Conservation of the Circle is easily observed as the most basic dynamic in nature, the most important thought paradigm of all time... a strategic insight  and the most realistic way to interact with reality...

The foundation and destination of symbolic and physical systems is the circle-line relationship mediated by pi. Man shares a circle with nature. Nature shares a circle with man. Thus, a two-state system defines everything (foundation and destination, symbolic and real). This is the archetype for reality.

All behavior symbolizes a circle. Movement articulates a line, diameter of a circle, symbolic, real.  Thus, a hidden circle between any X and Y means two (not one) is the basis for reality... Thus, circular logic (50-50 everything) is required if you want to get to the truth (for world peace, individual clarity, foundation of physics and mathematics)... the line and the circle (M-F, 1-0) are the two basic elements in nature...

Symbolic

The symbol (language, mathematics, art) defines reality (influences, directs, articulates behavior). Everybody knows this (media, technology, politic, economics). Thus the 0-1 decision-making process (on-off, Y-N, T-F) (zero-one, one-two) leads to...
  Three is  two-two's (E-W/N-S 1-2 2-3). Me-not-me, you-not-you. Two (not-one).

Thus reality is dependent on intelligent observation (X or Y is X and Y is X is Y is X). One (and, also, three) is not possible without two. Thus two (not-one, plus and-or minus one) is the correct name for any number. This means there are only two constants in nature: a zero and a one, also known as zero and infinity, more realistically circle and line. Again, two (not-one). In normal terms, any object (subject) is a two-state system (background-foreground, black-white).

Confusion originates from the misplaced understanding: three is never two (two is never one, one is never zero, etc.). Confusion serves its purpose as demonstrated by camouflage in nature. Duplicity and negation are the same. Thus the lie is a protective mechanism in nature. So everything is hiding its opposite. Everybody's two-faced. From the circle's point of view all units are the same, thus normal observation is 50% incorrect.

Real

Sexual reproduction (reproduction in general) articulates (conserves) a circle (conservation of the circle). Thus reproduction and survival share an ever-present (never-present) circle. Any observation shares a circle with its observer thus it's very easy to see a circle in the background produces any foreground... every foreground.

The circle produces pairs of opposites, meaning every movement is a basic yang and yin, thus the reproduction and survival of a circle produces the reproduction and survival of the line reproduces the reproduction and survival of everything (you, me, it). The destruction of one element is the reproduction of another.

Thus pi is the only observer, the directionless, dimensionless, coupling constant in the background, making observation possible (holding zero and one together and also keeping them apart) thus light is not moving (relativity is an oscillation between constants two and one (plus and minus one is two)). And you can begin to see numbers duplicate and thus negate each other.

Thus light originates as the circular relationship within space (space and space, inside, outside). Oscillation is fluctuation is vibration is perturbation is movement found in any word number picture object (subject) (symbolic-real). Complementary opposition. Duplicitous singularity. Oppositional duplicity. Singular complement. Observation is deduction is reproduction.

Thus the hidden neutron in hydrogen surrounds 'everything...' (space). The hidden circle within a unit surrounds a unit (all units share a circular relationship with space). Thus everything changes. Nothing changes.

Hidden

The hidden circle with its hidden diameter is the most basic unit of space (thus space and time articulate a circle (you cannot have one without the other)). X is X (X is-not X) (2X is X). The opposite (opposition) is always hidden in the background, thus the hidden, abstract, symbolic always shares a circle with reality. Thus the villain, good and bad, true and false.

X is always 1 (plus and-or minus one, plus is minus one). Absolute zero is perpetual motion. Thus the (w)hole in (is) space. One unit always negates (duplicates) another (black shares a circle with white, circumference shares a circle with center). Thus circle is the correct description and dynamic for (any, every) unit. Also known as cycle, circuit, switch.

Thus the death wish is embedded in life (life is a defense mechanism for death and vice versa, 0-1, 1-0). The archetype is articulated and balanced by its opposite. Absolute zero is perpetual motion. This explains everything.

