Saturday, March 20, 2021

Squaring the Circle

 

Conceptual impressions surrounding this post are yet to be substantiated, corroborated, confirmed or woven into a larger argument, context or network.


All is vibration. In essence vibration participates in the emergence of a quantum field of virtual potential (QFVP) that might well be likened to Consciousness. Design describes this observation as in-form-ation - energy discovered and interpreted as a language in symbolic transformation appearing from within the parameters of its own field of awareness/observation.

Design attempts to reveal through a set of conditions and circumstances, certain symbolic attempts to define and describe the meaning and purpose underpinning a particular object, process, event or experience. Like consciousness this phenomenon continues ad infinitum both prior to and after dimensional re-presentation.


The Circle

“God is a circle whose center is everywhere and whose circumference is nowhere” 

Hermes Trismegistus


"The circle is a universal symbol with extensive meaning. It represents the notions of totality, wholeness, original perfection, the Self, the infinite, eternity, timelessness, all cyclic movement, God The circle is a two-dimensional shadow of the sphere which is regarded throughout cultural history as an icon of the ineffable oneness; the indivisible fulfillment of the Universe. All other symbols and geometries reflect various aspects of the profound and consummate perfection of the circle, sphere and other higher dimensional forms of these we might imagine.

The ratio of the circumference of a circle to its diameter, Pi, is the original transcendental and irrational number. (Pi equals about 3.14159265358979323846264338327950288419716939937511...) It cannot be expressed in terms of the ratio of two whole numbers, or in the language of sacred symbolism, the essence of the circle exists in a dimension that transcends the linear rationality that it contains. Our holistic perspectives, feelings and intuitions encompass the finite elements of the ideas that are within them, yet have a greater wisdom than can be expressed by those ideas alone." 

Squaring the circle

The mathematical challenge of squaring the circle originated with the ancient Greek mathematicians and geometers.  The problem was to construct for a given circle a square with the same area as the circle, all to be done with only a compass and straightedge. It was repeatedly demonstrated that the challenge was impossible to do. 

The circle represented woman, spirit and infinite wholeness, the square man, earthly circumstances and all things material. Ancient Greek philosophers distinguished all things material within the context of fours, e.g. the seasons of the year, the elements of earth, air, fire and water. Squaring the circle was proven to be algebraically impossible until 1882 when the Lindermann-Weierstrass theorem proved that pi π is transcendental and not an algebraic irrational number.
“Philosophically and spiritually, to square the circle means to see equally in four directions—up, down, in, and out—and to be whole, complete, and free. Circles often represent the spiritual because they are infinite—they have no end. The square is often a symbol of the material because of the number of physical things that come in fours, such as four seasons, four directions, and the four physical elements—earth, air, fire, and water, according to ancient Greek philosopher Empedocles—not to mention its solid appearance. The union of man and woman in alchemy is a merging of spiritual and physical natures. The triangle is then a symbol of the resulting union of body, mind, and soul. In the 17th century, squaring the circle had not yet been proved impossible. However, it was a puzzle no one had been known to solve. Alchemy was viewed very similarly: It was something few if any had ever fully completed. The study of alchemy was as much about the journey as the goal, as no one might ever actually forge a philosopher’s stone.” Catherine Beyer  https://www.learnreligions.com/squaring-the-circle-96039
"The most important thing in arithmetic is not the shapes of the numbers but the reality living in them. This living reality has much more meaning for the spiritual world than what lives in reading and writing."Rudolf Steiner
The Classical Elements

