Yin-Yang: The Geometric Equivalent of The Golden Ratio

I have discovered that Yin-Yang and Golden Ratio are different representations of one and the same metaphysical principle. The metaphysical principle of our interest is Unity Within Duality which states the complementary character of conflicting tendencies. This is of course similar to the Hegelian trinity in his interpretation of history: Thesis-Antithesis-Synthesis.

After giving a short account of Yin-Yang and Golden Ratio I proceed to prove their equivalence. Since after a year of research I have found no one else who has discovered this equivalence I stick a copyright notice at the end of the article just for the publication purposes in case the finding turns out to be of significance.

Yin-Yang and Golden Ratio are the two representations of the principle that maximally opposing tendencies, or aspects, complement one another to form a unity: The former represents it geometrically and the latter represents it numerically.

Yin-Yang in Chinese philosophy is the geometrical expression of the following concept: The apparently opposing and contradictory tendencies complement one another; being interconnected they add up to form a unity. In the Yin-Yang symbol a whole circle is divided into two maximally opposing aspects. The two aspects enjoy maximal opposition both in color and orientation: The color of one cut is the negation of the color of the other; and the orientation of one is the inverse of the orientation of the other.

YinYang

Notice that the two opposing sides have the same shape; they are the opposites of one another only in the attributes color and orientation. In other words, one side is the negation and inversion of the other side. But this cannot be done with just any shape; not every shape can be inverted and then added to itself to form a perfect circle which represents unity.

Golden Ratio is a number in mathematics; it has the numerical value of 1.61803398875…. When the ratio of two quantities is this number we say that they are in golden ratio. This number has huge significance in mathematics because it is the corner stone of spiral geometry which is observed everywhere in nature. It is also the limit of the Fibonacci Sequence. In fact when the ratio of two lengths is the golden ratio they have an inherent tendency to make up harmonious and beautiful structures.

golden-ratio

It is time to see how Yin-Yang and Golden Ratio are equivalent to one another, both being the representations of one principle.

We saw that Yin-Yang represents the idea that maximally opposing aspects add up to form a unity; each aspect is both the negation and the inversion of the other aspect. Numerically speaking, one being the inverse of the negative of the other. Let us try to represent this idea numerically, using number instead of shape: We need a number that when maximally opposed to itself, namely first negated and then inverted, can be added to itself to form a unity which is represented by number 1.

We don’t yet know if such number exists, but it will soon be proved that it actually does. First remember that by negation of a number of course we mean its negative, -2 being the negative of 2. By inversion we mean the inverse of the number, 1/2 being the inverse of 2; thus, the inverse of the negative of 2 is -1/2; but notice that when we add 2 and -1/2 we get 3/2 and not 1. We are after a number that gives us 1.

Let us call our desired number x and try to write down the concept behind Yin-Yang in the language of numbers and see if such number exists: We have x as our number; negate it to get -x; invert the negation to get -1/x. To express Yin-Yang is to add up these two numbers and have them equal 1. Thus, the algebraic equivalent of Yin-Yang would be the equation [x+(-1/x)]=1 which can be simplified as the following:

X – (1/X) = 1

This already looks like Yin-Yang :). For those with mathematics background this equation should blow their minds; it is none but the infamous equation that is the very definition of the Golden Ratio: Golden Ratio is the exact solution, and the only solution, of this quadratic equation. You will soon see that the second solution is just the negative of the inverse of the Golden Ratio, its maximally opposing complement which we call the Golden Complement. Let’s call this equation, the algebraic form of Yin-Yang, the Golden Equation since its solutions are the Golden Ratio and the Golden Complement; thus, this equation has two solutions in real numbers:

X – 1/X = 1               The Golden Equation (Equivalent of Yin-Yang in Algebra)

First Solution:        X1 = 1.61803398875…              The Golden Ratio       

Second Solution:   X2 = -0.61803398875…            The Golden Complement

X1 + X2 = 1             The Golden Equation in terms of its two complementary solutions

The first solution is the Golden Ratio and the second solution is interestingly the inverse of the negative of the first solution, namely the Golden Complement. See that the two solutions corresponding to the two complementary aspects of Yin-Yang add up to unity, hence completing the Yin-Yang equivalent in algebra. Notice that the Golden Complement has the exact same decimals as the Golden Ratio itself which is the reason why the decimals cancel out in the Golden Equation, hence leading to unity.

We saw that there actually exists a unique number whose inverse of its negation can be added to it to become unity, the number 1, hence expressing the Yin-Yang principle in the realm of numbers, and this unique number is none but the Golden Ratio, the solution of the Golden Equation. Thus one side of Yin-Yang corresponds to the Golden Ratio and the other side corresponds to its maximally opposing counterpart, the negative of its inverse which is the Golden Complement, and the two adding up to unity by definition. Only the Golden Ratio has this property, and one can see as we showed above that the principle behind Yin-Yang, leading to the Golden Equation in algebra, is the very definition of the Golden Ratio.


