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Suit Yourself™ International Magazine #35: Archetype - Monkey See, Monkey Do

 

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Suit Yourself™ International Magazine  #35: Archetype - Monkey See, Monkey Do

 

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MONKEY SEE, MONKEY DO:

 ARCHETYPE EMERGENCE IN THEATRE, VOLKERGEDANKE, MATHEMATICS

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This is the 35th in our articles series and I hope this information is helpful.

All previous articles in the series can be found in our Library:
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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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MONKEY SEE, MONKEY DO:

 ARCHETYPE EMERGENCE IN THEATRE, VOLKERGEDANKE, MATHEMATICS

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Owls, hiboux, in the pose of the famous 3 wise monkies; Horen, Zien en Zwijgen.

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Energy emerges following the same process pattern, no matter, pun intended, what path it takes when emerging, for example, as artistic expression, mathematics, chemistry. 

Energy manifests as polarities, concave - convex continuously and endlessly combining - recombining.  This three-state process itself has been referred to in endless ways, including but not limited to coming / going / enduring,   positive / negative / neutral,  plus sign / minus sign / equal sign,   x / y / infinity,  major / minor / augmented,   idea / implementation / result,  yin / yang / and the circle containing them.  There are three states to every process.

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        Endless geometric shapes emerge from combinations of the same basic forms.

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Atoms can group together to form elements, and elements can be linked together to form molecules. 
Letters of the alphabet can be grouped together to form endless words, and words can be linked together to form sentences. 
Numbers can be grouped together to form endless equations, and equations can be linked together to form functions. 
Musical notes can be grouped together to form "movements", and movements can be linked together to form compositions.
Isolated events can be grouped together to form movements, and movements can be linked together to form ages.

Atoms-elements-molecules,  alphabet letters-words-sentences, musical notes-compositions, numbers-equations-functions, archetypes - these are all "building blocks"; they form from linked groups of causes and effects, through a common denominator.  The concept of "building block" is itself archetypal. Each archetype is capable of endless development and differentiation, and can be more or less developed. 

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Earth seen from space: a Google time lapse imaging of a river flow changing over time, from 1984 to 2012.

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THE EMERGENCE OF ARCHETYPES IN THE THEATRE

William Shakespeare was an English poet, playwright, and actor, widely regarded as the greatest writer in the English language and the world's pre-eminent dramatist. His dates are given as  26 April 1564 (baptised) – 23 April 1616. Wikipedia tells us he produced most of his known work between 1589 and 1613 and published his work during his lifetime. His work has been re-performed continuously since he first created it, enduring for approximately 430 years, "repeatedly adapted, rediscovered, constantly studied, performed, and reinterpreted in diverse cultural and political contexts throughout the world." (https://en.wikipedia.org/wiki/William_Shakespeare). 

Whether intentional or not, Shakespeare's body of work is a codification of plot variations; by 'plot" I mean narrative.  English novelist E. M. Forster described plot superficially, as the cause-and-effect relationship between events in a story. As we shall soon see, "plot" is archetypal blueprint and far more than just "the cause-and-effect relationship between events in a story".
 

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1913 Marionette Theater and Puppets At the Marionettemuseum in the Hohensalzburg Fortress.

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Approximately one hundred years after Shakespeare, beginning in the 1500's in Europe, we begin to see a similar codification process emerge via the Commedia dell'Arte, but with the emphasis on representations of people as typical characterisations, in brief fixed situations, rather than an emerging "plot" situation underlying developing characters. The codification of characters that emerges is what we now call "stereo types"  or, if you prefer, "role models". 

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Guignol, animé. 

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By the 1500's, Carnivals, special event outdoor parades, had become spectacular, elaborate, highly stylized events. Carnivals were, and are, far more than simple gatherings of local trade groups displaying their relative ingenuity.  Certain aggrandizements of human traits are standard representations at these events.  The Commedia dell'Arte was an early form of professional theatre, the 16th Century version of the modern "GIF" and "cartoon. It developed as an adjunct to these occasions, and became so popular, it separately took on a life of its' own; traveling troupes formed and performed through various towns.  

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Outside performance, Vrai Guignolet Theatre, France.

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Commedia dell'Arte performances were "shorter and sweeter" than full length performances; they favored brief life highlights over slowly developing characters entwined in complex plots. Their subject matter was always a pastiche,  portraying exaggerated traits of fixed social types in typical situations. They confined themselves to stock characters, exaggerated the brief situations, and always ended with a "punch line" ending, known as a lazzi. A lazzo is a witty, or foolish joke. 

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Ah! The element of Surprise!

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One frequent performance was on having a tooth pulled. To fit whatever audience and town was at hand, they used spontaneous improvisation and pantomime. Their short-sweet format required emphasizing one character trait, exaggerating it to the exclusion of all others. While there was nothing particularly sophisticated in these performances, it is here that we find the dynamic beginnings of depth psychology and insight into humanity.

