, qualifies them for a specific identity called "parenthood", just as the measurement of the line specifically qualifies it for the same.  

The drawing of the line is the action of manifesting the archetype. The measured line, complete, is the finished work, that now qualifies, by its' attributes, to be seen, heard, and enjoyed, i.e. responded to, let out into the world.

The measured line become the radius of a circle. There is only one radius of any circle, only one center, and consequently two diameters. This radius line is thus the composite of being: Causers and the Effects of Causes, or Expressers and Reactors.

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Construction of circular radii for the foundation of a building in Spain.

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The archetype of the point thus also represents the archetype of the artist. Recall from above that an artist illuminates the consciousness of others.  The artist has the ability to perceive archetypes and to manifest them, is both manifestor and interpreter, and "interpreter" means "teacher" as well as "performer".  

An artist is thus inherently also a scientist and a scientist is inherently also an artist. The two are inseparable; they are the right and left of the same number line, the two diameters of the circle with only one center, and the circle is the archetype manifested as mastership.  

 

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"All right, I accidentally called you 'Rover"; don't I sometimes call the dog 'Kevin'? Cartoon children04 by Stanley Harris. 

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THE END = BEGINNING

How is the "end" of anything symbolized? Consider the fulfillment of the point, the circle.

The circle is considered the supreme symbol of spiritual realization, and the perfect fulfillment of potentials.  The circle, as emanation, returns to the radii-line-point as successive octaves. 

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An involute is pictured on the top here, over a circle, pictured on the bottom; the circle as emanation, returns to the radii-line-point as successive octaves.

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Subsequent to realization and potential-fulfillment comes perfect releasement, in perfect timing, from bondage to form. "Form" can mean a specific relationship, a specific experience-pattern on a particular octave, a specific state of manifestation, or a specific evolutionary cycle.

 

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The Archimedian Spiral.

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To illustrate this, draw an equilateral triangle. Note that the mid-points of each of the 3 sides are the 3 points closest to the center of the triangle.  However, as you move along the triangle, away from any of these 3 points, you also recede from the center, until you come to the next angle-point. 

Now draw a square. Note also that the mid-points of its' sides are the four points closest to the center, and the angle-points are most removed, farthest the center. 

All three-or-more-sided enclosed figures are crystal symbols; they represent static states. Movement around them isn't constant in relation to the center, even though it is rhythmic when the figures are equilateral. 

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Equilateral triangular showing midpoints movement.

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In this respect, the circle differs from all other enclosed figures. Trace your pencil point from any place on the circumference of a perfect circle, around the wheel and back to the starting-place. Your pencil point remains the same distance from the center at all times.   

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The roots of Unity.

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ACTIVE & PASSIVE SYMMETRY GROUP TRANSFORMATIONS

Consider this; a flat circle can be draw in four ways, known in physics as a pair of active and passive symmetry group transformations.

1. A circle can be drawn in a clockwise or counterclockwise direction, onto a stable surface such as a chalk board, white board, or piece of paper. 

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Left: Alexander Overwijk draws a circle on a chalkboard, clockwise, from the bottom.

Right: Actress Sarah Michelle Gellar draws a circle on a white board, counterclockwise, from the top.

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2. Or, by keeping the pencil point stationary, and instead rotating the paper (or rotating whatever surface is used), the circle can be drawn by rotating the paper in a clockwise or counterclockwise direction.  

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A circle can be drawn by rotating a piece beneath a stable pencil point held by a stable hand and arm.

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Thus, a flat circle can be "drawn" in different ways, as an active or passive "transformation", in either of two directions, clockwise or counterclockwise, and when drawn, there is nothing to indicate which of these methods was used. 

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Antique engraving showing a hand using a compass to create a circle.

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Active and passive are two ways to consider any transformation. In the active transformation, the axes remain fixed, while the object moves (a vector v becomes vector v' when rotated about the origin through an angle θ.) On the other hand, pun intended, with the passive transformation,  the object remains fixed, while the coordinate axes rotate through an angle θ. Note that the sense of the rotation is opposite in these two cases, but the effect on the coordinates describing the object is the same. The circle has inherent "polarity". 

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Active and Passive Rotation matrix, Dr. J. B. Calvert,  http://mysite.du.edu/~jcalvert/index.htm

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The circle is not a "chemical symbol" or a "dot";  it is an archetypal symbol of the manifestation of the inherent perfection of a chemicalized expression.  Again, by "chemicalizing" and  "chemicalized" I mean changed by its' action or use.   The circle symbolizes both perfection and completion.  It is perfectly symmetrical: a continuous, perfectly controlled, "flow" from a given point. The circle represents the ideal of rhythmic, harmonious expression of potentials and their perfect fulfillments.  As such, it is also the symbol of the Hero's Journey.