Digression:

{Notice that the two solutions of the Golden Equation, which correspond to the two maximally opposing aspects of Yin-Yang, have these two interesting properties:

 X1 + X2 = 1                     X1 × X2 = -1

If these two solutions, the Golden Ratio and the Golden Complement, are considered to be the diagonal elements, or eigenvalues, of a 2×2 matrix called the Golden Matrix G, then G is an orthogonal matrix with determinant -1 and trace 1, hence:

Det(G) + Tr(G) = 0

Which is only an interesting observation besides our main point.}

End of Digression


Therefore, the principle that the maximally opposing tendencies complement one another and form a unity is represented geometrically as Yin-Yang and algebraically as the Golden Equation X-1/X=1 whose two solutions, corresponding to the two aspects in Yin-Yang, are the Golden Ratio and the Golden Complement. We saw that of all numbers one and only one, the Golden Ratio, has this property. More precisely, the Golden Equation X-1/X=1 is the algebraic equivalent of Yin-Yang from which the Golden Ratio is extracted.

Yin-Yang is the Golden Equation in geometry. Golden Equation is Yin-Yang in algebra.

This equivalence between Yin-Yang and Golden Equation which I discovered in the fall of 2013 has blown my mind to this day. Who could guess that the Golden Ratio is Yin-Yang in numbers while Yin-Yang is the Golden Ratio in geometry! Fascinating.

*[Note for the mathematician: In constructing the Golden Equation, the algebraic equivalent of Yin-Yang, I assumed a bijection from plane shapes to real numbers, hence defining the equation over R, the field of real numbers. Naturally a bijection from the inverse and the negative of a shape would fall onto the inverse and negative of numbers. Thus, in constructing the bijection from Yin-Yang to real numbers the only proper way of translating maximal opposition, namely both negation and inversion, would be to use both the additive inverse and the multiplicative inverse of a number, the only possible ways of defining opposites among real numbers, hence the field properties of the Commutative Division Ring R. In other words, the only way to translate the relation between the two opposing aspects of Yin-Yang is to relate a real number to the multiplicative inverse of its additive inverse, hence mapping the two different operations present in Yin-Yang, namely the spatial inversion and color-negation. It is seen that the only number whose multiplicative inverse of its additive inverse can be added to itself to become unity is the Golden Ratio.]

Copyright © Tomaj Javidtash and NOEMAYA, 12/30/2014

Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Tomaj Javidtash and NOEMAYA with appropriate and specific direction to the original content.

Interview with Tomaj Javidtash on Transcendental Experience & Quantum Mechanics

This Is Nonduality

Edited by Jerry Katz

Tomaj Javidtash is the author of Non-Dual Perspectives on Quantum Physics: A Layman’s Guide, which you may learn more about at his website www.tomajjavidtash.com

Tomaj is an Iranian-American author and physicist currently pursuing his graduate studies in theoretical physics at the University of Maryland. His area of research is foundational issues of Quantum Physics. His undergraduate major was physics along which he also obtained a minor in mathematics.

His writings are motivated by his discovery of shared truths underlying three different disciplines of Quantum Physics, Advaita Vedanta Metaphysics, and Husserl’s Transcendental Phenomenology.

Transcendental Phenomenology is a modern embodiment of Advaita Vedanta metaphysics; and Quantum Physics is an experimental contribution to their truths advocating the primacy of consciousness in the nature of reality which is essentially non-dual.

Favorite Books:
Vasistha Yoga
Physics and Philosophy by Werner Heisenberg
Cartesian Meditations by Edmund Husserl

Tracks:

0:00 – 5:13…

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The Living, Breathing Present

There is only a living, breathing now; everything happens in this narrow opening; it has to be there for everything else to be at all.

Now is a peculiarity of consciousness. In this infinitely small place the infinitely large cosmos is experienced. We are at once the site and the occasion in which the infinitely large fits into the infinitely small: We are black holes scattered in the void.

In and through the now we experience ourselves as human beings inside a world, but this world itself, including our humanity, is something experienced inside our consciousness; we experience the world as something that contains us, but this experience is itself something contained in our consciousness. To be more precise: The world that contains consciousness is itself contained in consciousness! How strange is that?! Yet few of us ponder this mystery. Ponder my friend, for therein lies the secret of all secrets.

There is a breathing now in the depths of void; its breath makes the tale of Being. In its exhale we are thrown into existence; in its inhale we are sucked into oblivion.

This living, breathing, eternal now daydreams both me and the world.

There dwells in the void only a singularity, a whirling dervish, whose dance makes Maya: We are all that.