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 Example of a lazzi: she gets him. Terry Gilliam for Monty Python's Flying Circus.

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Wearing masks was a long standing carnival convention, and the Commedia dell'Arte co-opted this as an icon, to represent theatrical intent, and the mask remains so, as a theatrical icon, to this day. 

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Decorativo mascaras de teatro.

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Commedia dell'Arte stereotyped characters wore masks, and so obvious was their character, that it made a joke of the mask's attempt at disguise.

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Marionette, Commedia dell'Arte Harlequin Arlecchino.

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Stock characters, and their traits, were codified into favorites, and included the Innamorati - the perfect lovers,  Il Dottore, the know-it-all doctor, and Pantalone the greedy old man, who became, by 1700, the masked Pulcinella, later to travel to England as Punch, the puppet in Punch and Judy. 

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Engraving of Pulcinella as he was seen in 1700.

From Maurice Sand's 1860 publication, Masques et bouffons (comédie italienne), available online here:
https://archive.org/details/masquesetbouffo00mancgoog
Publisher Michel Lévy frères, Paris.
Maurice Sand (né Jean-François-Maurice-Arnauld, Baron Dudevant) studied under Eugène Delacroix and was the husband of novelist and feminist George Sand.

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The Italian playwright Carlo, Count Gozzi (Italian,13 December 1720 – 4 April 1806) is credited by Georges Polti as identifying the sum total of human experience as falling into thirty six dramatic situation categories, under which are sub-categories and infinite variations.  Gozzi had access to all of Shakespeare's work, including A Midsummer's Nights Dream.

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Claude Gillot (1673–1722), Four Commedia dell'arte Figures Three Gentlemen and Pierrot, c. 1715.

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As Commedia dell'Arte was declining in popularity,  Gozzi produced a series of dramatic pieces based on fairy tales, and by introducing supernatural, mythical, and fairy tale elements into his Commedia dell'Arte scripts, he was able to revive the declining interest in Italian performances.   

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Punch and Judy, painting by Benjamin Robert Haydon (1768 - 1846).

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These dramatic fairy tale pieces were much praised by his contemporaries, by Goethe, the Schlegel brothers, Hoffmann, Madame de Staël, Sismondi, and Ostrovsky. One of these plays, Turandot (or La Turandotte), was translated by Friedrich Schiller and staged by Goethe in Weimar in 1802 to great acclaim. The tale was later turned into an opera in three acts by Giacomo Puccini and remains popular the world over to this day. The opera was completed in 1926 by Franco Alfano, two years after Puccini's death in 1924, and set to a libretto in Italian by Giuseppe Adami and Renato Simoni.

About this, Jack Weatherford has this to say in his article "The Wrestler Princess", Lapham's Quarterly, 3 September 2010:
In 1710, while writing the first biography of Genghis Khan, the French scholar François Pétis de La Croix published a book of tales and fables combining various Asian literary themes. One of his longest and best stories derived from the history of Mongol princess Khutulun. In his adaptation, however, she bore the title Turandot, meaning "Turkish Daughter," the daughter of Kaidu. Instead of challenging her suitors in wrestling, Pétis de La Croix had her confront them with three riddles. In his more dramatic version, instead of wagering mere horses, the suitor had to forfeit his life if he failed to answer correctly.
Fifty years later, the popular Italian playwright Carlo Gozzi made her story into a drama of a "tigerish woman" of "unrelenting pride." In a combined effort by two of the greatest literary talents of the era, Friedrich von Schiller translated the play into German as Turandot, Prinzessin von China, and Goethe directed it on the stage in Weimar in 1802 to great acclaim. (https://en.wikipedia.org/wiki/Turandot)

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Orchester Suite, aus der musik zu Gozzi's marchendrama Turandot von Ferruccio Busoni, Breitkopf & Harter, Leipzig, 1906.

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In 1921, Georges Polti published "The Thirty-Six Dramatic Situations". Using Gozzi's basic thirty-six situations and their sub-classes, he provides several examples of each using all known western literature.

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Scientist Gifts: Handing over a box of atoms,  "Here's a bike; some assembly required".

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He explains how the situations are derived, basically as a point of origin, then a second subsequent point inherently opposing the first, with a line joining the two points, the line produces a radii which then forms a circle. 

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Forget Pi. Use Tao radians for the circle: point + 2nd point, joined by line = radii  = circumference.

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Apparently, all dramatic situations emerge by varying these three attributes. This is basic mathematical combinatorics; ultimately a finite set is created that can be varied infinitely through introducing additional variables.

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Pascal's tetrahedron showing a complete polynomial of order m.  

Fundamentals for the finite element method, showing the progression from a constant term of 1, to linear, quadratic, cubic, and quartic terms. 

According to Von Franz, fairy tales share this structure.

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By varying the nuances of human emotion, time, place, etc. a finite set nonetheless contains inherent attributes granting it the possibility for infinite variations.  

