The Snefru Code – Part 3

THE THEORY OF RELATIVITY
IN SACRED ANCIENT EGYPTIAN ART ARCHITECTURE
AND IN THE PLATO’S TIMAEUS

With an outline of the theory of the unified fields probably codified in the Grand Pyramid and an appendix about its possible numerologic connections with the Maya calendar system Haab’-Tzolkin

To Ermanno, my uncle, for being my first teacher of philosophy.

Donc tu te dégages
Des humains suffrages,
Des communs élans !
Tu voles selon…
A. Rimbaud

First Part: THE THEORY OF RELATIVITY IN SACRED ANCIENT EGYPTIAN FIGURATIVE ART AND ARCHITECTURE

1. In the two previous articles (published in The Snefru Code part 1 and part 2) from the geometrical analysis of the Snefru relief of Sinai and other well known works of different ages and dynasties, it seemed to come out in a rather clear way that a common geometrical code was at the basis of the whole of the sacred iconography and architecture in the Ancient Egyptian culture across the millennia. The geometrical phenomenon that was first detected, was the one that we defined as a system of geometrical “meaningful intersections” between the Snefru relief and the IV Dynasty Pyramids. A system that seemed to allude to a hidden geometrical structure from which all these works were someway derived.
On the basis of other geometrical analysis, the following step in the research, was to hypothesize that this code should be surely based on the golden ratio, even though in that moment we could not do precise suppositions about the actual method with which this “golden space” was generated and used. But another step in the research was sufficient to get to the point ,and formulate a concrete and maybe credible hypothesis about the solution of this problem. A solution that resulted in a way totally unexpected and almost incredible – but we hope that at the end of this exposition it will seem a little less “impossible” as we could hypothesize at the beginning of these researches. High technology, which use is evident in the building of the Big Pyramid and other Ancient Egyptian monuments, presuppose high scientific and mathematical knowledge too, and in this sense what we are going to expose in this article seems to be in logical continuity with what we already know of these masterpieces of sacred art and architecture.

2. The computer analysis of a relief that became famous with the name of “Djoser running” – a work in which we have already recognized very meaningful examples of golden ratio space relations between its constituent parts – gave us a rather interesting result, as we discovered that the relation between its wideness and highness is more or less equal to the golden number (1,617 calculated on the image, as compared to the 1,618 of the golden number). So it was natural to observe that in this kind of space – a space that, whatever its real measures could be, always keeps some geometrical qualities connected with the golden number (and so with the golden ratio) – is fit to the purpose to be split in geometrical parts that conserve these qualities.
Going on more or less randomly, by trials and errors method, we believed to identify in the Pharaoh’s eye one characteristic point, and from there we have derived a system of logarithmic spirals of the same form, with the same method in which they arise in the sunflower inflorescence. Statistic researches tell us that in nature, in the common case, we can find 34 logarithmic spirals wrapping in a direction and 55 in the opposite. But also in the case of bigger sunflowers, we always find a couple of Fibonacci’ numbers, as 34 and 55 are: and the Fibonacci sequence is, as it’s well known, at the basis of the logarithmic spirals that we can find into the sunflowers. Particularly, we often see that in bigger sunflowers going from the center to the more external side of the inflorescence, the relation between the spirals does not remain constant, getting from a whatever couple of Fibonacci’ number to the next (for instance, if the first relation was 55/34, the second will be 89/55). We can see two typical schemes of the sunflower inflorescence in the images that follow

 

[1]. See particularly the article “The Ancient Egyptian reliefs and “the Snefru code”: first historical and symbolical considerations and new geometrical discoveries” and the gallery connected with the article.

 

Now, if we try to project a scheme like that on the image of that relief from which we started our analysis – “Djoser running” – the result appears really overwhelming, as the internal space and the drawing of the relief seems to find a system of characteristic points just like it happens in the case of the sunflower inflorescence that, as we said, we made arise from the Pharaoh’ eye.

Already in this first example we see how the number of “meaningful intersections” between the spirals and the drawing of the relief is rather remarkable, and that all these points have the fundamental characteristic of staying connected to each other in a geometrical relation determined by the golden number, even if in a very complicated way (practically, the co-ordinates of each point of this strange spiral-formed space are determined by a system of logarithmic spirals).

3. It’s possible, and intuitively it seems rather obvious, that to obtain a space in which the points are in a sufficient number to be sufficiently close and equally distributed, so that it would be possible to trace complex figurative and hieroglyphic images, we have to hypothesize that this kind of subdivision of the space – that from our point of view appears very complicated and uncomfortable – not to say almost completely absurd – must be generated starting by a multiplicity of geometrical poles, even though it is not still clear how we can determine their exact number and positions. But anyway, to start from a single center and to pass from a Fibonacci’ couple of number to the successive one, as it happens in the case of the inflorescence of a big sunflower, could be insufficient to create the drawing of a relief as complicated as “Djoser running” is.
On the contrary, it’s probable that the expansion poles of these dense logarithmic spirals vortexes are distributed in such a way to assure that in the whole space of the relief we can find an equal distribution of equally close points. Points which co-ordinates always result from the crossing of at least two spirals (but, as we can see in the above images, already at that level of complication some points are determined (and so determinable) from the crossing of three spirals. It’s easy to imagine that going on with the subdivision – and so with the multiplying of the poles – the number of spirals crossing over each point could grow in a dizzy way). Actually, if we move our “sunflower” from the Pharaoh’ eye to other points of the relief, more or less randomly chosen, we find that the system of “meaningful intersections” magically rises up again .

[2]. This is the mathematical name of this spiral, that is maybe best known with the name of “Fibonacci’ spiral”.

Now, if we imagine to use a space subdivided by this method to trace a whatever drawing joining the points determined by the crossing of two spirals (or more), it comes out as a logical or even obvious consequence, that between these points and these lines there must be a no matter how complex form of golden ratio relation – in the same way as we can find it inside the sunflower inflorescence.

4. With this hypothesis it seems possible to explain in a somewhat “simple” and satisfactory way all that kind of geometrical phenomenon – rather incredible at first sight – that we have seen in the two precedent articles and particularly into their photographic galleries. The Pyramids codified into the reliefs, the reliefs in which we can always find “meaningful intersections” even overlapping two works carried out at many centuries of distance (and so with different styles, as you can see comparing the Djoser and the Ramses relief), or even overlapping the drawing of the same relief with itself. And it’s useful also to remember that this kind of geometrical phenomenon, surprising and almost unthinkable in so ancient works, went on also in the case where we have changed the dimensions of the overlapped images.
For instance, we have already seen in the first article (The Snefru Code part. 1) that the Red Pyramid keeps congruent with geometrically meaningful parts of the Snefru relief of Sinai also in the case that we project it in bigger or smaller scales – and the same happens with the Big Pyramid, etc. We can seen new examples of these phenomena in the below imagines

 

 

But if our hypothesis is true, all these geometrical phenomena would be explained by a fundamental characteristic of the logarithmic spiral, that is precisely to preserve in a constant way its accretion form, so that the proportions between the adjacent spires keep on growing identical to the infinitely big as lowering to the infinitely small. So, it results rather clear that all the figures constructed on the basis of co-ordinates of the kind that we have seen above, should always remain somehow proportional and congruent (even in a very, very complicated way), as we have traced them joining points determined and connected to each other by means of a system of logarithmic spirals congruent and proportional too.
But it’s essential to remember that the phenomenon that we analyzed in the two previous articles concerned both the Pyramids and the reliefs, as two big architectonic spaces – like Giza and Dahshur – and a “rough” megalithic circle as Nabta Playa. The logic consequence is that the space of all these works, even belonging to different ages and styles and having very different forms and functions, was generated in the same way, as for example in an apparently similar way to the one that we can find in nature in the sunflower inflorescence. And we can give a basis to this hypothesis right now, looking at the images that follow, images in which we can find out that this rather particular way to determine the co-ordinates of the points forming the lines of the drawings was used to make reliefs belonging to very distant eras from which in that “Djoser running” – the work we started our analysis – was sculpted (this relief presumably belongs to the II Dynasty (2700-2800 BC)). We are talking about the Snefru relief of the Sinai, “Ramses with Sekhmet”, and “Seti I worshipping Osiris, Isis and Horus”

 

From what we can notice by means of these images – even if not being in possess of an exact derivation formula – we are anyway driven by the visual-geometrical evidence to hypothesize that in the Ancient Egypt culture at the basis of all the sacred art and architecture we can’t find an aesthetic intuition, in the sense in which we are inclined to interpret this words in the modernity, but instead a geometrical-mathematical system, that probably had astronomical origins.
Actually, it seems very evident and clear that the figures that we have seen above can’t be a copy of reality, made rough guess. On the contrary, they seem really to have been obtained joining points determined by means of a system constituted by vortexes of logarithmic spirals, so that what is decisive to determine their forms and their proportions it’s not the artist look, but the mathematical function from which they are somehow generated. And this assertion results at the same time more credible and incredible when we become aware that the diagram projected on the Ramses relief is not that one of the sunflower inflorescence, but instead a bi-dimensional diagram of space-time realized by Vincenzo Fappalà, published on ASTRONOMIA.com , that we can see in the following image

 

Looking at the Ramses relief we can notice that this diagram seems at first sight capable to reproduce in a better way the geometrical system with which the Ancient Egyptian reliefs were derived. And if, for instance, we overlap it also on the Snefru relief, it seems to work in a more effective way then the “simple” sunflower diagram. And after what we have seen in the previous articles neither we can really be astonished that it works very well if applied also to the Big Pyramid and to other Ancient Egyptians reliefs, included obviously that “Djoser Running” that we have just analyzed in relation with the diagram of the sunflower inflorescence.

[3]. We could found our hypothesis also in the base of two other astronomical discoveries, that we made not observing the sky, but instead reading them into the Ancient Egyptian reliefs, but as this reading is rather complicate to explain, maybe it is better to remind the analysis of those reliefs to a next article.

