The principle of polarity
Hermetic principles and geometry 5/8
« Everything is double ; everything has poles ; everything has two extremes
similar and dissimilar which have the same meaning. » 
The principle of polarity finds its place halfway between the first and the seventh and last principle bequeathed by Hermes. Interdependence obliges, to explain the principle of polarity, I will call upon the previous principles, so there is still time to familiarize yourself with them if you have not already done so ! These are the principle of mentalism, the principle of correspondence and the principle of vibration. Are you familiar with them ? So here is a first approach to the principle of polarity.
Let us observe the caduceus of Hermes. The two snakes move away at equal distance, several times, on either side of the central strip of laurel. Like positive and negative numbers, similar in absolute value and dissimilar by their sign, which would be distributed around the central 0, thus representing the polarity.
Now imagine a coin : we cannot conceive of the heads side without the presence of the tails side. The coin represents one thing and its opposite, and yet it is one and the same thing ! Another example is the magnet which has two poles. Two magnets, attracting each other by their opposite poles, literally show that « extremes touch ».
Before looking at the physical dynamics that allow us to describe and reconcile the paradoxes of the principle of polarity — thanks in particular to the theory of Nassim Haramein — we will see that the principle of polarity applies above all to thoughts since the universe is mental.
The movement of thought is based on the principle of polarity
« (…) Choice is the essence of the movement of thought. » 
The principle of polarity refers to the question of choice . Indeed, polarity means choosing between different vibrations, which may be — or at least appear to be — opposite. The movement from one vibration to another is ensured by thought, a thought always attracting a thought that is vibratory similar to it, until it temporarily stops on a choice.
Then that thought is suspended. Temporarily, I said, because thought does not like to stop ! But at this stage, it has reached such a vibration that it is beyond duality. This passage is usually so fleeting that we do not perceive it. Nevertheless, it is one of stillness , in which there can be no choice. Why is this so ? Because there is no movement that can differentiate things in stillness, and allow for a choice.
Moral : if in the world of thoughts — in the relative world of polarity - we are spoilt for choice, in the absolute world of the Spirit, it is not so..
« All truths are but half-truths ; all paradoxes can be reconciled. »
The universe is mental does not mean that it is unreal. Nor does it mean that it is real. To consider the universe as unreal or real is to adopt the point of view of a half-truth. The principle of polarity teaches us that everything has to be considered from the absolute and relative points of view. The absolute and the relative are indeed the two poles of truth for the Hermetists, the absolute being « things as the Spirit of God knows them », and the relative « things as the highest reason of man understands them ». The expression of this wisdom being of course itself relative to the evolution of each person.
From the absolute point of view of the Whole, only the Whole is real, the universe is an illusion. Every illusion unfolds in the temporal sphere : doesn’t the universe have a beginning and an end ? And behind temporality lies vibration, as we saw in the article on the principle of vibration. Thus, the beginning and the end are relative. Indeed, on the scale of vibration, where does the beginning start, where does the end stop ? Every end is a new beginning.
From our point of view — human, mortal and relative — the universe is real, true, and must be considered as such. It is subject to laws inherent in its existence. Laws which, though mental in nature, are nonetheless implacable, compelling us to act as if constantly changing things were real and substantial. This is the divine paradox.
This paradox is expressed through the two « opposite » poles (absolute and relative) of the same thing, respectively : the Law and the laws, the Principle and the principles, the Infinite Spirit and the finite minds.
The principle of polarity or the reconciliation of paradoxes
The universe being subject to the law of paradox… there are many paradoxes in the universe ! Nassim Haramein’s theory of the connected universe is remarkable in that it reconciles many of them. I was inspired by these « paradoxes that can be reconciled » for the navigation of this blog. Here is a brief overview.
Let’s start with fractal geometry — linked to the correspondence principle — which reconciles :
Finite and infinite
A fractal is built by homothety : its structure is reproduced identically at all scales ad infinitum. In other words, a fractal tends towards infinity, and yet each of its levels generates a limit, hence the notion of complementarity between the finite and the infinite.