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The realization of the transposition of a matrix. La réalisation de la transposition de la matrice.  Comment ne pas se confondre par la réalisation d'une matrice de transposition.

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To create an entirely new"story", all one has to do is change, or alter to some degree or other, one of these 3 points, 2 of these 3 points, or all 3 points, or none, to a neutral, active, or passive aspect, or some combination, either sequentially or alternately, or both, etc.

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Changing the configuration, producing orthodox, paradox, and metaphysicians!

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Polti explains that Gozzi, Schiller, Goethe, Gérard de Nerval,  and many other theatrical contemporaries, spent considerable portions of their lifetimes working on this assiduously. 

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A clear Pythagoras square volume demonstration.  Une démonstration claire du théorème de Pythagoras.

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They were unable to find more than thirty-six major situation categories (and the sub-classes), even when combining the various classes and sub-classes amongst themselves and introducing all sorts of variables into them. 

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Trompe L'Oeil mathematic formula; erasing the top reveals embedded I Love You.

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A musical scale will likewise contain a fixed number of chordal arrangements, and likewise endless variations introduced from variables (such as loudness and softness and rhythm) regardless of the proportion on which the scale is based. Likewise, all atoms are fungible and it is their structure when in some configuration that is responsible for their chemical properties; the chemical property is not a characteristic of any individual atom. The "sum" may not be "greater than" the parts, however when in some configuration, it certainly does something entirely different, and has an entirely different effect,  than any single part does on its' own.

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Musical notation derivations shown using piano chords, keys, and notes.

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THE EMERGENCE OF LOCAL ARCHETYPES

The traveling Commedia dell'Arte troupes found it necessary to tailor their performances to local variations. For their jokes to be funny, they had to accommodate local tastes, adapting their performances to the "local accent". They used improvisation over fixed scripts, and pantomime, masks, and variable sets.

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Terry Gilliam swaps out his own head as he is the only member of the group who does not perform personally; he did the graphics. Monty Python's Flying Circus.

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Approximately one hundred years later, these local variations became the source of one man's lifetime of serious academic study: Adolf Bastian, who made a distinction between ethnic or folk ideas, which he called the Volkergedanke, and the underlying elementary ideas, which he called the Elementargedanke.

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Pongo lets you choose 3 items off his cartoon menu.

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Adolf Bastien, (26 June 1826 – 2 February 1905) was a 19th-century polymath best remembered for his contributions to the development of ethnography and the development of anthropology as a discipline. According to Bastian, the contingencies of geographic location and historical background create different local elaborations of the "elementary ideas"; these he called "folk ideas", Völkergedanken.  The Volkergedanke, the folk or local ideas, were held by the world's peoples, and the elementary ideas, Elementargedanke, underlay the various folk or local beliefs and practices.

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Visages et têtes; marionnettes anciennes en papier maché et carton bouilli. Antique marionnette heads in paper maché.

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Archetypes are analogous to the physical elements of the Periodic Table. Physical elements are microscopic configurations of patterns of matter, where nature always wants to get to the lowest energy (or highest entropy) state.   Archetypes, on the other hand, manifest recognizably on the macroscopic scale, primarily as a spectrum of configurations of patterns involving large groups of people, as the result of mass consensus.  An archetype's effects assume a spectrum of manifested guises, all of which depend on the immediate environment currently surrounding the manifestation, and all of which share the archetype as their 'common denominator, a commonly shared trait or characteristic.  

Archetypes emerge into a culture as the form of the culture.  As people group together, common shared situations emerge; there is an archetype of fraternity that emerges, "current" beliefs are assimilated, and a "culture" results, through pun intended, current beliefs and shared interpretations. Essentially, group energy emerges camouflaged, in the guise of local characteristics. It can grow to the extent that village life assumes a local rhythm, a local patterning, a unified force, and this force can in turn be used to sway the masses that create the pattern. This is not necessarily a bad thing.  For a culture to remain coherent, to prevent all-out chaos, members must behave tribally to some extent, assuming masks of behaviour with themselves and each other that support the structure of that culture.

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Aiowah University bounces the ball.

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In fact, what is right and moral in one culture may be considered immoral or inconceivable in another, but within a given culture, if it is stable, there will be consistency. These culturally specific masks, these personae, how to behave and what to do, are the Volkergedanke; the local manifestations of the underlying Elementargedanke archetype of fraternity. They bring you into relationship with others in that culture, and into relationship with your own character.

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Bucky Fuller's Cosmic Hierarchy combinatorics dodecahedron.