 

It is clear that the shock that results from the careful analysis of these images – as it happens any time that we discover that in prehistoric times man had already at its disposal technical and so intellectual instruments equal or even superior to those of modernity – could drive us to close our eyes and then to turn our heads elsewhere. As we grew up in a dogmatic evolutionist Weltanschauung, when we discover very advanced features in mathematics, geometry or astronomy of very ancient peoples we are inclined to explain anything with chance (or, better: with the Chance) and to scrape along with our historiographical dogmas. We are ready to anything, rather to get to the only possible conclusion: that in what we call “Prehistory” man had actually at its disposal very powerful technical instruments and so very advanced scientific knowledge, even if the evolutionism faith is founded on dogmas that exclude these facts.
But let’s put aside our prejudices and the connected intellectual indolence and let’s submit to our best attention the image of the Big Pyramid. This way we will be capable to detect in detail all the characteristic points of its section that the Fappalà’s space-time diagram is capable to single out and to realize how it seems capable to reveal the secret geometry from which Ancient Egyptian architects derived its project.

Actually, if we carefully observe the image, we can notice that the geometrical congruence between the space-time diagram and the section of the Big Pyramid – far from to appear as a system of random coincidences – seems on the contrary something organic, the fruit of a logical connection. Let’s enumerate some of the crucial points that the Fappalà’s diagram singles out: the base angle, the position of the King and Queen Chamber, the beginning and the end of the Ascending and Descending Corridors, the highness of the hillock that was incorporated into the structure, the position and the inclination of the two King Chamber shafts. If we sum to these most evident and important characteristics the many small and particular architectonic details, then we are almost forced to abandon the idea that all this could be the result of a Chance work: to claim this in a similar context seems the same as to claim that when we are in a restaurant and we order fried chicken then the fried chicken arrives to our table by the actions of Chance. What can have to do “the Chance” with geometric phenomena as those that we see in the below images?

In contrary, the Big Pyramid shows evident connections also with the Bohr’s hydrogen diagram of the first years of the last century

To give an idea of the miraculous complexity of this system, we have to think that if we move the Fappalà diagram on the Big Pyramid profile, or if we change the scale of the projection, the system of meaningful connections recreates itself inexorably, as we can see in the below images

As we have to exclude the idea of a chance, at this point, it seems historically and philologically possible to hypothesize that the space and the forms in the space of the Ancient Egyptian art and architecture were conceived in a way very near to our own one, and maybe mathematically more evolved. In these ancient works it seems that we can find a predecessor of that Pythagorean thought that says that “things are numbers”. On the basis of these images, we can interpret this strange assertion in this way: the forms of the visible world derive (or “are created”) by the abstract and so invisible forms of mathematics and geometry. These forms were religiously believed as the divine essence of those cosmic cycles that generate and re-generate life on Earth. But this essence – far from remaining a mythical matter – was empirically and mathematically understood, so that this knowledge results very similar, not to say identical or even superior to the one of our scientific method.
The probabilities that this hypothesis could correspond to reality grow up in an exponential way when we get aware that this same diagram seems to be capable to describe the principal characteristics of many Ancient Egyptian Pyramids, and not only of the Cheops one, as we can see in the below images.

5. If the hypothesis that we have made would result founded, then we should accept that the more ancient and powerful art and architecture that we can find in our planet were not the fruit of mythical fantasy joined with an artistic instinct – that it gave to that fantasy a material and stylistic body. On the contrary, a magnificent architectonic masterwork as the Big Pyramid would be the result of the application to the sacred architecture of very, very complex mathematical and geometrical formulas and of an enormous power of calculation too, that together were capable to synthesize in a single building all the fundamental physical laws known at that time. Beyond this, as we have seen in the previous articles, this golden code was capable to encrypt in the monument a big number of astronomic data, as the Sacred Angles of Orion, those of Nabta Playa, the position in the sky of some Duat and northern stars in a certain era (but it’s already known that in the measures and proportions of the Big Pyramid are encrypted other significant astronomic and physic data, as the circumference of Earth, the distance between Earth and the Sun, the distance that the Earth covers in a second wheeling around its axis, the light speed, etcetera.) .
Anyway, as we have already said, it is practically certain that all these notions were not conceived by the builders as merely quantitative, neutral, “laical” data, devoid of any kind of religious meaning, as it happens nowadays. On the contrary, all this scientific notions were considered as a reflex of the Divine Harmony that this people saw as the Ground of Hearth and Sky. A monument, for instance the Big Pyramid, could be “beautiful” only if it were insofar a reflex as exact as it was possible to be for those equations and astronomic data that constituted the secret law of the Divine Cycle.
And this must be the deep reason of the almost inhuman accuracy of its orientation to the cardinal points, of its orthogonality and of the precision – comparable with high optics – with which thousands and thousands of fine coating stones were worked: if the Big Pyramid should be the architectonic representation of a physical theory that has become famous in the present as “Theory of Relativity” and of a big number of astronomical and physical data, then the almost monstrous exactness of its building appears no more as a dizzy-crazy waste of energies, but as the logical consequence of the theoretical contents that by means of the monument this people would symbolize.
If this hypothesis would be verified, we would have that not only the Giza and Dahshur Plateaus were meant to represent the Duat sky around the 10500 BC, but also that any kind of sacred space – in its whole and in its parts, in its architectonic three-dimensional body as in any bi-dimensional decorative space – would be planned and realized to represent a knowledge that would be forgotten and then rediscovered in the western Europe after millennia of oblivion. But it is very difficult to hypothesize that this way to codify mathematical-scientific notions had the purpose to conserve them or even to pass on them to the posterity. We can say this because it seems that to be capable to read this kind of notions into the Big Pyramid design, presupposes to have already learned them in another way. To give an example, men who would not know the relativity theory and its possible geometrical representations, could not be able to recognize them in the measures and proportions of the Big Pyramid.
In the Coptic tradition there are stories in which it is told that in a very ancient time, a king knowing that the deluge was about to come, ordered to build the Big Pyramid to encrypt in it all the knowledge that they had in their time: but this tradition itself, at least in the form in which it has arrived to us, does not seem absolutely aware of the actual contents of this knowledge, even if the suggestion that it contains seems to be confirmed by the discovery of the hidden essence of the geometry of this building.

second part: THE THEORY OF THE RELATIVITY IN THE PLATO’S TIMAEUS

 

Every now and then it may happen to read overwhelming things: overwhelming, because we cannot believe to read them just in the place we are actually reading them. Their meaning appears evident, but it is as if we could not understand it, because we were educated to think that it must be different from what we are looking at. To explain this situation, maybe there is no better example than these words that we find in the Timaeus (62 C – 63 A)

 

The nature of the light and the heavy will be best understood when examined in connection with our notions of above and below; for it is quite a mistake to suppose that the universe is parted into two regions, separate from and opposite to each other, the one a lower to which all things tend which have any bulk, and an upper to which things only ascend against their will. For as the universe is in the form of a sphere, all the extremities, being equidistant from the center, are equally extremities, and the center, which is equidistant from them, is equally to be regarded as the opposite of them all.

 

This passage, at first sight, appears really obscure. But one point of clarity is maybe represented by the affirmation that “all the extremities, being equidistant from the center, are equally extremities”. This affirmation seems to contain another one that, at least because we heard it many times, sounds more familiar. Actually, thinking about an universe as the one that we look at every day, if all things are equally equidistant from the center, we are compelled to think also that all things must be someway considered the center of the universe (we shall soon see the reasons why we have drawn this conclusion that the expert reader of physics and logic probably would have drawn by himself). In a somewhat hermetic way, it seems that Plato, comparing the world to a sphere, relates to the definition that the story attributed to Hermes Trismegisto (the equivalent of the Greek Classical Ancient Egyptian god of wisdom, Thoth), and not to that of common sense. It is something that you also argue from the description that is given in Timaeus 33 C, D – 34 A, B , when he speaks of the creation of the world

 

And he gave to the world the figure which was suitable and also natural. Now to the animal which was to comprehend all animals, that figure was suitable which comprehends within itself all other figures. Wherefore he made the world in the form of a globe, round as from a lathe, having its extremes in every direction equidistant from the center, the most perfect and the most like itself of all figures; for he considered that the like is infinitely fairer than the unlike. This he finished off, making the surface smooth all around for many reasons;

(…)

Such was the whole plan of the eternal God about the god that was to be, to whom for this reason he gave a body, smooth and even, having a surface in every direction equidistant from the center, a body entire and perfect, and formed out of perfect bodies.

 

Now, it is evident that the world as it offers to immediate observation is not at all made this way. Furthermore, it appears particularly absurd the idea of ​​a three-dimensional sphere without an outside (or enclosed into a kind of space that Plato compares with a dream, or with a nightmare (Timaeus, 52, B). We must therefore try to understand what could be the meaning of this first sight very odd description.

3. In fact, if we take into account the sphere of common sense, the claim that all parts are equally distant from the center of the universe is nothing more than a non sequitur. Let’s suppose that the center of the universe imagined by Plato actually corresponds to the center of the Earth, as many commentators have argued on the basis of the affirmation, that we can find in Timaeus 40:

 

“The earth, which is our nurse, clinging around the pole which is extended through the universe, he framed to be the guardian and artificer of night and day, first and eldest of gods that are in the interior of heaven.”

 

As we can see, in the Timaeus the Earth, as all the other celestial entities, is described in the same way in which we conceive them nowadays. That is, as a sphere that turns on itself: a fact of which they were well conscious in almost all ancient and so-called “primitive” cultures. Indeed, the idea that in ancient times people generally believed that Earth was flat is nothing more than a modern superstition, due to the fact that it was not understood that in ancient cosmologies with the word “Earth” is not usually intended the planet Earth, but rather the ecliptic plane (which , for example, in the Apocalypse is called the “Heavenly Jerusalem”, with the Twelve Doors that are nothing more than the twelve “houses” of the zodiac; in the legend of King Arthur there is the Round Table with the Twelve Knights; the son of Parsifal, Lohengrin, travel with a ship dragged by a swan, a clear allusion to the constellation of the Swan; in the Wolfram von Eschenbach version of the myth the Temple of the Saint Graal is «smoothed and rounded off as for the work of a lathe» just like the universe described in the Timaeus, etc.).