"Classical elements typically refer to water, earth, fire, air, and (later) aether, which were proposed to explain the nature and complexity of all matter in terms of simpler substances.[1][2]Ancient cultures in Greece, Ancient Egypt, Persia, Babylonia, Japan, Tibet, and India had all similar lists, sometimes referring in local languages to "air" as "wind" and the fifth element as "void". The Chinese Wu Xing system lists Wood (木 mù), Fire (火 huǒ), Earth (土 tǔ), Metal (金 jīn), and Water (水 shuǐ), though these are described more as energies or transitions rather than as types of material. These different cultures and even individual philosophers had widely varying explanations concerning their attributes and how they related to observable phenomena as well as cosmology. Sometimes these theories overlapped with mythology and were personified in deities. Some of these interpretations included atomism (the idea of very small, indivisible portions of matter), but other interpretations considered the elements to be divisible into infinitely small pieces without changing their nature."1. Boyd, T.J.M. ; Sanderson, J.J. (2003) The physics of Plasmas, Cambridge University Press.p.1 ISBN9780521459129. LLCCN 20020246542. Ball, P. (2004). The Elements: A Very Short Introduction. Very Short Introductions. OUP Oxford. p.33. ISBN8970191578250https://en.wikipedia.org/wiki/Classical_element 
The Four Elements"The four elements[edit] Empedocles established four ultimate elements which make all the structures in the world—fire, air, water, earth.[32][43] Empedocles called these four elements "roots", which he also identified with the mythical names of Zeus, Hera, Nestis, and Aidoneus[44]"32 Wallace, William (1911) "Empedocles" In Chisolm, Hugh (ed). Encyclopedia Britannica. 9 (11th ed.) Cambridge University Press. pp. 344-345.43. Frag. B17 (Simplicius, Physics, 157-159)44. Frag.B6 (Sextus Empiricus, Against the Mathematicians. x.315)https://en.wikipedia.org/wiki/Empedocles
What might be the elements or "roots" needed to explain the nature of Design? What might be the basis from which we can describe and or comprehend design in reference to a "nature" that surrounds, penetrates and brings reflection to every event and experience?
First we must be willing to accept the premise that Design is transcendental. Likened to the inability to square the circle and finalizing the value of π  Design is just as immeasurable and just as never ending. Design is simultaneously visible and invisible, transitory, transforming, transcending, adaptive and timelessly changing in time. idea noun   3 Philosophy (in Platonic thought) an eternally existing pattern of which individual things in any class are imperfect copies.      (in Kantian thought) a concept of pure reason, not empirically based in experience.complementary adjective.  combining in such a way as to enhance or emphasize the qualities of each other or another: three guitarists playing interlocking, complementary parts | Internet technology is actually complementary to traditional technologies. 

Design Appearances

Design makes its presence through the use of symbols. Symbols make their appearance in three dimensional space/time in the forms of:

images (mental)  likeness, resemblance; depiction, portrayal, representation; statue, statuette, sculpture, bust, effigy; painting, picture, portrait, drawing, sketch.     2 : picture, photograph, snapshot, photo.      3 reflection, mirror image, likeness.     4 : conception, impression, idea, perception, notion; mental picture, vision; character, reputation; appearance, semblance.     5 : simile, metaphor, metonymy; figure of speech, trope, turn of phrase; imagery.     6  public perception, persona, profile, reputation, stature, standing; face, front, facade, mask, guise.     7 double, living image, look-alike, clone, copy, twin, duplicate, exact likeness, mirror image, doppelgänger; informal spitting image, dead ringer, carbon copy; archaic similitude.     8 a graven image: idol, icon, fetish, totem. verb envisage, envision, imagine, picture, see in one's mind's eye.
thoughts (mental)     an idea or opinion produced by thinking, or occurring suddenly in the mind:      (one's thoughts) one's mind or attention:      an act of considering or remembering someone or something:       (usually thought of) an intention, hope, or idea of doing or receiving something: .    2 the action or process of thinking: .      the formation of opinions, especially as a philosophy or system of ideas, or the opinions so formed:      careful consideration or attention:       concern for another's well-being or convenience: 

feelings(emotional)   1 an emotional state or reaction:      (feelings) the emotional side of someone's character; emotional responses or tendencies to respond:      strong emotion:      2 a belief, especially a vague or irrational one: [with clause] :       an opinion, typically one shared by several people:      3 the capacity to experience the sense of touch:       the sensation of touching or being touched by a particular thing:      4 (feeling for) a sensitivity to or intuitive understanding of:  adjective showing emotion or sensitivity: 
sensations(physical)   1 a physical feeling or perception resulting from something that happens to or comes into contact with the body:       the capacity to have physical sensations: .      an inexplicable awareness or impression: [with clause] :      a widespread reaction of interest and excitement:       a person, object, or event that arouses widespread interest and excitement: 