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This should, however, give you some idea of what can happen when "cultures clash". Just because cultures share a common Elementargedanke does not mean, nor does it imply, that their Volkergedanke manifestations will be in agreement. In fact, they often are not, and their systems often clash as a result. The Volkergedanke can manifest in completely differently ways simultaneously! Two co-existing cultures can have Volkergedanke that are completely at odds with one another. This is analogous to wearing colors that clash, or playing two notes together that make you cringe rather than creating a sonorous chord. For example, eastern and western traditions have manifested the Volkergedanke local personae masks and rules, in polarized ways; the two systems are polar opposites. It is difficult, if not impossible, to integrate convex and concave, introvert and extrovert, individual ego and group identity, without annihilating both with the result becoming neither. These are two entirely different paths that coexist, and both, as the saying goes, are barking up the same tree. 

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"For our purposes there's no crash or explosion; they just intersect." Cartoon by Mark Anderson.

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Modern psychology owes Bastien a great debt; his theory of the Elementargedanke led to Carl Jung's development of the theory of archetypes. His ideas had a formative influence on the "father of American anthropology" Franz Boas, and also influenced the thought of comparative mythologist Joseph Campbell. 

According to Joseph Campbell, Bastian's concept of Elementargedanke, elementary ideas, influenced Carl Jung in his work on the archetypes of the collective unconscious, the common psychological heritage of humankind. Campbell writes: "Nowhere, [Bastian noted,] are the "elementary ideas" to be found in a pure state, abstracted from the locally conditioned "ethnic ideas" through which they are substantialized; but rather, like the image of man himself, they are to be known only by way of the rich variety of their extremely interesting, frequently startling, yet always finally recognizable inflections in the panorama of human life." (The Masks of God: Primitive Mythology, Chapter 1 Part I.)

In mythology and religion, we rely on experts such as Joseph Campbell, Carl Jung, and Adolf Bastian, to point out common traits in the vast collection of world symbols and stories, mythologies, and religions, in the thousands of tales told in different places and times across all the ages. These 'mythologists' isolate the "folk ideas", the Völkergedanken, the symbol, character trait, or story characteristic representing the local or cultural manifested part of the whole, and place it above the theme representing the whole, the elementary ideas, Elementargedanke. They then draw a mental parallel inbetween them, indicating that the local concept shares the traits and characteristics of the whole and is actually a part of a much larger "picture", a larger more general universally shared "bottom common denominator" concept. 

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Variations on a theme; the structural results are visualized here.

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ARCHETYPES IN MATHEMATICS AND UNREASONABLE EFFECTIVENESS

Archetypal symbols and stories also appear in our dreams, where they are a wholly subjective "local" experience. 
 

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Rube Goldberg's Self-Operating Napkin; the narration "explains" the discovery was made whilst sleep walking.

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Carl Jung recorded and analysed the dreams of the nobel laureate physicist Wolfgang Pauli. In Psychology and Alchemy, the Collected Works of C.G. Jung Vol.12, Carl Jung interprets a monumental series of over 400 of Pauli's dreams. Interpreting the dreams as series, Jung elucidates the spectrum of motifs and symbols reoccurring in Pauli's dreams. The process culminates with a symbolic cosmic order clock, an amalgam of several interrelated devices, operating simultaneously on different scales, colors, levels, and planes, as Pauli's personal comprehension orrery symbol representing order of a vast underlying grand cosmic principle. These dreams are also discussed in their correspondence in Atom and Archetype: The Pauli/Jung Letters, 1932-1958 (Meier, C.A., ed., Roscoe, D., trans.).  Princeton University Press. 

The mathematician Jacques Hadamard investigated the inspiration and clarification scientists have found in their dreams in his work "The Psychology of Invention In The Mathematical Field", Princeton University Press, 1945.  In science, the term "gedanken", "thought experiment",  refers to any experiment carried out in the mind, theoretically, because it can't readily be carried out physically. Albert Einstein developed much of his relativity theories in this way.

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Not a flip book; the animated imagined journey of a falling yellow sticky!

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Archetypes manifesting as various shared traits or characteristics not only appear in mathematics, they're found using mathematics.

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"That just sort of happened!" Benedict Cumberbatch as Sherlock Holmes, folding origami napkins for the wedding of John and Mary.

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The physicist Eugene Wigner wrote a remarkable essay on this subject, titled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," in Communications in Pure and Applied Mathematics, vol. 13, No. I (February 1960). New York: John Wiley & Sons, Inc. Copyright © 1960 by John Wiley & Sons, Inc.  A copy of it can be found online here:
http://www.dartmouth.edu/%7Ematc/MathDrama/reading/Wigner.html

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One, two, three, and four dimensions: a line, a square, a cube, and a tesseract created via folding.

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Wigner has this to say: "Mathematical concepts turn up in entirely unexpected connections. Moreover, they often permit an unexpectedly close and accurate description of the phenomena in these connections."

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Animated tesseract, forming three intersecting crosses, (in antiquity a.k.a. cardinal x, fixed y, mutable-cadent z).

