The principle of correspondence
Hermetic principles and geometry 3/8
« What is Above is like what is Below ; what is Below is like what is Above. » 
The principle of correspondence emanates from the principle of mentalism, introduced in the previous article. The essence of the principle of mentalism lies in the link it establishes between the Whole and the Universe, between Being and Becoming. The other six principles — including the principle of correspondence — reveal their interactions at the level of the universe only.
To give an image, it’s a bit like if the principle of mentalism was a flower bud that we didn’t know it could « become », until suddenly, it blossomed and expanded. A sort of biological Big Bang, simultaneously giving birth to the principles and laws that form the universe in which we evolve.
The notion of correspondence reveals precisely this simultaneity, this appearance in dependence  of the other six principles. Perhaps this is the reason why Hermes stated it just after the principle of mentalism ?
In any case, the principle of correspondence provides fertile ground for the science of relationships proposed by the physicist Nassim Haramein. Both this principle and this science are based on unity, similarity and harmony.
Before detailing these aspects, and in order to better understand them, I will focus on the manifestation of the correspondence principle from the point of view of geometry, the basis of the unified field theory and the main theme of this series of articles.
« The law of correspondence (…) reaches only that aspect of the Whole which we can call « the aspect of becoming ». Behind this aspect is ‘the aspect of being’, in which all laws are lost in the Law, all principles merge in the Principle ; and the Whole, the Principle and the Being are identical, one and the same. »
The previous article highlighted the simplest and most mysterious geometry of the mentalism principle : the point. This one, symbol of the link between the Whole and the universe, constitutes literally the point of passage between the absolute and relative worlds. Where the Laws and the Principles merge and mix. Where all the observable differences in the universe — up and down, feminine and masculine, cause and effect, positive and negative… — do not exist.
According to Nassim Haramein, in the universe two geometric structures at the base of all others emerge from the point : the cuboctahedron and the tetrahedral star.
The cuboctahedron is formed by 8 tetrahedra pointing in, while the tetrahedral star is formed by 8 tetrahedra pointing out . The interaction of these two geometries — which have and can never exist independently of each other — is the vacuum structure.
The perfect, necessary and sufficient symmetry of this solid illustrates that what is above is like what is below, and vice versa.
If up and down are the same, it is like saying that there is no up or down. However, there are differentiated things in the universe. We will see in the next article how vibration allows this reality to occur.
For now, let’s continue our exploration…
The principle of correspondence, a good principle in all respects
Three notions will help us to make the principle of correspondence more explicit : unity, similarity and harmony.
The Hermeticists teach that in the universe there are three great planes : the physical plane, the mental plane and the spiritual plane. They are each composed of 7 sub-planes, themselves composed of 7 sub-planes. All these planes are divided in appearance, but in reality they form a unity. Otherwise, no correspondence could be established between them.
Unity is materialized by the point, which always remains present in the heart of the geometric structure of vacuum from which it originates. Everything that grows from the point remains in unity. Nothing is ever separated from anything. Everything is One, intertwined and interdependent. Everything comes from unity and remains there forever.
The principle of correspondence applies all the time and everywhere, whether we are aware of it or not. It allows and maintains constant relationships and similar manifestations on the different planes of existence.
Thus, unity and similarity ensure agreement and full correspondence between the different planes. And as they form a whole and work towards the same end, harmony appears.
I propose to discover more concretely how the physics of the unified field reveal the unity, the similarity and the harmony which structure the universe.
The principle of correspondence is expressed in the unit
« If it is true that everything is in The Whole, it is also true that The Whole is in everything. »
The similarity that characterizes the principle of correspondence allows us to deduce that if the whole is in the part, it is also true, at the universe level, that the part is in the whole. In other words, there is as much information in the universe as there is in each point that makes it up. In physics, this is explained by holography.
In order to understand holography, we must think in terms of information . In physics there is a so-called holographic principle, according to which all the information contained in a volume is stored on the surface that contains it . This principle applies to black holes, i.e. to the universe according to the unified field theory. To the universe and also to the smaller and smaller black holes it contains, down to the proton found in the nucleus of atoms .