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Olympics Rhythm Gymnastic

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The equilateral triangle, on the other hand, because of the "closeness" of its' mid-points to the center, symbolizes the ebb and flow of human perfection. A person, from time to time, manifests the highest and best of their attributes, but doesn't remain at the 3 high points, closest to the center.  Instead, humans tend to recede from their center towards the next angle point, which in turn symbolizes a new identity, for further releasements. There is a rhythm, an ebb and flow as with a tide, toward awareness and self-perfection.

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Olympics Rhythm Gymnastics, rotation 180.

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The conclusions of the experience of a manifested archetype will assume the shape of an involute: the process of creating ever smaller and smaller circles inside ever smaller triangles, eventually reducing the original circle to the original center point of origin, from subjectivity through objectivity then back to subjectivity. Fading from view. Pulse, beat, rhythm, smaller and smaller circles, tinier and tinier, contracting to what seems to be a point, yet at that instant, the cycle begins radiating anew. 

 

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Group symmetries as a triangular rotational maypole group performance, Olympics Rhythm Gymnastics.

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IN CONCLUSION

By analogy (or rather I should say "fraternity" as it's more accurate) it is possible to say that The Thirty-Six Dramatic Situations (of Polti, Carlo Gozzi, Goethe, von Schiller, et al.) can be referred to in mathematics as a group theory point set isomorphic to the unit sphere, the unit circle in three dimensions plus time. This finite 36-situation point set of infinite variation represents the transformations of Elementargedanke energy into the local Volkergedanke forms specific to their manifestation time, place, events, and persons. So do the Greek Gods, and so does the Mahabharata. Likewise, the Periodic Table of Elements is a pictorial representation of otherwise fungible Elementargedanke energy into Volkergedanke forms, and synthetics by analogy are Volkergedanke local forms specific to their manifestation time, place, events, and persons. 

For more information on synthetic chemistry, please see my article BASIC CARE INSTRUCTIONS  #15: Synthetic Fabrics
https://suityourself.international/appanage/index.php?_a=newsletter&newsletter_id=63
This discusses synthetic fabrics commonly used in clothing; synthetic fabric blends have been manufactured since 1894 and commercially used since 1905.  For better or worse, synthetics are here to stay, at least for the foreseeable future. Understanding their remarkable nature is of practical utility; it helps us regulate their not inconsiderable impact on our health and the environment. 


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Yes, things are interesting with only two points, one radii, and two diameters. However, as I have just pointed out, Nature really starts getting interesting when there is more than one circle. The plot thickens! SYMMETRY: that's what I'm discussing next.

 

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Stolen food tastes better! Translation symmetry, as these puppies swap themselves to exchange their mutual food dishes.

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ADDITIONAL RESOURCES

 

The sources for the material in this Archetypes series are listed in one place,  #40 Archetypes Additional Resources:
 https://suityourself.international/appanage/index.php?_a=newsletter&newsletter_id=88
or
https://www.suityourself.international/appanage/magazine-40.html

If you're interested in exploring these topics further, then I recommend the resources at the above links. 


Here are some of the resources used here, in #37:


DANTZIG, Tobias
(1930, 2007) Number: The Language of Science (1930); reprint of 4th edition. Penguin. 2007.
ISBN 978-0-452-28811-9.
(1955, Dover reprint 2006) The Bequest of the Greeks (1955); Dover reprint. 2006.


KAPLAN, Robert 
(2000) The Nothing That Is: A Natural History Of Zero, Oxford and New York.

LaVIGNE, Eric
"Creation by Numbers", Parabola 24/3, 1999.

SCHMANDT-BESSERAT, Denise and HAYS, Michael
(1999) The History of Counting, New York.

SEIFE, Charles
(2000) Zero: The Biography of a Dangerous Idea, New York.


WIKIPEDIA:
https://en.wikipedia.org/wiki/0

 

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I sign our magazine articles "See Into The Invisible". Thanks for reading.

Best Wishes, 
Debra Spencer

All Content is © Debra Spencer, Suit Yourself™ International. Technical Library FAQ Index ISSN 2474-820X. All Rights Reserved. Please do not reproduce in part or in whole without express written consent. Thank you.
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All Content is ©2019 Debra Spencer, Appanage™at www.suityourself.international Suit Yourself ™ International, 120 Pendleton Point, Islesboro Island, Maine, 04848, USA 44n31 68w91 Technical Library FAQ Index ISSN 2474-820X. All Rights Reserved. Please do not reproduce in part or in whole without express written consent. Thank you.

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All Content is ©2019 Debra Spencer, Appanage™at www.suityourself.international Suit Yourself ™ International, 120 Pendleton Point, Islesboro Island, Maine, 04848, USA 44n31 68w91 Technical Library FAQ Index ISSN 2474-820X. All Rights Reserved. Please do not reproduce in part or in whole without express written consent. Thank you.
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