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Wigner continues: "Just because of this circumstance, and because we do not understand the reasons of their usefulness, we cannot know whether a theory formulated in terms of mathematical concepts is uniquely appropriate. We are in a position similar to that of a man who was provided with a bunch of keys and who, having to open several doors in succession, always hit on the right key on the first or second trial. He became skeptical concerning the uniqueness of the coordination between keys and doors....The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it."Wigner continues: "Just because of this circumstance, and because we do not understand the reasons of their usefulness, we cannot know whether a theory formulated in terms of mathematical concepts is uniquely appropriate. We are in a position similar to that of a man who was provided with a bunch of keys and who, having to open several doors in succession, always hit on the right key on the first or second trial. He became skeptical concerning the uniqueness of the coordination between keys and doors....The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it."

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A skeleton key, turning in a lock.

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"Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories."

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We cannot know if it is uniquely appropriate: Ferris Wheels.

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Physicist Paul Dirac, in his preface to the first edition of his book "The Principles Of Quantum Mechanics" states his reasons for breaking with "the historical line of development", choosing to approach his subject using a symbolic method, rather than the method of coordinates or representations.

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Bird biology to a physicist: it's all "bird". So what do you get when you cross a bird with a zero?  A flying none

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Dirac writes, "Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.  For this reason a book on the new physics, if not purely descriptive of experimental work, must be essentially mathematical. All the same, the mathematics is only a tool and one should learn to hold the physical ideas in one's mind without reference to the mathematical form."  He continues, "With regard to the mathematical form in which the theory can be presented, an author must decide at the outset between two methods. There is the symbolic method, which deals directly in an abstract way with the quantities of fundamental importance (the invariants, etc. of the transformations), and there is the method of coordinates or representations which deals with sets of numbers corresponding to these quantities. The second of these has usually been used for the presentation of quantum mechanics... It is known under one or other of the two names 'Wave Mechanics' and 'Matrix Mechanics' according to which physical things receive emphasis in the treatment, and the states of a system or its dynamical variables. It has the advantage that the kind of mathematics required is more familiar to the average student and also it is the historical method. The symbolic method, however, seems to go more deeply into the nature of things. It enables one to express the physical laws in a neat and concise way, and will probably be increasingly used in the future as it becomes better understood and its own special mathematics gets developed.  For this reason I have chosen the symbolic method, introducing the representatives later merely as an aid to practical calculation. This has necessitated a complete break from the historical line of development, but this break is an advantage through enabling the approach to the new ideas to be made as direct as possible." (St. John's College, Cambridge, 29 May 1930, preface to the first edition, The Principles Of Quantum Mechanics, Oxford Science Publications, reprinted in 2011 as ISBN 978-0-19-852011-5.)

One of the best examples of revealing archetypes by working with mathematical concepts is via the "common denominator".  Dictionary definitions don't adequately explain what a mathematical "common denominator" really is, or why we benefit from thinking about it. 

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"Math analysts like to pull things apart into infinitely many pieces and see if a finite sub-collection can represent the original thing." Cartoon by Courtney Gibbons.

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Dictionaries state only that the "common denominator" is a mathematical quantity shared by a group of fractions that indicates the number of parts into which one whole can be divided. Hah hah hah. This definition is only partially accurate and it hardly gives you, pun intended, the whole picture. It is much more than that.

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A soap bubble is an example of a continuous surface. Here is compendium of other continuous surfaces known as gyroids.

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The mathematical common denominator is used to show that some group of apparently unrelated parts, such as amounts, or fractions, or myths from different ages, or deities from different cultures, or constellations of world events, or medical symptoms, are in fact actually parts of one same whole thing. It is used to trace emanations back to source, to trace effects back to whatever caused them, to trace the effects of radiation. The mathematical common denominator qualifies as archetypal. 

For all practical purposes, and in other words, the concept is essential to trace apparently unrelated events and their effects back to a common cause or source. It helps you find links, and thus, beginnings. 

If these separate parts, or aspects, all share a number which can divide into each of them without leaving a remainder, then that number is their "common divider", and it indicates that no matter what they may "look like", they are all part of the same one whole thing. 

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Common denominator and equivalent fractions:  "I understand they all have the same value, but I have to tell you, the ones on the right feel like more bang for your buck." Cartoon by Mark Anderson.

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Another way to state this is if these separate aspects all share a basic trait or characteristic, then that basic trait or characteristic is their "common divider", and it indicates that no matter what they may "look like", they are all part of the same one whole thing.  

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"Hieroglyphics" c.1800; objects composed as portraits of those who use the objects.  
http //publicdomainreview.org/collections/arcimboldo-esque-composite-portraits-of-trades-ca-1800/

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The mathematical common denominator is used to show that some group of apparently unrelated parts, such as amounts, or fractions, or myths from different ages, or deities from Another way to state this is that if all your symptoms share a common trait or characteristic, then that basic trait or characteristic is their "common divider", and it indicates that no matter what your symptoms "look like", they are all part of the same underlying event, or dis-ease.

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Hipparchus on Compound Statements n=2 n=3.