But if Plato was aware of so refined astronomical data, it becomes difficult to realize how it could have come to believe that the universe is a sphere absolutely uniform, since all observations immediately refute this hypothesis. The tip of the mountains, with all the evidence, is not far from the center of the Earth in the same way that the bottom of the sea. In turn , the clouds are far from the center of the Earth more than the tip of the mountains, and the moon more than the clouds etc. Even kids know it. So, how come that Plato did not know this, as he showed the possession of a very much deeper astronomical knowledge?

 

 

 

However, in spite of any sensible evidence, Plato insists at length on the concept of the absolute uniformity of the universe, and seems to want at all costs to dissuade his reader from the idea that in the universe could exist a place that can be called up or one low, even in a relative sense

 

Such being the nature of the world, when a person says that any of these points is above or below, may he not be justly charged with using an improper expression? For the center of the world cannot be rightly called either above or below, but is the center and nothing else; and the circumference is not the center, and has in no one part of itself a different relation to the center from what it has in any of the opposite parts. Indeed, when it is in every direction similar, how can one rightly give to it names which imply opposition?

 

But here we must note again that the claim that the universe is an entity “uniform in all its parts”  cannot possibly be referred to the universe object of sense-perception. This is because, as it is clear to everyone, in whatever place we establish the center of the universe, immediately we see that there are places that are nearer or further from it. But Plato insists anew in his idea

 

For if there were any solid body in equipoise at the center of the universe, there would be nothing to draw it to this extreme rather than to that, for they are all perfectly similar; and if a person were to go round the world in a circle, he would often, when standing at the antipodes of his former position, speak of the same point as above and below ; for, as I was saying just now, to speak of the whole which is in the form of a globe as having one part above and another below is not like a sensible man.

 

 

4. This Plato argumentation, taken superficially, seems a quibble about abstract ideas  rather than a description of the cosmos as we can observe it in the everyday life. Let’s suppose that the Earth is really to be thought as the center of the Universe. If we take the points that are at the same distance from this center, we find that taking one of them as a point of reference and then another, we would be tempted to define the same point now as low now as high. Therefore, we would fall into the contradiction of which Plato speaks about.

But, assuming this, however, it remains clear that the universe is not an uniform sphere. So, it is not true that all the entities of which it is composed are located away from its center in the same way. Even if we implement the Copernican revolution and take the Sun as the center of the universe, we immediately notice that there are planets that are closer to it and others more distant. If we take any star the conclusion that we draw must be the same. But from the reading of the Timaeus we can see that Plato, far from being a naive, was fully aware of these things, since he speaks of spheres nearer or more distant from the axis of the Earth. So why  he insists then on the concept that the universe is absolutely uniform?

In order to give a sense to this part of the Timaeus, we must turn away from common sense and from the Euclidean sphere. Instead, we have to think about the “absolute sphere” Hermes Trismegisto was talking about it when he said that “the universe is a sphere whose center is everywhere and whose surface is nowhere”. It is only on the basis of a concept of this kind that you can sensibly say that all the entities that make up the universe are at the exact same distance from the center. They are all located at the same distance from the center because every point in space is conceived as a possible center. But as we move into a similar space, we can never reach a privileged point, a point that we can define a “center unique and absolute”.

On the contrary, into this absolute sphere each of its endless centers must be considered absolute, because this sphere is constituted exclusively by center-points.

 

 

5. No modern commentator posterior to the invention of the Theory of Relativity has realized, or dared to realize, that the sphere mentioned by Hermes Trismegisto (and consequently also by Plato) is a perfect metaphor for the relativistic space. Even those readers with a deep scientific background, or even scientists didn’t notice that. Yet, according to Einstein’s theory, just as in the sphere of Hermes Trismegisto each point of the space that surrounds us has the same importance in relation to the whole. Therefore, each point is an equally valid basis to get to a true description of the universe. Translated into modern terms, we say that every point of the space is one of the infinite absolute centers of the relativistic universe.

This statement get more consistent when we remember that Plato was heir, through Socrates, of the Pythagorean thought, which came in large part from the contact with the ancient Egyptian hermetic culture. The most obvious clue is the way in which Plato describes the phenomenon of vision in Timaeus 45 , B, C.

 

And so in the vessel of the head, they first of all put a face in which they inserted organs to minister in all things to the providence of the soul, and they appointed this part, which has authority, to be by nature the part which is in front. And of the organs they first contrived the eyes to give light, and the principle according to which they were inserted was as follows: So much of fire as would not burn, but gave a gentle light, they formed into a substance akin to the light of every-day life; and the pure fire which is within us and related thereto they made to flow through the eyes in a stream smooth and dense, compressing the whole eye, and especially the central part, so that it kept out everything of a coarser nature, and allowed to pass only this pure element. When the light of day surrounds the stream of vision, then like falls upon like, and they coalesce, and one body is formed by natural affinity in the line of vision, wherever the light that falls from within meets with an external object. And the whole stream of vision, being similarly affected in virtue of similarity, diffuses the motions of what it touches or what touches it over the whole body, until they reach the soul, causing that perception which we call sight.

 

So the human eye, according to Plato, is an active source of light. This Platonic conception gives us the clearest explanation of why into the sacred Ancient Egyptian iconography the Sun is almost systematically represented like an eye. This happened because, with all the evidence, the Ancient Egyptians believed the sun the eye of a god who, far more than human, was able to enlighten the world .

But above we have already reached the proof that this is not the only ancient Egyptian doctrine that we can find in the Timaeus. In the first part of this article we have seen that the Ancient Egyptians knew some version of the theory of relativity, and that they inscribed it in all their sacred spaces. So it becomes historically very reasonable to say that the universe as an absolutely uniform sphere that we find in the Timaeus is the one that has been inscribed in the Pyramids and the Ancient Egyptian reliefs: it is an universe that results from a mathematical contemplation, not from the immediate perceptions of the senses. This is not much surprising , if

 

“to look up or down with his mouth open or closed it is the same thing until we investigate any kind of sensitive subject … The only real way to look “up” is to investigate the pure Being, that you cannot see at all”. [ Plato, quoted by de Santillana ]

 

 

6. We have good reasons to attribute to Plato the Ancient Egyptian version of Einstein’s theory, not only because it seems that the doctrines of the Timaeus are an Ancient Egyptian heritage, but also because other ideas do not seem to be able to clarify his conception of the universe. For example, Newton has imagined the absolute space as a kind, so to speak, of infinite cube, not as a sphere made ​​up of an infinite number of centers . Moreover, within the Newtonian conception , the points of observation are not equivalent, because the only point of reference to be considered “true” it is just the absolute space, not the entities that move into it. In relation to it, all the other points of reference are to be considered relative, that is: the descriptions of the universe that can be obtained by them are, strictly speaking , false, or deceptive .

On the contrary, in the sphere of Hermes Trismegisto all points are equivalent. Which means that from each of them you can get a true description of the cosmos. In the modern times, we can find an idea of space like this –  that is, an idea of space seen as an absolute sphere – only in the vision of Einstein. Almost without realizing it, he built a theory at the same time metaphysical and quantitative-mathematical such that the universe, just as the absolute sphere of Hermes Trismegisto, cannot be defined properly nor as infinite neither as finite (by the way, even in the Buddhist thought, a concept of this kind was alluded when it was stated that the number of worlds in the universe cannot be defined either as infinite nor as finite) .

In fact, in the conception of Einstein the universe must be understood as a finite system, at least if we think of the amount of substance of which it is composed. But this matter moves in a space where every point can be thought of as its center, since it is a point of view of equal dignity as any other. So, no point of the Einsteinian space can be thought of as its limit. Consequently, to explain the mathematical concepts of the Einstein theory we could easily use the famous words of Hermes Trismegisto: “the universe is a sphere whose center is everywhere and whose surface is nowhere”.

 

 

7. And it is not less interesting and near to our conception of the world the explanation that Plato gives of the phenomena connected with gravity. Let’s see what he says about it in Timaeus 63

 

The reason why these names (high and low) are used, and the circumstances under which they are ordinarily applied by us to the division of the heavens, may be elucidated by the following supposition : if a person were to stand in that part of the universe which is the appointed place of fire, and where there is the great mass of fire to which fiery bodies gather, if I say, he were to ascend thither, and, having the power to do this, were to abstract particles of fire and put them in scales and weigh them, and then, raising the balance, were to draw the fire by force towards the uncongenial element of the air, it would be very evident that he could compel the smaller mass more readily than the larger; for when two things are simultaneously raised by one and the same power, the smaller body must necessarily yield to the superior power with less reluctance than the larger; and the larger body is called heavy and said to tend downwards, and the smaller body is called light and said to tend upwards. And we may detect ourselves who are upon the earth doing precisely the same thing. For we separate earthy natures, and sometimes earth itself, and draw them into the uncongenial element of air by force and contrary to nature, both clinging to their kindred elements. But that which is smaller yields to the impulse given by us towards the dissimilar element more easily than the larger; and so we call the former light, and the place towards which it is impelled we call above, and the contrary state and place we call heavy and below respectively.

 

Prima facie, an argumentation of this kind could seem to us completely ingenuous and anti scientific. But, looking better, the concepts expressed by Plato are analogous to those that we can get from the law of Newton, that on this issue is rather different from the one of Einstein. The law of Newton, in its essential mathematical form, is usually written this way

 

F = G [(m₁ x m₂) : d²]

 

If we have to translate in words the meaning of this mathematical formula, we say that the mass is attracted by other mass. And the force of attraction is bigger if bigger are the quantities of mass in relation to it. This means that, just like Plato, we believe that the similar attracts the similar. And, again like Plato, we believe that as much the mass is bigger as much it has the tendency to stay joined (that is to be attracted) by other mass.

 

 

 

To be more precise, we can try to quote again the same passage of Plato that we have just quoted, replacing the concept and the name of “earth” with that of “mass”. With the name and the concept of “air”, not being able to do better, we will replace it with that of “vacuum” (but it is clear that if with the word “earth” Plato probably alludes to a concept very similar to the modern concept of “mass”, with the word “air” he refers instead to something else than to the modern concept  of “vacuum”). And we will see that still in this way the discourse of Plato still works perfectly.

 

For we separate entities endowed with mass,  and draw them into the uncongenial element of vacuum by force and contrary to nature, both clinging to their kindred elements. But that which is smaller yields to the impulse given by us towards the dissimilar element more easily than the larger; and so we call the former light, and the place towards which it is impelled we call above, and the contrary state and place we call heavy and below respectively.