Figurative

Pi has two values, 0,1,2,3... or 0-1,1-2,2-3,3-4,4-5 etc. an infinite number of 'values' (constants) (50-50 constant-chaos). Pi limits this in all directions to two values (independent of the symbolic representation of the value, two is the natural limit)... more thoroughly explained at www.Circular-Reality.com. See Conservation of the Circle, Conservation of (a) Constant, Conservation of Chaos. Thus reversion to the mean, law of least resistance, 50-50, is more accurately designated diameter of a circle is circumference.

The symbolic nature of man (life, death, everything) is thus circular (any X and Y articulate a circle, thus gravity, light, sound) (pi, line, circle). Language and mathematics are symbolic systems. Everything articulates the symbolic relationship between a zero and a one (a unit and a group). Thus mind and matter are this zero and its one (mind can only operate with symbols).

Group (Unit)

From the circle's point of view, unit and group are X and X, joined and separated by pi. Thus, reality ensues.

All observers articulate a 50-50 choice which is the result of the observer's assumption. Thus 50% assume a linear reality and 50% assume a circular reality (0-1,1-2,2-3)(101,10,01) thus reality (by nature) is balanced. 

However you symbolize it, any unit is a copy, and thus he-she-it copies, another unit. Thus units reproduce units (nothing more or less). Conservation of the circle forces any unit to find a reason to be unique (one-not-two, two-not-one). Thus constant conflict. Peace. Reality. Repetition.

The symbol operates as a unit (two is one, two as one) thus the correct designation for a unit is two (not-one). This provides the foundation for language and mathematics. Unit is fungible. The integrity of any unit is conserved by its relationship (circular thus linear) to any other unit. X (X') is X (X is XX is XXX) (X is-not XX is-not XXX). Duplication is negation (negation is duplication).

Is and is-not share a circle. Line is both diameter and circumference of a circle. Zero is necessarily one (thus the basis for religion).

Time (Space)

Temporal (time) and non-temporal (space) are joined and separated (physically and symbolically) by the dimensionless constant relationship (circle and linear, F and M) (also known as pi, nature, mind, God, intelligence, etc). Also energy, matter, movement. The circle between constant and variable unifies these movements (symbols) thus one symbol is easily exchanged for another.

Mythological structures (rituals) (stories, movies, math) articulate beginning-middle-end, thus one-two-three (one-two-one) is beginning-end in a continually perpetual symbolic circle more accurately identified: conservation of a circle (also known as reproduction, observation, deduction, conservation of a line). A line reproduces circle (line is always diameter and circumference of a circle). The metaphor, then, defines reality.

Divination systems (including mathematics and technology) revolve around a 50-50 circle, thus, randomly, everything is true. The circle and line provide the most basic archetype (symbolic relationship to reality). All archetypes articulate the circular relationship. Thus everybody lies (breaks all of the commandments) which is why we have to exercise forgiveness and-or punishment (this process articulates a circle) (1,0).

Proof

The proof for this is simple: the line is always diameter of a circle. Any set of symbols forms eventually a line all lines reproducing thus conserving and preserving the symbolic circle.

More thoroughly discussed at www.Circular-Reality.com 

The skeptic always shares a circle with the stoic. Meaning...all observers are entangled thus entrapped within the 50-50 point of view.

In other words, we're all stubborn with our point of view. This is a convenient explanation for: arguments, hatred, war, and all the other things we don't 'like' about life. X must always elaborate, re-articulate, disintegrate another X's point of view.

Conflict

Thus reality: we can get along, agree, 50% of the time. The rest...well...you know...

Strange, but true, if you want to see conservation of the circle in action, watch 'dancing with the stars...' More conventional...the weather, day and night... an argument between two or more people.

Everything evolved from reality's relationship to and with light... more accurately articulated 'infinite line...' reproducing infinite circle (look up in the sky). Ancient people resolved (reproduced) this relationship with pictures, numbers, letters, words, sentences, paragraphs, stories (movement reproducing movement).

Protection

It is easy to deduce symbolic systems were (are) used to anticipate the sun (seasons for food and survival, warnings for danger). Thus symbolic systems are used in the same way today (man uses language, mathematics, art and technology in general, to survive).

This comes directly from the circular relationship between survival and reproduction (conservation and symmetry). Symbolic behavior  also produces arguments (symbolic behavior and systems are used for protection). Symbolic behavior proves (the constant) (variable) movement is beneath reality.