My friend, existence is a misunderstanding, world a hearsay, and I am just a word.

Yet there is concealed behind this I the I of all Is: We are all the many faces of that one whirling dervish whose breath is the eternal now and whose dance is the ephemeral Maya the Noema.

The Eternal Now

Now

Now is a whirling dervish,

one hand sweeps the future into the past, one hand projects the past into the future.

The whirling gives the illusion of time and history, of existence and cosmos; but there is no time or history, no existence, no cosmos; there is no past, no future: There is only the eternal Now, the whirling dervish, the living present, the sole dweller of the void.

Cosmos is its whirl, truth is its face: The bystander sees only the whirl, the cosmos. One who whirls with the dervish sees the face, the truth.

Now

Everything is made of Now.

Everything is Now in disguise: Past is a falling Now, future a rising Now; falling and rising, too, are the Now.

I am the Now; cosmos is the Now. There is only Now, the whole Now, and nothing but the Now.

Now is a whirling dervish.

Now 

The Now

Now

Now is a whirling dervish,

one hand sweeps the future into the past, one hand projects the past into the future.

The whirling gives the illusion of time and history, of existence and cosmos; but there is no time or history, no existence, no cosmos; there is no past, no future: There is only the eternal Now, the whirling dervish, the living present, the sole dweller of the void.

Cosmos is its whirl, truth is its face: The bystander sees only the whirl, the cosmos. One who whirls with the dervish sees the face, the truth.

Now

Everything is made of Now.

Everything is Now in disguise: Past is a falling Now, future a rising Now; falling and rising, too, are the Now.

I am the Now; cosmos is the Now. There is only Now, the whole Now, and nothing but the Now.

Now is a whirling dervish.

Now 

Quantum Strangeness & Becoming Oneself

Our classical world is composed of mutually exclusive alternatives: Everything is either something or something else; it is a this or a that, though we may be unaware of these identities due to ignorance. A color is always either red or not red; two socks in a closed box are either a pair or not a pair whether we look inside or not. There is never a middle case in the classical world.

Quantum world, however, is quite different. Besides the two/many mutually exclusive alternatives everything in between too exists. A color is at once all colors until we pick one color by looking at it! A particle has no particular place until we force it to pick a place by measuring its place!

It turns out that mutually exclusive alternatives, our classical world, is only a small and often filtered portion of the underlying reality. Which reality we pick is determined by which reality we are inclined to pick, namely the reality that we desire.

The mutually exclusive alternatives of the classical world constitute a space of all possibilities existing at once, that is, a state of pure potentiality.

The logical principle that collapses in the quantum world is the principle of identity which says “Everything is itself.” Not anymore: Everything is both itself and not-itself until we make it into something that it is. In the quantum realm this new peculiarity is translated into the indistinguishability of identical particles. Quantum particles don’t have a history any more; they don’t have a memory or identity. They can at once choose to turn out at the other corner of the universe without being subject to Einstein’s principles of relativity. In fact, entanglement is a consequence of particles lacking fixed identities: No two electrons can be distinguished in principle.

Identity is a construct that we ourselves carry on our shoulders; it has no substantial reality; it is just like a name we are attached to. For us to be our ideal person we only need to be it; that is it. Actions don’t make people; it is people who make actions.

Data and census don’t determine people’s behavior; it is people who determine data and census.

You should not think twice about what you want to be, its chances, whether it is possible or not, or what the data or others say. You determine data and others by what and who you choose to be. Then choose to be your own idol and hero.

You are what you consider yourself to be.

The Reign of Quantity

The body of human knowledge, including self-knowledge and self-understanding, is dominated by quantity. We know and value things based on their quantitative content. This manner of understanding experience is so rooted in the subject that one can even define human as that which sees only quantity.

I weight 140, age 30, earn 11111, spend 1111, have # of houses and cars, have slept with this # of objects, have this much or that much in my resume, walk # of steps and burn # of calories, have a 1000 friends and get a 1001 likes everyday, have this # of years of experience, have an IQ of sqrt(2), obtained a PDH which is really the number of years of solitary confinement in a subject chosen to be superior to others by # of people who hijacked my commonsense a # of years ago, etc.

At the end of the day, we are the average of the number of things we have and the number of things we don’t have: We are just so average insofar as we are dwellers under the reign of quantity.

For us it is all about having it or not having it; no one is anymore into just seeing.

To define human more precisely: Human is that which sees only quantity and likes only to have.

The mystic, on the other hand, who has transcended its humanity is that which has only quality and likes only to see.

Is it possible to arrive at a self-perception, a worldview, an understanding in general that is not ruled by quantity?!

Quantity defines us, yet quantity itself is something defined and determined by ourselves.

Or as is always the case with our species: We determine the very things that determine us.