No new event or experience can exactly parallel the meaning or purpose symbolically ingrained in past events and experiences. Impressions from all these experiences are the products of our imagination. All events and experiences are extremely complex, symbolic in character and appropriately configured for the time and space in which they occur, both past and present. All observations and perceptions are symbolic cognitions and figments of the imagination. 
Our experiences appear to be real because they've been imagined in a "timely" framework and found to be appropriate for a particular space and time. Energy in motion is how we might describe time in a linear fashion, interpretations of experiences and events that together bring relevance to our concept of Reality (POV). Remembrances are linked together by design, i.e. signs, symbols, metaphors, analogies, etc. that together veil design's hidden language affecting our images, thoughts, feelings and sensations from the past, the present and into the future. 
These engaging states of mind create their own field of energy, guided by feelings and impressions that in linear time, can alter our POV. Together they contribute to our concept of Reality. These thoughtful engagements allow our imagination to adapt to every situation we may encounter, formless impressions from a quantum field of virtual potential.
Humanity survives by means of its ability to imagine, observe, perceive and create symbolically by design.
3,700-year-old Babylonian Stone Table gets Translated, Changes History 
Reality can best be described in the moment. Clear, concise, intentions are energized through symbolic interpretation, adjustment and adaptability. Realities self-truths are timelessly cloaked in a POV veiled both in form and formlessness.Your source of origin will be revealed to you while observing your own reflection in the moment.
"Nowness or the magic of the present moment is what joins the wisdom of the past with the present."Chogyam Trungpa
Find balance and harmony about the core of a central presence you know is real at the moment. There are many moving parts involved in the process of acknowledging the singularity within. You are an observer, a personalized awareness symbolically known, felt and impossible to measure. Your center marks a point surrounded by a field of energy, light and information in perpetual change, a point where the squaring of the circle meets within the parameters of space and time.
Design is a concept whose methods of abstraction are symbolic in representation. Design is real but not capable of being fully described or explained through simple logic. Design is transcendental and like consciousness is presupposed, a priori and fundamental to Life. All signs are at the root of design.


Frozen in space and time the question of how to measure the area of a circle had been geometrically interpreted and mathematically approximated by means of a system of symbols. Symbols (numbers) were placed into certain correspondences, patterns and formations. Impressions were drawn with instruments made to describe and represent the relationship (ratio) between the circumference of a circle to its diameter. 

Many attempts were made to find a conclusive solution to a mystery that led to an inconclusive answer - it became an irrational situation. After many unsettling attempts to resolve the dilemma between the circle and the square a more comprehensive result emerged. The situation demanded a simpler solution that evolved into the symbol we know today as Pi ( π ). 
 
"Like all real numbers, irrational numbers can be expressed in positional notation, notably as a decimal number. In the case of irrational numbers, the decimal expansion does not terminate, nor end with a repeating sequence. For example, the decimal representation of π starts with 3.14159, but no finite number of digits can represent π exactly, nor does it repeat. Conversely, a decimal expansion that terminates or repeats must be a rational number. These are provable properties of rational numbers and positional number systems and are not used as definitions in mathematics." 

A mathematical inconvenience has found resolution by means of applying a newly designed re-presentation of itself, bringing an sense of wholeness, continuity and agreement to a circumstance that could not be completely determined. Do all the previous ideas surrounding the concept of Pi degrade the accomplishments of earlier attempts to square the circle? Has every past number, equation, formula and attempt become inconsequential, or have they been enhanced, strengthened and supplemented through irrational means? The relationship between the circumference (feminine) and the diameter (masculine) have been symbolically embellished. Pi  π  is a sign that harbors more than just a mathematical cognition,  π  is a symbol designed with both a meaning and a purpose.   

 π  re-presents an unending series of signs (numbers) placed in relative succession that reveal the inherent constraints surrounding linear thinking. Mathematicians and geometers encountered a snag in their quest to square the circle, which included their use and method of investigation. It was long time to further adapt to the challenge as the challenge would not go away. 

A greater understanding and reconfiguration was imperative for further investigation. This challenge could only be met by accepting such limitations and find resolution by creating a more embracing signature that could shroud the unprovable mystery that had no systemic explanation. 

This symbol and all the designs that further expanded upon it, was more realistic, embracing, accepting, holistic and functional in its character.  Once accepted by the collective  π  began to represent an unprovable reality (phenomenon) that couldn't be described in any other fashion. In other words, the entire concept of squaring the circle was transformed due to the context in which the event was now being observed, a circumstance that required change/action for the sake of mathematics as a whole. 

Mathematics became transformed by transcending a fixation upon interpretations brought forth through the use of earlier methods of instrumentation. Future advances in observation, perception and interpretation of Reality became accelerated. Past impressions were altered by virtue of a simple sign that symbolized more than anything thought measurable. 


 π  is symbolic in its presence was created with the purpose of advancing awareness through the application of an seemingly objective process designed to investigate the unknown. 