 

These are exactly the concepts taught by  Newton. The “low”, in the Newtonian view, is the center of a body with mass. What we call “high” is the space that is located farther away from it. And the greater is a mass, and the greater is the portion of mass that we try to tear off, the greater is the effort that we must employ to make this work. So “light” we call bodies which are composed with a little quantity of mass and “heavy” the bodies made ​​up with a great quantity of mass.

However, it is true that Plato does not introduce in its metaphors the concept that the greater is the distance between two masses, the smaller is the attraction that these exert between them. This could be happening because, on one hand, with its written doctrines Plato does not seem much interested in clarifying the meaning of the unwritten doctrines. The written doctrines, as far as we can tell, are a complicated and sometimes confusing system of metaphors with which he alluded to a knowledge that only the initiated of a certain level could achieve. A kind of knowledge that it seems that Aristotle never got. In fact, his descriptions of Plato’s thought seems nothing more than a pattern of misunderstanding and disorientation, in particular with regard to the importance of geometry and mathematics, which were fundamental to Plato, and that instead Aristotle considered with irony and perhaps even with contempt. Even when in the famous passage of De Anima speaks of the Platonic conception of the soul as a two-dimensional entity, he does not realize that Plato and the Platonists alluded to an entity that can be described by means of a certain kind of high mathematics, not of something that can be perceived with the senses, like a geometrical body.

This is clearly another heritage that Plato got from the Ancient Egyptian science. As we have seen in the first part of this article, the Ancient Egyptians represented human figures and goddesses in a two-dimensional way by means of a very complicated system of logarithmic derivatives. So their “two-dimensional” concept of soul was not, as it has hitherto been believed, the result of the naivety of a dreamy mythical inspiration, but a science that for the moment we are not be able to understand.

So it may be that the reason why the concepts of chemistry and physics that appear in the Timaeus results incomprehensible to us also for one more reason – in addition to the well-known Platonic reluctance to transfer in a clear way his unwritten doctrines in his writings. Maybe, the physics and chemistry that – along with Socrates and Pythagoreans – he had inherited from Ancient Egyptian Hermetic doctrines, were structured at mathematical and conceptual level in a very different way from those that are familiar to us in the modern West. So different that we cannot understand or even imagine the profound meaning of the concepts that are exposed in the Timaeus.

 

 

 

Very often it is spoken of the Platonic doctrine of the four elements (earth, water, air, fire) as a kind of naiveté, or as a complex of almost inexplicable superstitions related to the world of magic and of numerology. For sure, no one has ever tried to explain in depth the reasons why a man like Plato, who certainly was not a fool, could get to convince himself of the truth – that’s to say of the “correspondence to the facts” – of a certain kind of doctrines. Because if it is true that their deeper meaning coincides with the one that appears to men with our mentality and culture, we do not see how an intelligence such as that of Plato was not able to realize their gross falsehood.

Below we quote a passage in which Plato speaks about the chain of transformations from an element to another. Between brackets we put some comments to indicate to the reader the problematical points – even at a psychological level – of the traditional interpretation of the philosophy that Plato expressed in the Timaeus

 

In the first place, we see that what we just now called water, by condensation, I suppose, becomes stone and earth (we notice that no one  has never explained or asked about the reason why Plato – or whatever reasonable person – could get to believe that the water, by “condensation” (!?), could become stone: here is completely clear that the “water” to which Plato alludes it is not that one of the commonsense; and this is true also for “fire”, “air” and “earth”: in another passage, Plato attributes to the fire the origin of some obscure substances); and this same element, when melted and dispersed, passes into vapor and air. Air, again, when inflamed, becomes fire; and again fire, when condensed and extinguished, passes once more into the form of air (here it is impossible to understand what Plato means saying that fire, extinguishing, becomes air or that air, inflaming, passes into the form of fire; all these descriptions are only truisms of the form “if X become Y it is no more X, but Y”); and once more, air, when collected and condensed, produces cloud and mist; and from these, when still more compressed, comes flowing water, and from water comes earth and stones once more (no one in the world has never “seen” a thing like this: water transforming in earth and stones: so we have the problem to understand what Plato means with these words); and thus generation appears to be transmitted from one to the other in a circle. Thus, then, as the several elements never present themselves in the same form, how can anyone have the assurance to assert positively that any of them, whatever it may be, is one thing rather than another? No one can.

Timaeus 48 E, 49 A, B, C.

 

 

 

Here we should try to understand what is exactly the meaning of these propositions because, taken literally, they do not mean anything. You might say: Plato thinks like a child , builds castles in the air, fantasizing  about things without looking at reality. But children do not say things like these! Hands up anyone who has ever heard a child say that the fire, extinguishing, comes back in the form of air. On the contrary, the Plato’s words seem to allude to a knowledge of a chemical type someway similar to ours, although not equal. In particular, it may be that the old chemistry to which Plato refers with his doctrine of the elements, as well as to make use of different concepts, could also have different potentialities than ours, potentialities that for the moment remain completely inaccessible. In The Snefru Code part 7 and 8 we will see the empirical evidences that prove in an irrefutably way that in ancient times people were able to reduce the stone in a liquid and/or pasty state. But if this is true, then it is possible that a concept such as “condensation” could allude to phenomena quite different from those to which we allude to, with the same word (that therefore it is not the same word).

Instead, the Platonic doctrine that everything changes into anything else, should not seem strange at all to us: this is what we think too, since we believe that the different substances with which we are in contact in the everyday life, despite their extraordinary diversity, are ultimately composed by few elementary particles, electrons, protons and neutrons. Plato, with his doctrine, seems to allude to a process of this kind. Perhaps, earth, water, air and fire, represented as geometric bodies, are nothing more than a schematic way of alluding to the atomic structure of matter, that’s to say to four different classes of elements that can be obtained from our table of the elements. But we will have the proof that this hypothesis corresponds to the truth only at the moment in which future investigations will be able to put in a quantitative-mathematical contact our scientific doctrines with those of the Ancient Egyptians, that seem at the origin of the Platonic speech. A task that is expected to be very difficult, since these people had a way to encode scientific data that, as we have seen above, did not have many points in common with ours, as which we write with pen on paper they used to symbolize with geometry and stone.

Horst Bergmann and Frank Rothe have calculated that the Cheops Pyramid has a volume of almost 2.600.000 m³, the one  of Khefren arrives to 2.300.000, and the one of Menkaure to about 252.500, with a total of 5.082.500 m³. It seems that the two authors had not noticed that the first figure corresponds more or less to ɸ² · 10⁶ = 2,618033… · 10⁶ ≈ 2.618.000, and that the total corresponds in a practically exact way to ɸπ · 10⁶ = 5,0832… · 10⁶ = 5.083.200.

To have an idea of what could be the importance of a number like ɸ in science, we can say that the speed of light could be obtained this way (we recall that √5 = ɸ + 1/ɸ)

 

π : ³²√(2√5) = 2,9979285.. ≈ c = 2,9979246

 

Or, the ratio between the mass of an electron and its classic radius is equal to

 

9,1091/2,8177 = 3,232733 ≈ 2ɸ = 3,23606.

 

This is a inquiry that we will develop in a deeper way in The Snefru Code part 7. But already in the following pages we have a way to get aware that to this people, very probably, sciences as astronomy, physics and chemistry were nothing more than a branch of geometry, in turn conceived as a branch of theology.

 

 

Appendix 1: AN OUTLINE OF THE THEORY OF THE UNIFIED FIELDS PROBABLY CODIFIED INTO THE BIG PYRAMID

 

 

 

In 1836-37 Howard Vyse, during a period of intrusive excavations performed ​​on the Great Pyramid by means of dynamite, discovered at the exit of the south shaft of the King’s Chamber (the one that points to the Orion’s Belt) an iron plate of rectangular shape. Following Hancock and Bauval, it was long about 304,8 mm, 101,6 wide and its  thickness was about 3 mm. Even at a first glance we see that a proportion around 3 seems to have a special role in their determination.

So we can try – as a mind experiment – to rebuild its original size, starting from numbers that to the Ancient Egyptians were very important. All we need to carry on in this experiment, is to assume that the measures have been taken with a minimum of approximation.

So, we suppose that the thickness has been determined with the formula 2ɸ (or √5 + 1) and that therefore it was originally 3,23606 … mm. Then we suppose that the width was determined by the formula

 

2ɸπ · 10 = 101,66407 … mm.

 

Regarding the length, as we have found the relativity diagram codified into the Big Pyramid, we suppose that it was determined using the constant that we need to calculate the speed of light, which is equal to c = 2,9979246 (and so with a number very near to 3, as 2ɸ and π are). So the length would result from the formula

 

2ɸπ · 10 · 2,9979246 = 304,7822.. mm.

 

This way, the difference compared to the measure of the length which is usually taken for good would be little more than two tenths of a millimeter.

If this mental experiment corresponded to reality, we would have that the speed of light would not have been codified only in the fundamental measurements of the Great Pyramid, but even in this so apparently anonymous iron plate that had been placed at the end of the South Shaft of the King’s Chamber.

Bouval and Hancock commissioned scientific tests on the metal, which have shown that the iron was not of meteoric origin and that, most likely, it was originally gilded. This latter fact is very important in relation to our hypothesis, because we can consider gold a perfect metaphor of light, of which the plate would contain a fundamental physical characteristic.

Neither we can rule out the possibility that also the other numbers that characterize the object could contain other scientific information. The case of the sarcophagus of the King’s Chamber has taught us that in measurements – which in our culture are considered meaningless – can be contained scientific data that were important to these people, because they were considered directly connected with the Creation intended as a divine-mathematical project.

For example, if we take the length of the plate in decimeters we see that it results 3,047822. If we make the ratio between π and this number we have a result of 1,030766.., a number that seems at first sight quite insignificant. What can we say then, when we discover that the ratio between the number of days of a solar year (365,25) and that of one year of moon phases (354,36) gives a result almost equal to this, namely on an amount equal to 1,03073..? As we have seen above, a number very similar comes out also from 2ɸ : π = 3,23606.. : 3,14159.. = 1,030072.. (and of course also from ɸ : π/2).