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In mathematics, we use numbers as symbols; we place a number representing the size of the part of the whole above the number indicating the whole, and we draw a horizontal line inbetween them, or a slanted line, to indicate that the top number is actually a part of the bottom.

The word "Archetype" can thus be understood as representing the "point of origin", or "the point of departure" of some aspect of consistently radiating matrix configuration of source. "Archetype" as "the point of origin / departure" from source, then becomes common to all its' manifested parts ("part and parcel" of the whole).

 

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The Pythagorean Triangle for the Eight's.

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This Bastian>Jung>Campbell concept, of local Volkergedanke micro manifestations of macro archetypal Elementargedanke is also very much "in evidence" in the current theories of physics where a similar situation exists.  Physics currently has the challenge of reconciling the theory of quantum phenomena with the theory of relativity and as Wigner states in his article, these two theories have their roots in mutually exclusive groups of phenomena: quantum theory with the microscopic, and relativity with the macroscopic. 

Remarkably, Wigner and Campbell describe the same phenomena, and their presentations and descriptions of it are fungible, point for point. The comparison is so precise that the two descriptions could have come from the same Archetypal Author, were it not for the fact that this isn't the case.  Wigner and Campbell are experts in completely different fields, and we know they didn't write each other's work.

 

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Recursive Mona, La Gioconda. Original by Leonardo da Vinci, endlessly repeated by others.

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Eugene Wigner, in the The Unreasonable Effectiveness article, in the section subtitled "The Uniqueness Of The Theories Of Physics" has this to say: "Every empirical law has the disquieting quality that one does not know its limitations. We have seen that there are regularities in the events in the world around us which can be formulated in terms of mathematical concepts with an uncanny accuracy. There are, on the other hand, aspects of the world concerning which we do not believe in the existence of any accurate regularities. We call these initial conditions. The question which presents itself is whether the different regularities, that is, the various laws of nature which will be discovered, will fuse into a single consistent unit, or at least asymptotically approach such a fusion. Alternatively, it is possible that there always will be some laws of nature which have nothing in common with each other. At present, this is true, for instance, of the laws of heredity and of physics. It is even possible that some of the laws of nature will be in conflict with each other in their implications, but each convincing enough in its own domain so that we may not be willing to abandon any of them. We may resign ourselves to such a state of affairs or our interest in clearing up the conflict between the various theories may fade out. We may lose interest in the "ultimate truth," that is, in a picture which is a consistent fusion into a single unit of the little pictures, formed on the various aspects of nature."

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Newton's cradle on the playground. Cartoon by Kanin.

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Wigner continues: "It may be useful to illustrate the alternatives by an example. We now have, in physics, two theories of great power and interest: the theory of quantum phenomena and the theory of relativity. These two theories have their roots in mutually exclusive groups of phenomena. Relativity theory applies to macroscopic bodies, such as stars. The event of coincidence, that is, in ultimate analysis of collision, is the primitive event in the theory of relativity and defines a point in space-time, or at least would define a point if the colliding panicles were infinitely small. Quantum theory has its roots in the microscopic world and, from its point of view, the event of coincidence, or of collision, even if it takes place between particles of no spatial extent, is not primitive and not at all sharply isolated in space-time. The two theories operate with different mathematical concepts; the four dimensional Riemann space and the infinite dimensional Hilbert space, respectively. So far, the two theories could not be united, that is, no mathematical formulation exists to which both of these theories are approximations. All physicists believe that a union of the two theories is inherently possible and that we shall find it. Nevertheless, it is possible also to imagine that no union of the two theories can be found. This example illustrates the two possibilities, of union and of conflict, mentioned before, both of which are conceivable."

In the next paragraph, Wigner struggles with reconciling apparent opposites; some theories known to be false give amazingly accurate results. He states "..these theories are considered to be "false" by us just for the reason that they are, in ultimate analysis, incompatible with more encompassing pictures and, if sufficiently many such false theories are discovered, they are bound to prove also to be in conflict with each other. Similarly, it is possible that the theories, which we consider to be "proved" by a number of numerical agreements which appears to be large enough for us, are false because they are in conflict with a possible more encompassing theory which is beyond our means of discovery." 

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A genuine original escape, by the Gordian Knot dog!

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BEYOND DISCOVERY?


Is this really "beyond our means of discovery" ? Apparently, pun intended, it is not.  Again, read Wigner's original article, and not just the quotes from it here. Wigner not only suspects there is a third factor influencing the polarity, he says as much, and he recognizes it may well be a subjective third factor when he says "beyond our means of discovery". 

Subjective events and effects are certainly not amenable to direct measurement or direct perception, and subjective cause and effect is far from obvious. 

 

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Do you see a duck or a rabbit? A classic optical illusion. Lapin ou canard? Magie illusion d'optique.