Holographically speaking — in terms of information — the proton contains the mass of the universe. This means that the holographic mass of all the protons in the universe is contained in one black hole proton. Thus, the information of all protons is contained in each proton.
What does this have to do with the principle of correspondence ? It’s simple : the holographic mass of the proton only makes sense if we consider the proton in relation to all the other protons present in the universe, thus in a unit. Contrary to the standard mass of the proton, which amounts to considering it as separate from the others.
Only the holographic mass of the proton reflects the principle of correspondence, because it makes the proton a black hole among all those which compose the universe. It thus evolves in a unity, a similarity with its peers, and a harmony thanks to…
From the infinitely small to the infinitely large, we observe the same gap between two black holes, namely a proportion of 1.618 (the golden ratio).
A relationship of proportionality also exists between certain opposites. This is all the more interesting to observe as it brings into play the principle of polarity, which we will have the opportunity to develop in a future article.
In particular, there is a proportional relationship between :
- The gravitational force and the electromagnetic force, the only two forces present in the universe. The cuboctahedron and the tetrahedral star produce equal and opposite forces — respectively the gravitational force and the electromagnetic force — which evolve in a feedback dynamic. Within this unit, each force is proportional to the other.
- Entropy (disorder) and self-organization. The entropy of a black hole measures the amount of information it contains. Entropy is proportional to volume and inversely proportional to gravity, which is a ratio between the amount of information contained in the volume of a black hole and the amount of information expressed at its surface. Thus, if it is true that the entropy of the universe increases, it can never increase disproportionately because it is intertwined with gravity, which balances it permanently by creating order . This process is made possible by the fractal nature of the universe.
« The structure of the microcosm is in accord with the structure of the macrocosm. » 
Who says similarity, says fractal. A fractal is a structure, a pattern that repeats itself ad infinitum by an iterative process. This characteristic, called self-similarity, can be stated as follows : an enlargement of a part of the fractal structure invariably makes the whole structure reappear. This is similarity — not similitude — because the level of information always differs, even slightly, from one fractal level to the next. No level is completely similar to another.
A fractal is built by homothety, which means that its structure is reproduced identically at all scales, and ad infinitum. In other words, a fractal tends towards infinity, and yet each of its levels generates a limit. It illustrates the complementarity between the finite and the infinite .
Black holes are distributed from the quantum scale to the cosmological scale according to a fractal law and a holographic model. Nassim Haramein speaks of a holofractographic universe. This is how our universe includes smaller black holes, while being itself included in a larger black hole.
Using the correspondence principle, we can observe the lower and higher fractal levels to solve complex paradoxes. Indeed, the same dynamics are found at all scales : what works for planets, for example, also works for atoms.
Closer to home, another aspect of similarity is also revealed through the law of attraction.
The law of attraction
The law of attraction is the result of the combination of the 7 hermetic principles, each of which explains one facet. The principle of mentalism, as its name indicates, has taught us that it is based on the mind and does not depend on time.
With the principle of correspondence we become aware of the relationship of similarity that underlies the law of attraction. To put it simply, let us say that a thought attracts a similar thought. Similar thoughts can only exist by virtue of the principle of correspondence. It has nothing to do with time, in fact, it is a question of two frequencies, or vibrations, which attract each other, or better, which resonate.
For each frequency emitted, the universe must find a similar frequency. By emitted frequency, we must understand not every thought we emit but our most frequent thoughts  AND with which we feel good. Our most frequent thoughts AND the ones we feel bad with will have an equally great power of attraction… but will not create the same thing ! We need to monitor our thoughts AND how we feel with them. This will ensure that we create what we want instead of what we don’t want. For we cannot stop creating !
The law of attraction establishes a correspondence between what is created mentally and what is manifested . It is a mirror between the invisible (the mental) and the visible (the manifestation), between the inner and the outer. We could say that the manifestation is the proof of what we vibrate.
The law of attraction is thus based on similarity. However, there is a special case of similarity : similitude. And the latter manifests itself when the inner and the outer correspond exactly here and now. This is the case when a synchronicity occurs .