Moreover, taking every millimeter as the equivalent of a million km, we see that the length of 304,78 mm corresponds almost perfectly to twice the maximum distance between the Sun and the Earth, which is equal to 152,1 million kilometers (x 2 = 304.2). We can also note that, in numerological terms, there is a great similarity between the average distance between the Earth and the Sun and the speed of light divided by two (149.5978875 against c/2 = 149.89623). One thing that for us has no importance, but that, for those people, might have a very deep meaning.

 

 

 

Furthermore, we recall that the Southern Shaft of the King Chamber points to the Orion Belt. Alnilam, the brightest star of this part of the constellation, is about 1000 light years far from Earth. Interpreting each tenth of milliliter as a light year, we could suppose that the width of the plate (1016 tenth of millimeter) represents the temporal distance between the Earth and Alnilam. Instead the length could represent this same distance in terms of space (because the length results from the width multiplied by the constant from which we derive the speed of the light).

It’s not impossible that the dimensions of the King and the Queen Chamber could contain similar references to Orion and/or to other stars and constellations very important to the Ancient Egyptians. For instance, its length (that we measure along the East-West axis) is about 10,479 meters: talking each tenth of a meter as a light year, we have once again a very good approximation of the distance from Earth and Alnilam (let us bear in mind that at Giza at the vernal equinox Orion rises in East direction).

Other interesting data can be derived from the characteristic angles of the Pyramids. For example, the base angle of the Bent Pyramid is approximately 54°30′ . If with a numerological operation we  transform the sixtieth of a degree in hundredths of a degree, we have an angle almost identical to 54°,303.. At this point, if we make the summation of sine and cosine of this angle, we obtain the cubic root of the number of Euler, as

 

(0,81211… +  0,58349…)³ = 1,39561…³ = e = 2,71828…

.

We can find this number codified also in the measurements of the Great Pyramid, since its side is 440 cubits, and dividing this figure by e = 2,718291828.. we obtain an approximation of ɸ very, very near to the one that results from the division between the division of the area of the base and the one of the four triangular faces (ɸ_Cheops = 1,61859034..)

 

440 : e = 161,8670.. ≈ ɸ_Cheops · 10² = 161,59034..

 

This discovery could be judged as astounding: this people has find the way to codify in the same monument the three more important constant of mathematics, as the ratio between half of the perimeter and the height is equal to a very good approximation of π (π_Cheops = 22/7 = 3,142857..). This fact become less shocking when get aware that these constants have some sort of harmonic relation between themselves, as we can see in the below formulas

 

e – ¹²√π = 1,618189449.. ≈ e – 1 – 1/10 = 1,618281828.. ≈ ɸ = 1,618033988..

 

(π – ɸ²)/2 = 0,2617793324.. ≈ ɸ²/10 = 0,218033988.. (-0,000024..

 

(e – Ln π) · 2 = 3,147103.. ≈ (e – ɸ)¹² = 3,146924.. ≈ π = 3,141592..

 

(π – e) · 1/ɸ = 0,2616204.. ≈ ɸ²/10 = 0,2618033.. (-0,0001829..

 

(10π – e^e)/10 + (ɸ + 1/ɸ)² = 1,626166.. + 5 = 6,626166.. ≈ h = 6,626 ≈ 5 + ⁴√7 = 6,626576..

 

10 – π – ɸ – e = 2,52209152.. ≈ e^ɸCheope/2 = 2,522986097.. ≈ e^ɸ/2 = 2,521582..

 

³√(10π – 10e) = 1,617657.. ≈ ɸ = 1,618033

 

√(10e – 10ɸ)/2 = 1,054548980.. ≈ ħ = 1,054571688..

 

(e^ɸ)^π = 161,28995248.. ≈ ɸ · 10³ = 161,8033988

 

⁸√(e^ɸ)^π = 1,887777.. ≈ (2/ɸ)³ = 1,888543..

 

inv. Ln ⁴√(e – 1) = e^{1,144915933..} = 3,142177.. ≈ π_Cheops = 22/7 = 3,142857..

 

^10ɸ√10π = 1,23745367.. ≈ 2(ɸ_Cheops – 1) = 1,23718068.. (-0,00027299..

 

e – Ln ɸ = 2,237070003.. ≈ ɸ_Cheops + (ɸ_Cheops – 1) = 2,23718068..

 

In a similar way we can find a relation between these numbers and some very important physical constants

 

(π^e)^ɸ = 153,674057.. ≈ r_p · 10³ = 153,5

 

⁸√(ɸ^e)^π = 1,671426.. ≈ m_p = 1,6725

 

^10π√10e = 1,110848.. ≈ ħ² = 1,112121..

 

√(Ln π^π/ɸ/2) = √(2,222620../2) = √1,111310.. = 1,054186.. ≈ ħ = 1,054571..

 

[³√(^ɸ√π)]² = 1,602643.. ≈ c_u = 1,6022

 

π_Cheops – Ln π_Cheops = 1,9977248.. ≈ c – 1 = 1,9979246

 

(ɸ_Cheops – Ln ɸ_Cheops)⁴ = 1,671455.. ≈ m_p = 1,6725

 

This three mathematical and geometrical constants seem to have a very important role also in the trigonometry based on the round angle divided by 360 parts, because they correspond to three moments of uniqueness in the system. We will treat deeply this issue in a successive work. For the moment we can see the formulas, first of all those regarding π and ɸ

 

Lim_x→0 [360 : (x : sin x)] = 360 : 57,295779513082.. = 2π

 

Lim_{tg x → cos x} = 0,786151377.. = 1/√ɸ;     x = 38°,172707..;    sen 38°,172707.. = 1/ɸ

 

The situation regarding the Euler number is little more complicated. We can summarize it saying that the sine and the cosine of the angle equal to 360/e² = 48,720701965. .are the x and the y  capable to solve the equations that we see below. As it is clear, the meaning of those equations is that the three numbers that constitute sine, cosine and tangent of 360/e² can be obtained by function of only one of them

 

y = x/{1/√[√(1/x⁴) – 1]}

 

x = ⁴√1/{[1 + (1/(x/y)²]²}

 

x/y = x/{1/√[√(1/x⁴) – 1]}

 

The base angle of the Pyramid of Menkaure is about 51°,367..  That means a tangent equal to 1,2511.., a number very similar to √(π/2) = 1,25331.. (if the tangent is equal to √(π/2) the angle results 51°,4141.., very near to 50 + √2).

The base angle of the Red Pyramid is about 43°35.. Multiplying it by 2 we get an angle practically identical to 86°,7812.. and in this case the sum of sine and cosine gives us 1.054571.. , which is the value of ħ, a variant of the Plank constant developed by Dirac.

Another very good approximation to this number is the summation of the sine, the cosine and the  tangent of an angle equal to π/2; the result of this summation is 1,054458.. but, using the figure of π that we find in the Big Pyramid (one of the so called Pythagorean numbers, 22/7), the result of the summation is 1,054480.., that’s to say nearer to the numbers that nowadays we judge more exact, that is ħ = 1,054571688..

This way it seems that we discover that two empirical data – that usually we are inclined to judge as casual and inexplicable, the minimum error that is possible in the determination of the speed and of the position of a particle and the quantum of action  – result both enclosed into a fundamental constant of geometry, that until this moment we have believed completely abstract  and detached from the empiric reality – as we have that

 

(sine π/2° + cosine π/2° + tangent π/2°) ·2π = 1,054458.. · 2π = 6,625359.. ≈ h = 6,626..

 

The Planck constant seems to have some kind of connection also with the Fibonacci series, as we can obtain it by means of the sixth and the seventh numbers. Very similar results can be obtained by a function of 2 or of 5 (we recall that (ɸ + 1/ɸ)² = 5, so that (1 + √5)/2 = ɸ)

 

(13 – 8) + 13/8 = 5 + 1,625 = 6,625 ≈ h = 6,626

 

(√2 – 1) · 2⁴ = 6,627416..

 

1 + 5 + 5⁴/10³ = 6,625

 

Considering that both π and ɸ was coded into the measurements of the Big Pyramid, it seems very significant that another good approximation of ħ comes out from the golden number too, as

 

 ⁹√ɸ =1,054923.. ≈ ħ = 1,054571688 ≈ ⁴√(2/ɸ) = 1,054412.. ≈ ⁴√[2(ɸ_Cheops – 1)] = 1,054649..

 

sine 2ɸ + tg 2ɸ = 1,054945.. ≈ ħ = 1,054571688

 

This means that the formula to determine the quantum principal number (n), that we write nh/2π

after having derived it by means of empirical researches – could have been written only on trigonometric basis, with a sort of a priori deduction. And a figure very near to the actual value of π/2 seems to have a meaning also in relation to the speed of light. In fact, we can obtain it doing this operation

 

0,6349975..^0,6349975.. · 4 = 0,7494811644872 · 4 = 2,9979246…

 

But

 

1/0,6349975.. = 1,574809… ≈ π/2 = 1,57079.

 

So, the approximation to π that we need to obtain to get the speed of light in this strange way is 3,149618. The difference between this approximation ant the precise number remind us again to the speed of light

 

3,149618.. – π = 0,00802534.. ≈ (c/10)⁴ = 0,00807760..

 

This rather eccentric mathematical procedure could become more convincing when we discover that, as strange as it could seem, trigonometry could contain a big amount of numbers that are very interesting for all the rest of the mathematical sciences. For instance, we can obtain a figure very near to the constant of Planck h = 6,626.. dividing the round angle by the one of 54°,3718624.. That angle, that apparently has nothing particular, is instead characterized by the fact that it is very similar to 20 times the Euler number, as

 

20e = 20 · 2,718281828459.. = 54,365636.. ≈ 54°,3718624..(-0,006225830..

 

In this case, also the difference between the approximation and the actual value seems very meaningful, as we can obtain it from the approximation of ɸ that we can find in the Big Pyramid.

 

1/(2/ɸ_Cheops)²⁴ = 1/(1,235643109..)²⁴ = 1/160,484552.. = 0,006231129.. ≈ 0,006225830..(-0,000052..

 

Incredible as it could seem, the same happens with the difference that comes up between, let’s say, the difference between the two differences

 

1/0,00005299298.. = 18870,423531.. ≈ (2/ɸCheops)³ · 10⁶ = 18865,970656..