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We find traces of this subjective factor  "all over the place"; over and over, it is "there".  However, the delineation process has been rather like using soda bottle openers to puncture triangular holes in the tops of giant tin cans, in order to shake out some of the contents.   It is not "beyond our means of discovery", but it's not all that easy to "get at" either. 

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The Knight and The Snail; Terry Gilliam for Monty Python's Flying Circus.

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Until Sigmund Fraud discovered the "unconscious" and Carl Jung mapped it by externalizing its' subjective tracks for decades, our inner world was similar to Helen Keller's.  We suspected something was there, but had no means for working with it more directly than that; as she says "Through an inner law of completeness my thoughts are not permitted to remain colorless." Freud, Jung, and Campbell all recognized this subjective factor, and spent their lifetimes delineating various manifestations of it, in as objective a way as possible. 

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Do you see the old woman or the young woman? A classic optical illusion. Magie illusion d'optique.

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Joseph Campbell compares the process to tracking an animal by their scat.  His prodigious work is groundbreaking for many reasons. He traces these tracks throughout all known human history. He tracks, as he says, up hills and down dales, over the rivers of time, and through the woods of countless civilizations, countries, ancient times, and places.  One striking result is his creation of  a working model of subjective experience, made from the connections of the trail it leaves behind in vast amounts of objective data. The results that he uncovers are tantamount to discovering that his trip to Grandma's House hasn't landed him anywhere near there. Instead, by following a trail left by lost children wandering through a forest, he arrives at a witch's gingerbread house, and discovers the gingerbread is made from a generic cake mix! 

Science's search, notably as Wigner describes it, uses precisely the same search and identification processes, and according to Wigner, with similar results.

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Geometric optical illusion: rotating square behind attention-disappearing dots.

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To find and connect these threads has always required geniuses to see the patterns. The work to discern the patterns has always required what we now refer to as "big data algorithm crunching": the interrelation, coordination, and mapping, of vast amounts of verifiable space-time data. Yes, I know this sounds daunting, but remember, until very recently, people could perform calculations in their heads, without calculators.

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Isomorphs by Alvaro Catalán de Ocon.

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Over the past two centuries, humans have finally left enough tracking "scat", as Campbell calls it. We've been around long enough, and been stable long enough, to leave analyzable records. It's a sizable challenge to objectively and honorably connect dots in all this data; it presents a daunting task, in spite of the help of modern computers. At this juncture, the compilation of all these life works is as far as Science has been able to get. 

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Harry Whittier Frees photograph, 1926. Two Kitty dunces!

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Eugene Wigner elaborates on what might occur should we establish a "theory of consciousness or of biology" which doesn't resolve the present polarized dilemma but instead, polarizes it still further. He says "The reason that such a situation is conceivable is that, fundamentally, we do not know why our theories work so well. Hence, their accuracy may not prove their truth and consistency."

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Harry Whittier Frees photograph, 1926. One Kitty Dunce!

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Wigner states: "The free-electron theory raises doubts as to how much we should trust numerical agreement between theory and experiment as evidence for the correctness of the theory. We are used to such doubts. A much more difficult and confusing situation would arise if we could, some day, establish a theory of the phenomena of consciousness, or of biology, which would be as coherent and convincing as our present theories of the inanimate world. Mendel's laws of inheritance and the subsequent work on genes may well form the beginning of such a theory as far as biology is concerned. Furthermore,, it is quite possible that an abstract argument can be found which shows that there is a conflict between such a theory and the accepted principles of physics. The argument could be of such abstract nature that it might not be possible to resolve the conflict, in favor of one or of the other theory, by an experiment. Such a situation would put a heavy strain on our faith in our theories and on our belief in the reality of the concepts which we form. It would give us a deep sense of frustration in our search for what I called "the ultimate truth."  The reason that such a situation is conceivable is that, fundamentally, we do not know why our theories work so well. Hence, their accuracy may not prove their truth and consistency. Indeed, it is this writer's belief that something rather akin to the situation which was described above exists if the present laws of heredity and of physics are confronted. Let me end on a more cheerful note. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning."

 

We now have the means for "big data algorithm crunching", for the cross-discipline interrelation, coordination, and mapping, of vast amounts of verifiable objective / subjective space-time data. 

Perception experiments would however seem to indicate that the odds are stacked against our succeeding. The framing effect from behavioral economics states that people draw different conclusions from the same information, depending on the context in which they receive that information, how the information is presented to them, and by whom the information is presented. This is the Volkergedanke "at work", manifesting the local manifestations, of the underlying Elementargedanke archetype of fraternity. 


Use the triad gif, below, to help you rotate the black cat in counterclockwise and clockwise directions. View these gifs back to back, at the same time. It will help to have the triad on the screen to watch as you also watch the cat; your mind will use the triad as a direction reference for the cat (your mind will map one set of images onto the other set). When you can make the cat rotate either direction, then practice alternating the motion of the train, so it can either enter or leave the station. 