Determinism and indeterminism
Nassim Haramein explains that :
« A fractal equation is a repetition of an equation that is deterministic, but when you repeat it it converts to an open backfeed to infinity so that you have completely nonlinear, nondeterministic behavior. So from a very deterministic equation you get a complex nonlinear result, and you justify both sides of the universe, the deterministic part and the non-deterministic part. » 
A fractal universe ultimately implies that determinism and indeterminism coexist, so that everything is always determining itself. The feedback loop is like a dance between determinism and indeterminism.
Order and chaos
Not only do indeterminism and determinism coexist, but they are necessary for the progress of the universe. Indeed, they lead to the formation in the universe of structures that are constantly on the border between order and chaos : this is how they both do not dissolve and evolve. These structures, called dissipative structures, are open systems. In connection with their environment, they use the permanent internal and external fluctuations to which they are subjected to spontaneously organize their structure and develop. They have been highlighted by the chemist and physicist Ilya Prigogine.
Nassim Haramein also made the most complex and restrictive choice, that of considering systems as interdependent (and not isolated). In the end, he came up with one and only one theory of physics, simpler, more efficient and more objective.
And many other paradoxes…
Like fractal geometry, the vibrational continuum - linked to the principle of vibration — allows us to reconcile paradoxes :
Now let’s look at what connects, from the point of view of physics, the opposites. Specifically, what does the theory of the connected universe teach us ?
The principle of polarity from the point of view of physics
In the universe, everything is rotating. Space-time rotates at the finest level — at the level of the Planck field — and in doing so creates polarity, which propagates to the infinitely large .
But there is no polarity without geometry. We saw in the article on the correspondence principle that the geometry of the vacuum — the basis of all others — combines two geometries : that of the cuboctahedron and that of the tetrahedral star.
The tetrahedral star is composed of two inverted tetrahedrons. On the representation below, in two dimensions, we observe 12 Fibonacci spirals. They all start from the same central point — there is no rotation without a reference point — and meet at the 12 nodal points of the star, 6 of which delimit a central hexagon (or cuboctahedron in 3D).
Let’s look at the Fibonacci spiral. Based on the golden ratio, it is a self-similar fractal.
« [The golden ratio ] φ is the ratio of the length b to the width a of a rectangle R such that, if the largest square it contains is removed from R, the remaining rectangle R′, of length a and width b‑a, is similar to the original rectangle (the ratio of length to width is the same as for R). » 
We can also say it in another way : (a + b) / a = a / b = 1.618 = φ
To draw the Fibonacci spiral, simply repeat the Rectangle / Square construction — which can be done ad infinitum. The spiral will then appear in the successive squares.
The golden ratio is the ratio that the universe uses to multiply and divide itself at all scales. Nassim Haramein talks about highly organized systems that generate « peculiar » — actually fractal — structures throughout nature.
The geometric dynamics of the universe
But let’s go back to the 12 Fibonacci spirals that form the tetrahedral star. We notice that half of these spirals are oriented in one direction, and the other half in the other direction. This double orientation creates a field composed of two inverted polarities, and reveals the geometric dynamics of the universe.
To better understand, we can represent things in 3 dimensions, i.e. using the geometry of the double torus. The basic structure of the universe, the double torus allows information to flow. Not in a straight line towards the center, but by winding in the opposite direction from the poles towards the center. This double movement can also be seen as a double rotation, where the two toruses turn in opposite directions. From this double motion, the gravitational and electromagnetic forces  of the universe are born.
The Chinese have represented this dynamic by the symbol of Yin and Yang, called Taijitu, which is none other than the double torus seen from above. Note that Yin and Yang can each divide into Yin and Yang sub-elements, ad infinitum, thus illustrating a fractal process.
The Yin and Yang principles represent the incessant transformations of all aspects of life and the universe. Our western vision presents them as opposites, although they are in fact complementary. They evolve in a movement that invariably produces a transition from one to the other, thus offering a continuous experience of each principle.
This passage is only the result of a mutual limitation since Yin manifests itself as soon as Yang reaches its maximum, and vice versa. One can only express itself in relation to the other. This is the reason why each principle is always present — and represented as such — in its « opposite », we will come back to this.