 

1/18865,970656.. = 0,000053005..

 

The second, very peculiar characteristic of the angle equal to 54°,3718624.. is that subtracting the sine and the cosine from the tangent we have 0 as result. From the symbolically point of view this could be a very important fact, because it is as trigonometry said to us: under this number/angle the transmission of energy is equal to 0 (we note on passing that the peak angle of the Big Pyramid is extraordinarily near to the double of 38°,1727…, the angle which has as a fundamental characteristic that the difference between the tangent and the cosine is equal to 0: but this angle is a function of ɸ, because both the tangent and the cosine are equal to 1/√ɸ, and the sine is equal to 1/ɸ):

 

360° : 54°,3718624… = 6,62107… ≈ h = 6,626…

 

At the symbolical level, it seems very, very meaningful also that if we multiply this the same angle by a function of π and ɸ we obtain the duration of a solar year. In this way we find a deep numerological connection between the microscopic world and the macroscopic one

 

  {[(1/ɸ)π²] + 1/ɸ} · 54,3718624…  = 6,717784964.. · 54,3718624… = 365,2584..

 

Instead, if we divided the length of a solar year for the approximation to h we have calculated with

 

360° : 54°,3718624… = 6,62107

 

we have that

 

365,25 : 6,62107… = 55,164799…

 

If we make the summation of the sine, the cosine and the tangent of this angle we get to a number practical identical to 2√2

 

sine + cosine + tg 55,16479.. = 0,820798.. + 0,571217.. + 1,436926.. = 2,828943.. ≈ 2√2 = 2,828427..

 

A number very near to √2 results also from the tangent of the angle that comes out dividing the length of the solar year (excluded the 0,25 days) by the gravitational constant of Newton, as

 

365,25 : 6,672… = 54°743..;      tg  54°743.. = 1,414637.. ≈ √2 = 1,414213..

 

 

3. Taking into account  all of this, we can hypothesize that the plate found by the Colonel Vyse, far from being a banal object, could contain important scientific-astronomical data, that, as we are going to discover, reach an unimaginable level of refinement.

From the bigger face of the plate we can derive two twin rectangle triangles, whose hypotenuse coincides with the diagonal of the rectangle. The angle opposite to the major cathetus is 71°,5531526028, whose tangent is equal to c = 2,9979246..

We note by passing that this is not, obviously, the only way to obtain the constant “c” via trigonometry. For instance, we can obtain it by the angle of 58°,34347.. doing  sin + cos + tg = 2,9979245.., or by which of 76°,61445.. doing tg – sin – cos = 2,997924604.

But the more interesting one is surely that of 66°,2699.., from which we can obtain c in the way we see below

 

tg 66°,2699.. · (sin + cos 66°,2699..) = 2,9979222.. ≈ c = 2,9979246

 

In this case the very important thing is that we can obtain this angle via numerology from the Plank constant, doing

 

10h = 6,2599 · 10 = 66°,2599 ≈ 66°,2699.. (-0,01..

 

This fact creates a very deep connection with the solid  we were dealing with. If we go back to the analysis of the plate found at the end of the south Stellar Shaft of the King chamber, if we multiply the cosine of 71°,5531526028.. (0,316424..: a number very near to √10/10 = 0,31622…) for the tangent and then we make 1/x, we obtain a number equal to 1,054165…, that’s to say another approximation of ħ, the value with which very often we replace h, the Planck’s constant (we recall that ħ = h/2π = 1,054571..).

 

1/(0,316424771.. · 2,9979246) = 1/0,948617.. = 1,054165.. ≈ ħ = 1,054571..

 

The cosine of the angle of 71°,553152.. has another  characteristic that seems rather interesting. If we multiply it by 10 and then we make the fifteenth root, we obtain a result very meaningful in relation to ɸ and the speed of light

 

¹⁵√(cos 71°,55.. · 10) = ¹⁵√3,1642477.. = 1,079819… ≈ 2ɸ/c = 3,236067… : 2,9976246 = 1,079436.

 

A very similar things happens if we divide the base perimeter of the Big Pyramid by 6 times the height. This time we find a good approximation of π/c that, as we will see in a future article, is at the basis of the measurements of the east-west side of the King Chamber (10,479 ≈ 10π/c)

 

(440 · 4) : (280 · 6) = 1760 : 1680 = 1,047619… ≈ π/c = 1,047922..

 

If instead of multiplying the height by 6, we multiply it by the Plank constant h = 6,626, we can get to ħ in this way:

 

 (280 · 6,626) : (440 · 4) = 1855,28 : 1760 = 1,054136.. ≈ ħ = 1,054571..

 

If we multiply the height by this particular approximation of h – 6,62179273.. – very near to the one that we can get by the ratio between the round angle and the angle which tangent is equal to the summation of sine and cosine – we get to a very special number as

 

(280 · 6,62179273..)/10³ = 1,854101966.. = 3/ɸ

 

If we raise this number by the power of itself, we get to a very good approximation of π

 

1,854101966.. ^{1,854101966..} = 3,141572320295.. (-0,000020333293867..

 

Curiously, the difference from the 27^th root of the approximation that we have just obtained and the actual figure of π is very similar to G – 6, a little like the fourth root, that is very similar to (G – 6)/10

 

²⁷√0,000020333293867.. = 0,670.. ≈ G – 6 = 0,672

 

⁴√0,000020333293867.. = 0,067150.. ≈ (G – 6)/10 = 0,0672

 

Coming back to the plate found at the end of the Stellar Shaft of the Big Pyramid, it seems very interesting to notice that if we divide the round angle by the angle that has c = 2,9979246 as a tangent multiplied by π , we obtain a result very near to the value that is very close to that of the measure in joules of an electron volt (1,60217..)

 

360° : (71°,55315.. · π) = 1,601488..

 

This number seems very similar also to the approximation to the golden number that we find in the Pyramid of Menkaure. This approximation, in turn, is very near to the figure that comes out from the ratio between the typical number of the Dog Star cycle with the solar constant, if we raise the result to the seventh power

 

(1461 : 1366)⁷ = 1,06954612…⁷ = 1,601

 

The angle of 71°,553152.. is numerologically very similar to the duration in solar years of a particular version of an ancient unity of time, that is called Precessional Day. Its length results from the division of the 26,000 years of a Precessional Year in 365 parts instead of the canonical 360, as

 

26000 : 365 = 71,2328..

 

We obtain a result more exact if we divide the 26000 years by the actual duration of a solar year (365,25) minus 2/ɸ

 

26000 : (365,25 – 2/ɸ) = 26000 : 363,361.. = 71°,554094573.. ≈ 71°,553152602..

 

All these mathematical connections that we have indicated may at first seem a little forced . But the extent of the ramifications that we are discovering make us suspect that the numbers characteristic of astronomy, physics and geometry may eventually form something like a system.

Going on with this – let’s say – “mental experiment”, multiplying the exact value of ħ by the constant from which we get the speed of light we obtain a result equal to

 

ħ · c = 1,054571.. · 2,9979246 = 3,161524..

 

This value corresponds to the tangent of an angle equal to 72°,4476, that at a numerological level corresponds in an almost perfect way with the duration measured in solar years of a canonical Precessional Day, equal to 26000 : 360 = 72,222.. solar years, or also to 90° : ^π√2 = 72°,180799.. Curiously, the fifth root of 360 gives a result of

 

⁵√360 = 3,24534.. ≈ 2ɸ = 3,23606..

 

that’s to say a value very near to the thickness of the plate found by Colonel Vyse. But this relation become more interesting in the moment in which we become aware of the fact that from this number we can obtain also a very good approximation of the so called “Planck length” (ℓ_p), that is the length below which the concept of “distance” have no more any physical meaning.

 

1/3,24534.. : 2 = 1/1,62267.. = 0,616268.. ≈ ℓ_p – 1 = 0,616258..

 

Interestingly enough, we can obtain a very good approximation of the classic radius of the proton precisely starting from the Planck length in the way that we see below

 

³√(ℓ_p + 2) = ³√(1,616258.. + 2) = ³√3,616258.. = 1,534922.. ≈ r_p = 1,535

 

The 360 seems a very particular number. In fact, if we make its πɸ-root we find a very good approximation of 10/π

 

^πɸ√360 = ^5,083203..√360 = 3,183405.. ≈ 10/π = 3,183098.. (-0,0003..

 

But, on its side, the characteristic number of the solar year seems no less interesting, as if we make the π-root of the exact duration of a solar year is equal to ^π√365,25 = 6,5418, a number very similar to the value of h calculated by Plank at the beginning of the last century (the actual number is 6.55).

We have also to remember that 10 raised to ten times the cosine of 71°,55.. gives us a number very near to 1460, this is one of the two characteristic numbers with which the Ancient Egyptian symbolized the cycle of Sirius (the other was the more famous 1461)

 

10^{10 · cos 71°,55..} = 10^3,16424.. = 1459,646586..

 

We will see in a next moment the numerological coincidence between this operation and the characteristic numbers of the Ark. But the cosine of 71°,55.. appear even more significant when we get aware that it is very similar to the half of the value of the constant with which we can obtain G from ħ

 

2ħ · 10 cos 71°,55.. = 2,109143376.. ·  3,164247.. = 6,673.. ≈ G = 6,672

 

As the value of G is rather uncertain (checking it out on Internet we find values that start from about 6,673 to arrive to about 6,69) we could also obtain a good approximation by

 

2ħ² · c = 2,224242.. · 2,9979246 = 6,668112..

 

The solar year and the precessional cycle are perhaps an element of uniqueness, almost the fingerprints of the Earth in relation to the other heavenly bodies that we see in the universe. But, as it seems, in the numbers of these cycles are coded the constants of our most important scientific laws. So also the ancient calendars probably contain, even though in an hermetical way, the fundamental numbers of all the fundamental laws of physics.