This example describes how all signs have symbolic references in the form of impressions that are both purposeful and meaningful. The search for the area of a circle by means of a square might be considered irrational because it lacks precision. One might glean that the concept of a circle is an example of irrationality in its own right and that the concept of wholeness is an unreachable goal if not complemented by its opposite. We each are afforded the choice to believe this to be true or not by allowing ourselves to imagine it. Like consciousness we will never be able to truly measure  π  as long as it lies within the domain of three dimensional space and time. 

Physicist Prove That the Imaginary Part of Quantum Mechanics Really Exists!  https://scitechdaily.com/physicists-prove-that-the-imaginary-part-of-quantum-mechanics-really-exists/


Why are complex numbers needed in quantum mechanics? Some answers for the introductory level  https://aapt.scitation.org/doi/10.1119/10.0000258 

“In physics, complex numbers were considered to be purely mathematical in nature. It is true that although they play a basic role in quantum mechanics equations, they were treated simply as a tool, something to facilitate calculations for physicists. Now, we have theoretically and experimentally proved that there are quantum states that can only be distinguished when the calculations are performed with the indispensable participation of complex numbers,” explains Dr. Streltsov.

 Signs and symbols (numbers) prove that measurements can be inconclusive and that only through the imagination might the concept (idea) of perfection be felt, reflected or recognized. All forms of language symbolize what could be Real by virtue of their design and the context in which these designs appear. 

imagination noun the faculty or action of forming new ideas, or images or concepts of external objects not present to the senses:      the ability of the mind to be creative or resourceful      the part of the mind that imagines things: 

Beauty is the only concept in space and time where the idea of perfection can be vividly felt and/or fully experienced. Beauty brings to form and formlessness a third type of non-duality.

The circle attracts energy-in-motion towards its center. A one pointed focus of energy cannot be sensed without motion nor understood without direction, it will always be an obstruction in the path of science. Energy trans-form-ations appear as reflections in the Light of observation. Within this context the circle finds its purpose by virtue of its meaning and meaning by virtue of its purpose. To find balance in all fields energy in motion they must all be designed.

The line possesses the potential for creating an assemblage of forms where wholeness might be rediscovered, remastered, redirected, refined and realized. The line is the vector that incorporates the geometry of the Cosmos. Every dance between line and circle has a meaning and a purpose in a complementary quest for harmony - a grand Design that symbolically veils the Source of its perfection.


"The Ancient of Days", William Blake 


The observer is central to every circle whose focus is appointed by intention. The act of observing appears as a disturbance within a quantum field of virtual potential, i.e. a position of single pointedness is known by means of its impression upon the greater whole. The point becomes a line giving direction (measure) to its purpose and meaning to its intent. A point is a line in motion. (see Design Metaphysics: Design In Motion)

Multidimensional and holistic in essence the point no longer appears pointless as it hurls through a field of virtual potential. Splitting from itself for purposes of self realization, the point becomes both one (particle) and the same (wave) - expanding beyond pointlessness (line, wave, geometry) a reflection of its self returns to its pointedness (center, source, intent). Experience invites an expansion and contraction of the field within. Forms emerge and disappear in a feedback loop that never ends. What was once real now changes every moment. Projection, reflection, internalization, illumination ... cyclically spiraling, expanding and contracting in a Design revealed in moments of timeless Awareness.

“The present issues from the past, and the future from the present. Everything is made one by this continuity. Time is like a circle, where all the points are so linked that one cannot say where it begins or ends, for all points precede and follow one another forever.” Hermes Trismegistus, Corpus Hermeticum 


Design is irrational. Design can be imagined, but not always measured.

Design is not as precise as mathematics would like it to be, yet without it nothing would add up.


The design process is dependent upon the proper use of language made in reference to the concept of coherent resonance. If a common language, i.e. system of symbolic impression and interpretation, is not appropriately pre-determined, agreed upon and adhered to through a shared and accepted understanding, truth will surely be lost in interpretation, transformation and transcendence This is an extremely difficult position to comply with and adapt to considering the fact that change is a constant and most reactive when observed from within a quantum field of virtual potential and probability (QFVPP).

The observer/perceiver interprets every event and experience (situation) symbolically. The observer both absorbs (input) and responds (output) with a coded language of signs and symbols recognized solely within the context and constraints that surround every observation.

An observer never stands alone for there will always appear a context upon reflection.

To be design conscious you must be more than an observer.



Edited: 02.11.2021, 02.15.2021, 02.16.2021, 03.01.2021, 03.24.2021, 04.12.2021, 04.29.2021, 07.13.2021, 12.01.2021, 02.08.2022, 03.15.2022, 03.28.2023

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