 

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Use the triad gif, above, to help you rotate the black cat in counterclockwise and clockwise directions.

View the triad and cat gifs back to back, at the same time. It will help to have the triad on the screen to watch as you also watch the cat; your mind will use the triad as a direction reference for the cat (your mind will map one set of images onto the other set).

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When you can make the cat rotate either direction, then practice alternating the motion of the train, so it can either enter or leave the station. 

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Christopher Chabris and Daniel Simons, in their book "The Invisible Gorilla" discuss their now famous unseen gorilla experiment, first conducted at Harvard. Their experiment has since been repeated in endless variations. Approximately half the volunteers watching a distracting sports video, failed to notice a walk-on, halfway through, by a girl wearing a full body gorilla suit. She stopped in the middle of the sports players, faced the camera, thumped her chest, and then walked off, spending about nine seconds onscreen.  he same experiment was repeated at Heidelberg University using eye trackers; those subjects who failed to notice the gorilla spent, on average, a full second looking right at it, the same amount of time as those who did see it.  As is usual for the people who do see the gorilla, they're genuinely surprised that anyone could possibly miss seeing something so obvious to them.

Christopher Chabris and Daniel Simons, The Invisible Gorilla, 1999,  ISBN 978-0-307-45966-4 , Broadway Paperbacks, an imprint of Crown Publishing Group, a division of Random House, Inc. New York, www.TheInvisibleGorilla.com (chapter one, and pages 13 and 250).

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The Pink Panther movie; look alike gorillas simultaneously break into either side of the double sided safe.

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Given the means to sort the data, we still have to know what we're sorting the data for; we're attempting to recognize, in a haystack of preconceptions, a thread of something completely alien to expectations, something never seen before, totally unexpected. Even astronauts have a hard time training for this sort of thing. If this were easy, more people would do it, and we would have found it by now.  We need more than algorithms. ability, intelligence and intuition. We also need morals, ethics, self-discipline, sustained focus and attention, and exceptional levels of multiple cross interdisciplinary skills. We also need somebody to pay us while we search.

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The X is not located as it first appears.

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All this partly explains why it takes us so long to connect these dots, even with vast amounts of data, and computers to help sort. To give you an example, it's as if we're still discovering that the earth is rotating around the sun. Locally, we say the "sun is coming up", the "sun rises".  But as we say the sun is coming up locally, as our local Volkergedanke, elsewhere, somewhere else on the earth, other people are saying at exactly the same instance that the sun is going down there, and their local Volkergedanke is that the sun is "setting".  Until the two locations get together and compare notes, neither of us may realize that it is the earth that's rotating around the sun, and not the sun around the earth, and the fact that the earth is rotating around the sun is the Elementargedanke.

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Optical illusion with a Rubik's cube.

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Connecting the dots requires a special sort of genius, and geniuses of any sort are always in short supply. 

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What do you see? Que voyez vous? Illusions optique.

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ADDITIONAL RESOURCES


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

BOOKS:

 Campbell, Joseph 
 (1990) Transformations of Myth Through Time. Harper and Row

Chabis, Christopher and Simons, Daniel 
(1999) The Invisible Gorilla, ISBN 978-0-307-45966-4 , Broadway Paperbacks, an imprint of Crown Publishing Group, a division of Random House, Inc. New York, www.TheInvisibleGorilla.com (chapter one, and pages 13 and 250).

Jung, C. G., Pauli, Wolfgang  Atom and Archetype: The Pauli/Jung Letters, 1932-1958 (Meier, C.A., ed., Roscoe, D., trans.).  Princeton University Press.
Jung, C. G., Pauli, Wolfgang  Psychology and Alchemy (Collected Works of C.G. Jung Vol.12).  Princeton University Press.

Keller, Helen
(1903) The Story of My Life
(1908) The World I Live In 

Polti, Georges 
(1921, reprinted 1991) The Thirty-Six Dramatic Situations, translation from the French, ISBN 0-87116-109-5, 1921 James Knapp Reeve, 1977 The Writer, Inc.

Sand, Maurice
(1860) Masques et bouffons (comédie italienne) available online here:
https://archive.org/details/masquesetbouffo00mancgoog
Publisher Michel Lévy frères, Paris.
Maurice Sand studied under Eugène Delacroix and was the husband of novelist and feminist George Sand.


Slonimsky, Nicolas 
(1947) Thesaurus Of Scales And Melodic Patterns


Von Franz, Marie-Louise  (1974) Number and Time, Northwestern University Press, 1974

Wigner, Eugene 
(1960) "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," in Communications in Pure and Applied Mathematics, vol. 13, No. I (February 1960). New York: John Wiley & Sons, Inc. Copyright © 1960 by John Wiley & Sons, Inc.  A copy can be found online here:
http://www.dartmouth.edu/%7Ematc/MathDrama/reading/Wigner.html

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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.
Success consists of going from failure to failure without loss of enthusiasm. ~ Winston Churchill