Pi – the constant that determines the circle and the sphere and, as we have seen above, the relation between the Planck and the Dirac constants too – is enclosed together with ɸ in some cosmic cycles concerning the Earth, as we have seen in The Snefru Code part 4. This means that in some empirical facts are contained the fundamental numbers of the physical laws that describe these facts themselves. To make another example, the tangent equal to π is characteristic of the angle of 72°34.., an angle that, at a numerological level, is practically identical to that fundamental unity of time that was for the ancient people the Precessional Day (we recall that it result equal to 72,222.. solar years): but in π, as we have seen above, are enclosed the fundamental numbers of the quantum mechanics.

This way we have maybe discovered what Plato meant when he got Timaeus saying that

 

“The earth, which is our nurse, clinging around the pole which is extended through the universe”.

 

With these words Plato did not mean – as we have believed until this moment – that the universe wheels around the Earth, but that into the fundamentals numbers that are contained into the earthly cosmic cycles are in turn contained the fundamental numbers of those physical-mathematical laws that are the logical form of all that happens and could happen in the whole universe.

 

 

 

In fact, this Platonic thesis seems to have really some foundation.  Beyond what we have already said, we can add that the connection that we have seen above between the Newton’s constant (G) and the Planck’s one  (h) appears in part to contain and in part to allude to harmonious relations between the abstract world of the geometric theories and the one of the empirical measurements  of the astronomical cycles regarding the Earth. For instance, the relation between G and h – raised to the eighth power – gives us a good approximation of ħ, as we can see

 

 (G/h)⁸ =  6,67/6,626 = 1,006640..⁸ = 1,054375.. ≈ ħ = 1,054571…

 

Instead, if we raise G/h to the 72th power (we recall that the 72 is a number typical of the measurements of the Precessional Cycle) we obtain a result rather near to ɸ

 

(G/h)⁷² = 6,67/6,626 = 1,006640..⁸ = 1,610427.. ≈ ɸ = 1,618033..

 

Considering that as G as h are uncertain numbers, that depending on the experimental context and the intellectual and psychological inclinations of the scientists can change in a significant way, we could have take two figures such that the value of ɸ would have been absolute precise.

This (G/h) ratio seems to have importance also in the relations that seems to exist between other physical constants, that relate to the structure of the atom.

For example, the classical radius of the proton r_p is equal to 1,535 · 10^-18 m, while that of the electron is r_e = 2,8179403267 · 10^-15 m. The ratio between these lengths (excluding the powers of 10) is equal to

 

r_p/r_e = 1,535 : 2,817940367 = 0,54472408..

 

If we raise this result to the third power we have a surprise, as we discover that it seems to have mathematical relations with other important scientific values

 

(r_p/r_e)³ = 0,54472408..³ = 0,161632.. ≈ ℓ_p/10 = 0,161625.. ≈ ɸ/10 = 0,161803..

 

This hypothesis seems to be reinforced by the fact that, if multiplied by 2 and then raised to the sixth power, this r_p/r_e gives us a good approximation of the characteristic number of the mass of the proton m_p = 1,6725

 

(2r_p/r_e)⁶ = (0,54472408.. · 2)⁶ = 1,08944817 …⁶ = 1,67201.. ≈ m_p = 1,6725

 

We note by passing that this figure can be obtained also via cosmological. From a point of observation like Giza, Osiris-Orion vanished from the horizon for about 70 days. If we divide the 360 “pure” days of the Ancient Egyptian solar calendar by these 70 days, we obtain a value equal to 5 + 1/7. If then we divide 70 by 5 + 1/7 we obtain 13,611.. If we divide 5 + 1/7 by 13,611.. we get to 0,377842… This figure, multiplied by π and raised to the second power gives us 1,67256, a number very near to that of the constant that we need to calculate the rest mass of the proton.

Anyway, going on with our analysis, if we divide the ratio G/h by the approximation of m_p that we have just obtained, we have new surprise, as we discover that this way we can obtain a good approximation of the unitary charge c_u = 1,6022

 

(6,67 : 6,62559..) : 1,67201227 = 1,006702… : 1,67201227 = 0,60209.. ≈ c_u – 1 = 0,6022

 

We know that the mass of an electron is about 1/1836 times that of the proton, because

 

m_p/m_e = (1,6725 · 10^-27) : (9,1091 · 10^-31) = 0,1836076 · 10⁴ = 1836,076

 

If we make the ratio between the classic radius of the electron and which of the proton we see that

 

2,8179403267 · 10 ^{– 15} : 1,535 · 10^-18  = 1,835 · 10³ = 1835,79177…

 

So, it seems that the mass is inversely proportional to the space occupied by the electric charge, as the radius of the proton results about 1/1836 times which of the electron. From this we can maybe deduct that the mass (and so the gravitational field expressed by the mass) is nothing more that – so to speak – magnetic energy concentrated.

So, hypothetically, if we could get to concentrate the energy of the electron in a radius equivalent to the one of the proton, we could get to increase his mass in a proportional way. Vice versa, expanding the space occupied by the electric charge of the proton we would reduce its mass (and so its weight) to a measure  similar to the one of the electron. And exactly this could be the way in which in the ancient times they could get to move and put in place that monstrous granite stones, which weight was beyond the thousands of tons, that nowadays we could not get to move even using our more developed technique. Furthermore, it is possible that this operation could create a situation of chemical-magnetic imbalance so that very hard materials could be reduced to a pasty state. This would explain also the reason why people like the Ancient Egyptian were able to work diorite with the same facility with which we work plastic or aluminum (and here we find also a clue of what could be that chemical phenomenon  that Plato called “condensation”).

If this hypothesis corresponded to reality, it would be possible to build dynamos that runs using what might be called a sort of “gravitational fly-wheel”, which in turn could operate without the aid of electricity produced by power plants, which presuppose the exploitation of coal mines, or oil wells , transmission networks for high voltage etc. And this will explain why the builders of the pyramids could have access to energy without the need of all those equipments that in our time are indispensable.

Furthermore, since the gravitational field is derived from charges of opposite sign, its action may in turn be alternately positive or negative as gradually expands in space following a wave-form. This could mean that the universe expands and contracts in a certain interval of time without ever reaching the thermal death and without any need to explain its current expansion phase by that original explosion that we call “the Big Bang”.

 

 

 

We note in passing that if electron and proton can be considered as spheres, then the electron would have a volume of over six billion times larger than the proton, given that the electron has a radius of about 1835,791.. times higher than that of the proton and 1835,791..³ = 6.186.859.530  (a number that is very close to 1/ɸ · 10¹⁰). We also  have to note that the constant which serves to determine the relation between the gravitational force and the magnetic one expressed by an electron, which is about 4.17, is also very close to the ratio between the constant figures ​​that determine the volume of the circle, since 4π/3 = 4.188…: considering the littleness of the measurements involved, it could be possible that the value determined geometrically could be more accurate than the one determined by the “classical”, empirical way.

But this does not seem the case, because if we make the proportion between the relation between the magnetic and the gravitational force expressed by proton with which of the electron, we realize that the result is determined by a value very close to 1835,791.. squared, and not raised to the cube

4,17 · 10⁴² : 1,24 · 10³⁶ = 3,3629032258 · 10⁶ = 3362903,2258

We have to note that this number seems very characteristic, as it seems an integer multiplier of 72 and of the  6^th power of 6, with a difference practically identical to 2 · 1835,79.. as we can see below

 

72 · 6⁶ = 3359232 ≈ 3362903,2258 (-3671,2258 ≈ 2 · 1835,79.. = 3671,58

 

Anyway, if we calculate the square root of this number , we see that

√3362903,2258 = 1833,822 …

 

Considering little errors and, above all, the inevitable quantum fluctuation to which are subject all the atomic constants, we can hypothesize that this ratio corresponds to 1835,791² or to 1836². Who knows, maybe this could mean that electron and proton must be considered as bi-dimensional entities, not  as three-dimensional ones. This, in turn, could mean that the modern scientific theories that consider the third dimension – the depth – as an illusion would find another foundation: and this could be the profound meaning of the adoption of the two-dimensional representation by the Ancient Egyptians .

Furthermore, if we make the ratio between the classic radius of electron and proton – excluding the powers of 10 – we obtain another interesting result, as

 

r_e/r_p = 2,8179403267 : 1,535  = 1,8357917437785016286644951140065

 

First thing, we have to notice that raising this number by the power of itself, we obtain a number very near to the diameter of the proton d_p = 3,07

 

1,835791743.. ^{1,835791743…} = 3,050175.. ≈ d_p = 3,07

 

Furthermore, if we make the ratio between r_e/r_p and the particular approximation of electric charge of proton and electron c_u that we see below we have that

 

1,835791… : 1,60217653 … = 1,145810692…

 

This number appears extremely meaningful, because it results practically identical to 1 + 1/ɸ⁴. In fact

 

1 + 1/ɸ⁴ = 1 + 0,145898.. = 1,145898…

 

As we can see, the difference with the constant empirically measured is only of about 8 · 10^-5 (curiously, the 8 and the 5 are the sixth and the fifth number of the series of Fibonacci. Their product gives us the result of that 40 that we find continuously in the Old Testament).

To this result we can add those that we have find above, that we write again to avoid to the reader the trouble to come back to the previous pages, where we have seen that excluding the powers of 10 and making the reverse ratio between the classic radius of proton and of electron, we find that

 

r_p/r_e = 1,535 : 2,817940367 = 0,54472408….

 

This number, raised to the cube, results 0,161632…, a figure this time extremely similar to ɸ/10. This proportion seems very characteristic, because if we make the cube root that

 

³ √(ɸ/10) = ³ √0,1618033988… = 0,544915..

 

At this point, we cannot help but conclude that the golden number has actually a very big importance in the internal relation between the physical quantities which determine the proton and the electron, as we recall that multiplied by 2 and then raised to the sixth power r_p/r_e gives us

 

 (0,54472408… · 2)⁶ = 1,08944817…⁶ = 1,672012..

 

this is a value extraordinarily similar to the one of the constant that we use to calculate the rest mass of the proton, that results equal to about m_p = 1,6725. Considering the quantum fluctuation of the atomic constants, we can suppose that the value of the relations that we have analyzed could actually correspond to  1 + 1/ɸ⁴ and to ³√(ɸ/10).

This fact seems very important, because it could explain the reason why Ancient Egyptians was so deeply interested in codifying as ɸ as π into the Big Pyramid: that was probably why we can describe the logical-physical and geometrical-mathematical form of all the events that happens in the world by these two numbers.