Eventually man noticed: you cannot resolve an argument that involves a hidden idea (symbols, shadows in a cave). Thus we came up with ways to deal with arguments (logic, rhetoric, archetypes). Also ethics.

This is where circular logic was formally eliminated. Archetypes took hold (skeptic, stoic). Arguments were transferred to games, plays, learning (colosseum, gymnasium, amphitheatre), laws (courts, government systems). This is because man realizes pi is the only observer (the correct name for the hidden constant called a unit).

Thus an unlimited number of symbolic names (archetypes) including one, God, mind, idea, evolved long after repercussion was (is) beat out on a drum. The archetype (symbolic constructions) took the place of circular logic. Thus the circle as the most basic symbolic construction delivers the truth. (Whatever you believe is half-true, thus always-true, eventually).

Binary

However, in a more realistic observation, circular reality means a binary system can only reproduce a binary system, thus in order for everything to move, nothing underneath (overhead) is moving.

Thus a constant in the background forces chaos (movement) in the foreground. Hydrogen, without its neutron, is an originating (destinational) binary system (allowing electrons, micro-organisms, macro-organisms, to move).

From a modern point of view then, everything is 50-50 (two units, not-one, one unit correctly named two).

To observe a binary system reproducing a binary system (sending ones and zeroes back and forth even though nothing is moving) see any human addictively engaged with his 'smart' phone. They share a circular relationship. Obviously. Symbolic.

Obvious

The man and his phone (nature and technology) prove (articulate and demonstrate) conservation of a circle (is the basis for reality).

The circle is the basic construct for all disciplines as it is the basis for a unit in any discipline. Any division or operation (action-reaction, co-action), any subject-object relationship, relativity, complementarity, entanglement, uncertainty, depends upon the circle as a constant.

Thus we find the circle embedded in physics, philosophy and psychology, as any movement produces a line, diameter of a circle. A circle can only circle and only a circle can circle thus circles (noun, verb - singular, plural) (duplication, negation) (subject, object).

Thus a whole and its parts articulate the conservation (reproduction, preservation, symmetry, asymmetry) of a circle.

Basic

Thus the circle is easily the most basic unit articulated thus understood by everyone (reader-writer, speaker-listener, leader-follower, friend-foe) (you and me, he and she, them and us).

Thus, in financial terms, an asset is always a liability, and vice-versa, thus an observer (you) always have the freedom to observe either, both, neither. This proves you already get it... the 50-50 circle balances, thus defines, everything.

'I don't believe it' is always balanced by 'I do believe it...' Thus, we all agree to disagree, and-or, thus, we fight. Any movement makes the opposing movement real.

Objective Self

You do not have to be a physicist to figure out the 'truth...' but, if you are a physicist, Conservation of the Circle allows you to symbolize your version of the truth. Thought leaders in physics, as soon as they were made aware of it, incorporated this logic into their work... thus you are now hearing 'what we thought before was untrue...' but this braiding back and forth is true throughout history as it demonstrates the truth: the circle is embedded in every person's work (etched as the unifying relationship between zero and one, mind and matter, brain and observation, observation and reproduction). Thus the copy is ubiquitous (meaning there is a natural limit to what science can achieve).

All great physicists eventually return to philosophy once they achieve this limit. Thus the connection between Einstein and Jung (physics and human behavior) exposes the circular relationship between them (identified correctly by Yardley as Conservation of the Circle). To move past Einstein and Jung (their names are now archetypes for certain incorrect ideas) you only have to recognize (observe, notice) the circle resident between them is the circle resident between any observer and his-her-its observation...

Thus the circle-line relationship forms the foundation (and the destination) for all symbolic relationships (archetypes) (conscious, unconscious, symbolic behavior). Thus, The Circular Theory (Circular Reality) is a strategic weapon (reasonable way to interpret reality) for intelligent people.

Do you have to be an academic to validate the work?

You have already answered that.

Text on this page from Archetype by Ilexa Yardley. Conservation of the Circle is correctly identified by Ilexa Yardley in 48+ books at Amazon. Pi is the coupling constant responsible for reality. Unsure where to start? Try Dominatrix (the core issue facing mankind)...