In Nassim Haramein’s theory, there is a direct analogy between the symbol of Yin and Yang and the dynamics of the universe. There are 64 possible combinations of Yin and Yang which, for the physicist, correspond to the 64 tetrahedrons forming the structure of the vacuum, from which everything emerges and to which everything returns .
Each combination is a six-lined symbol called a hexagram. In 3 dimensions, the only geometry that can be generated with six lines is a tetrahedron . Because of the polarity of the universe, a tetrahedron cannot exist without its opposite. But unlike the solid lines of the first tetrahedron, the lines of the second tetrahedron will have to be segmented so that the lines of the two tetrahedrons can intersect. This is the reason why, according to Nassim Haramein, the oldest Chinese text, the I Ching , is made up of solid lines and segmented lines.
A difference in degree
« Opposite poles have identical nature but different degrees. »
Taijitu allows us to visualize similar (of the same vibratory nature) and dissimilar (of different degrees) poles, generated by the principle of vibration. Thus, for example, hot and cold are apparently opposite but in reality one and the same thing ; they are distinguished simply by a difference in degrees.
For example, there is no such thing as absolute heat or absolute cold. The phenomena of « hot » and « cold » exist only in relation to each other. Hermeticists teach that « one degree is always hotter or colder than another, so it can be called hot or cold without departing from the truth. »
Note that the dominant activity is given to the positive (hot) pole, which is verified by the law of entropy : the heat transfer always goes from the hotter system to the colder one.
Principle of polarity, maturation and mutation
The following illustration offers a vision of the four seasons  in accordance with Yin and Yang : although summer and winter are on opposite sides of the world, there is only a difference of degrees between the two (in the sense of temperature and vibration). Taijitu also represents the fact that when it is summer in one hemisphere, it is winter in the other. Each principle can therefore never be expressed in absolute terms, it is always relative to its « opposite ».
The Yin/Yang dynamics is based on the tendency of each pole to ultimately transform into its « opposite ». The passage from one to the other is first of all done by a slow maturation, ineluctably followed by a mutation. In the case of the seasons, we know when the mutation will take place : at the solstices.
However, in a more general way, one may not be aware of the maturation phase, or more precisely of its state of progress. So when the mutation appears, it may seem to come suddenly, if not out of nowhere. If we are sure that an energy will inevitably transform into its complement, the difficulty is to know when this mutation will take place .
The principle of polarity and the law of attraction
« To destroy a bad period of vibration, put into activity the Principle of Polarity and concentrate your thought on the opposite pole of the one you want to annihilate. Kill the undesirable by changing its Polarity. »
The principle of polarity, like the other six, is above all mental, as we have seen. Perhaps the most important thing it teaches us is the practical and concrete application we can make of it through the Art of Polarization. To do this, we first need to realize that our daily transformation is already present and is only a question of moving the cursor : it is accessible by polarizing our consciousness and our vibrations differently.
And we will see with the next principle, the principle of rhythm, that everything is obviously not so simple !
Notes and references
 Unless otherwise indicated, all quotations are from the Kybalion.
 BOHM David and KRISHNAMURTI Jiddu, Les limites de la pensée [The Limits of Thought], Paris : Le livre de poche, 2006, p.115
 I distinguish choice from free-will, see the article Does free-will exist ?
 See the section devoted in the article on the principle of vibration.
 HARAMEIN Nassim, Nassim Haramein at Rogue Valley Metaphysical Library (1)
 See the article on the principle of vibration for more explanation
 See the article on space-time for more information
 BUZZI Jérôme (2013, May 29), Nombre d’or, fractales et symétries [Golden number, fractals and symmetries], in CNRS
 This is in fact the movement of black holes, present at all scales in the universe. See the section devoted to this in the article The fractal and holographic universe.
 See the explanation in pictures
 A tetrahedron is a pyramid with a triangular base.
 The I Ching is a book of philosophy and cosmology that can also be used for divination. It is based on 8 trigrams and 64 hexagrams, consisting of 3 and 6 broken or continuous lines respectively.
 Note that for the Chinese there are actually 5 seasons, the 5th season representing a mini season intercalated before each of the 4 others.
 See the section devoted to the butterfly effect in the last article.