The principle of correspondence is expressed in harmony
As we have seen before, the law of attraction is also based on resonance, a resonance that is itself closely related to harmony. In music, for example, harmony is created by the resonance of sounds — called harmonics — whose frequency is a whole multiple of a fundamental frequency. In other words, harmonics are — as if by chance ! — fractals. Of course, harmony is not limited to music, as the universe is composed of frequencies that resonate with each other to a greater or lesser extent .
In the universe, harmony manifests itself through resonance between the different planes of existence. This is made possible because each principle and law manifests on each plane.
According to the Hermetic philosophy, we evolve on three main planes of existence. In order to understand what we are talking about, we must think in terms of vibrations. Thus, we will understand that these three planes do not exist independently of each other, but within a vibratory continuum.
The different planes of existence
The plane we are the most familiar with is the physical plane. It corresponds to the visible universe, where forces, energy and matter are deployed. We have a direct experience of it, given by the physical and material manifestations that we observe and experience. In a natural way, it is on this plane that we base ourselves to try to understand the universe.
Then comes the mental plane, that of the thought processes. Its link with the physical plane is at the level of the emotions, the meeting point of the mind and the body. The vibrational spectrum of the mental plane is very wide, which is why our thoughts — and the experiences on the physical plane that result from them — can be the best or the worst…
Finally, the third plane is the spiritual plane. It represents our link with the Whole. As we saw earlier, everything is mental in the universe and the universe is contained in the soul of the Whole. We are therefore evolving simultaneously in the universe and in the Whole. When our thoughts are of great purity, they flirt with the highest vibrations of creation : they emanate from our spiritual mental.
As mentioned earlier, these three great planes are each composed of 7 lower planes, themselves composed of 7 sub-planes. However, these divisions remain more or less artificial due to the vibrational continuum in which they exist. Thus, for example, there is no clear division between the higher phenomena of the physical plane and the lower phenomena of the mental plane. Nor is there a clear division between the higher phenomena of the mental plane and the lower phenomena of the spiritual plane.
Continuum and limits
Finally, I would like to mention something rather intriguing. If we consider the 3 large planes each composed of 7 sub-planes, each composed of 7 sub-planes, we arrive at a total number of planes equivalent to 147 (7 x 7 x 3). This number is very close to the number of visible faces on the vacuum geometry, namely 144.
In contrast, the vacuum structure has a finite number of facets, which are however only vibration. The unified field theory states that the finite contains the infinite. We could say that matter, finite, is made of vibrations, which are in an infinite continuum. They are constantly evolving, changing degrees on the scale of vibrations.
So, just as the 144 faces of the vacuum structure are composed of vibrations that tend to infinity, so are the 147 sub-planes of the universe. Since the separations between the degrees are arbitrary — some of them can sometimes merge with others — the counting of the sub-planes cannot be very precise. It would then be rather a matter of multiplying infinite numbers close to 7, which would bring us to a result not close to 147 but close to 144.
And thus unify the two approaches.
Notes and references
 Unless otherwise indicated, all quotes are from the Kybalion.
 To better understand the notion of appearance in dependence, you can consult the article Quantum physics and reality.
 We can see there the principle of gender, we will come back to it in the dedicated article. You can also consult the interpretation of these geometries that I had given in the article Sacred Connection.
 For a detailed explanation, see the article on the holographic universe.
 Up to a quarter of this area.
 The holographic mass takes into account the energy of the vacuum contained by the proton : 1055 g. This is equivalent to the mass of the universe. Since this mass establishes the fact that the universe is a black hole, it necessarily establishes the fact that the proton is also one. For more information, see the article on the Schwarzschild proton.
 For a more detailed explanation, see the article on gravity, entropy and self-organization.
 The Emerald Table — Apollonius of Tyana : The Book of the Secret of Creation and the Art of Nature or Book of Balinus the Wise on Causes.
 See also the article devoted to fractals.
 This is related to the fact that if you feed a system enough of a certain intention, it cannot help but manifest it. You can consult the series of articles devoted to the butterfly effect.
 We are talking about similarity because what we create does not depend only on us : we co-create it. For more information, see the article on quantum consciousness.
 See the series of articles devoted to synchronicities.
 To learn more, you can consult the section devoted to resonance.