 

 

 

The connection of the reverse ratio between the classic radius of proton and electron and their mass with the rest of their physical characteristics is completed by the discovery – by this time not so much surprising – that this ratio seems to have something to do also with the average distance of the first orbit from the nucleus in the Hydrogen atom, which corresponds to 1bohr = 0,53 · 10^-10 m. A number only apparently so anonym insignificant, as we can obtain directly from ɸ_Cheops, as

 

1/(2/ɸ_Cheops)³ = 1/1,23564310..³ = 1/1,88659706.. = 0,530054.. ≈ 1bohr = 0,53

 

We can obtain this number also from this rather simple function of ɸ

 

Ln (Ln (4ɸ – 1) = Ln (Ln 5,472135..) = 0,530433.. ≈ 1bohr = 0,53

 

In fact, if we make the ratio between 1bohr and the classic radius of the electron we see that

 

1bohr/r_e = 0,53 · 10^-10 : 2,8179403267 · 10^{– 15} = 0,188080632… · 10⁵ = 18808,0632…

 

If we make the same operation with the classic radius of the proton we get instead to this result

 

1bohr/r_p = 0,53 · 10^-10 : 1,535 · 10^-18 = 0,345276872964 · 10⁸ = 34527687,2964…

 

This relation seems very peculiar and so very important, because it seems based on the Euler number and on 1/ɸ, as

 

[Ln (Ln 34527687,2964…) – 1]/3 = (2,854011.. – 1)/3 = 1,854011../3 = 0,618003.. ≈ 1/ɸ = 0,618033..

 

Anyway, if we divide this number by the one that we have obtained with the electron, obviously we have that

 

(1bohr/r_p)/(1bohr/r_e) 34527687,2964… : 18808,0632… = 1835,791

 

That is, we find again the number that defines the reverse mathematical relation that exists between the classic radius and the mass of proton and electron.

Instead, if we divide by 10 the figure regarding the proton and then we make the square root we have

 

√[(1bohr/r_p ) : 10] = √(34527687,296… : 10) = √3452768,7296… = 1858,162729

 

This number seems to assume some kind of meaning because, in first place, if we divide it by 10³ raise it to the power of itself, we discover that it is practically identical to that number that, raised to the power of itself, give us √10. In fact

 

(1858,162729../10³) ^{(1858,162729../1000)} = 1,858162729..^{1,858162729..} = 3,16228774.. ≈ √10 = 3,16227766..

 

Actually, the approximation of 10 that we can get from it seems really very good. So good that, considering the quantum fluctuation of the atomic constants, it would be easy to build the equation in a way to obtain a value of √10 absolutely exact

 

3,1622877..² = 10,00006380..

 

In second place, it seems to establish a mysterious proportion between the radius of the first orbit and those of the proton and the electron, as alluding to another constant.

The reason is this: if we divide the value regarding the electron by 10 and then we make the ratio with this new number, we find that

 

[(1bohr/r_e)/10] : √[(1bohr/r_p ) : 10] = (18808,0632 : 10) : 1858,162729 =

 

= 1880,0632 : 1858,162729  = 1,012186…

 

If we make the proportion between 1858,806.. and the ratio between the classic radius of proton and electron we find another time that

 

√[(1bohr/r_p ) : 10] : (r_e/r_p) = 1858,162729 : 1835,791.. = 1,0121864248..

 

1835,791.. · 1,012186..² = 1880,80628..

 

This number (1,012186…) corresponds rather exactly to the ratio between the value of h that nowadays is considered more accurate (6,626) and the one that was measured by Planck at the beginning of the last century (h_p = 6,55), as

 

6,626 : 1,012186.. = 6,5462.. ≈ h_p = 6,55

 

This number has another strange characteristic. If we multiply it by 10 and then we make the square root, we obtain a result very similar to 10/π, as

 

√(1,012186.. · 10) = √10,12186.. = 3,181487.. ≈ 10/π = 3,183098..

 

This kind of regularity could be very important, because we know that the distances of the orbits of the electrons from the nucleus are intimately connected with their energetic state, in turn connected with the main quantum number. So that constant that we have just discover could be at the basis of an intimate relation between the various radius that characterize the atom and the different kind of energies connected with them (for instance, between the mass and the connected gravity field of an electron and its wavelengths).

This means that the Ancient Egyptian theory of the unified fields would be, so to speak, a sort of generalization of the general relativity, in which the space – intended as the ratio between the classic radius of electron and proton – enters in the definition of the mass, of the charge and of the distance between the orbits from the nucleus, and vice versa.

That the Ancient Egyptians had come to an idea of this kind is a possibility to take into account not only in reason of all that we have seen into this article, but also from the proportions that we are going to show.

If we make the classic radius of the electron equal to 1, we see that the one of the proton corresponds to 1/1835,791 times this measure. If we round off this number to the superior figure (1836) and then we divide it by one of the two typical numbers (1461 and 1460) of the Dog Star cycle we have that

 

1836 : 1460 = 1,2575342465753424657534246575342

 

If we take this result, we raise it to the second power and then we multiply it by 2 we have that

 

1,2575342465753424657534246575342² · 2 = 3,162784762….

 

This number is extremely near to 10 times the cosine of that angle of 71°,553152.. (equal to 0,316424..) that we have seen above. We recall that its tangent is 2,997946 (that is identical to c ) and that multiplying the cosine of this same angle (0,316424..) by the tangent and then doing 1/x we have obtained a number equal to 1,054165.., which corresponds in a good way to ħ, the figure of the Dirac constant, with which often we substitute h, the Plank constant (ħ = h/2π = 1,054571..). Considering that, as we have seen, we can obtain a better approximation to this number adding up the sine, the cosine and the tangent of an angle equal to π/2, maybe we can say to have discovered that – someway – between geometry and reality there is no more any kind of difference. All those results that we have arrived to through means of long and arduous empiric researches could be deducted by means of pure geometrical conjectures, carried on with a completely a priori  method.

Who knows, maybe this is the reason why Plato gave so much prominence to geometry and mathematics: because in the ancient, hermetic scientific tradition there was not any difference between the empiric world, object of the sense, and the abstract, mathematic one, object of the thought .

 

 

 

In fact, if we try to summarize and put a little in order the results achieved during this perhaps a little too tortuous research, we see that they are quite meaningful. First, we will see in succession the values ​​of classical radius and mass of the electron and proton

 

rest mass of electron m_e = 9,1091 · 10^-31 kg

 

rest mass of proton m_p = 1,6725 · 10^-27 kg

 

classic radius of electron r_e = 2,81777 x 10^-15 m

 

classic radius of proton r_p = 1,535 × 10^-18 m

 

As we have already seen, at least in part, the relationships that we can build from these values ​​seem very interesting. They will become even more interesting when we realize that – once we have removed the powers of 10 – they correspond almost perfectly to various kind of mathematical relations between π and ɸ

 

m_e/r_e =  9,1091.. : 2,81777.. = 3,232733…  ≈ 2ɸ = 3,236067…

 

m_p/r_p =  1,6725 : 1,535 = 1,089576.. x 10^-9  ≈ (2ɸ/π)³ = 1,092957…

 

But, as we have seen 2ɸ/π corresponds almost perfectly to the relationship between the number of days of a solar year with that of the moon phases, since

 

365,25 : 354,36 = 1,0307314.. ≈ 2ɸ/π = ​​1,030072..

 

So the difference with the value that comes out of (m_p/r_p)³ is really negligible. And in fact we see that, as the ratio remains almost identical since m_e/r_e ≈ 2ɸ, we have that the proportion with ³√m_p/r_p should give us a number very close to π .

 

³√m_p/r_p = ³√1,089576… = 1,029009…

 

(m_e/r_e)/ ³√ m_p/r_p = 3,232733686…. : 1,02900917… = 3,141598… ≈ π = 3,141592…

 

Actually, the difference with π results at the end of circa 6 · 10^{– 6}. That seems a first, very important proof that the internal, mathematical relation between the constants that describe the atomic entities are based on the same numbers that are encoded in the Big Pyramid, that’s to say π and ɸ.

Given the context it seems very important to notice that a figure very near to 2ɸ comes out also from the number of the days of the lunar year

 

 ⁵√354,36 = 3,235109.. ≈ 2ɸ = 3,236067.. (-0,000958..

 

The number of days of the lunar year seems to have a relation with ɸ also by means of π_Cheops, if we use it as exponential of the root, as

 

 ^πCheops√354,36 = 6,474212467.. ≈ 4ɸ = 6,47436136.. (-0,000148..

 

where from the 13^th square we have an incredibly good approximation to π/2, as

 

 ¹³√354,36 = 1,570764.. ≈ π/2 = 1,570796..

 

This means that we can reconstruct the ratio 2ɸ/π using only the number of days of the lunar year as

 

⁵√354,36/2 · ¹³√354,36 = 3,235109.. : 3,141528 =

 

At the end, no one will now be astonished if also the constant of Bohr regarding the radius of the first orbit of the electron around the nucleus of the hydrogen atom can be derived in a very well approximated way from a function of ɸ. The value of this radius is 0,53 x 10^-10 m. We can obtain the constant 0,53 this way

 

1/(1 + 1/ɸ³)³ = 0,5295.. ≈ 1bohr = 0,53

 

So, if the length of the wave is λ = 2πr/n, where n is the series of the natural numbers, now we can obtain it by a function of π and ɸ, that we can write this way

 

λ = 2π [1/(1 + 1/ɸ³)³] /n

 

All that we have just seen acquires even greater significance when we become aware that all that harmonic relations that we found between the constants of physics without the powers of 10, continue to exist even when we make the calculation including these parts, as we can see by means of the below equations

 

⁵¹²√(1/m_e) = ⁵¹²√[1/(9,1091 · 10^-31)] = ⁵¹²√1097803295605493407691209889012,1 =

 

= 1,144650492.. ≈ Ln π = 1,144729885.. (-0,000079..

 

√(1/m_e) = 1,04776108.. · 10¹⁵ ≈ π/c · 10¹⁵ = 1,047922503.. · 10¹⁵

 

⁴√(1/m_e) = 3,236913787.. · 10⁷ = 2ɸ · 10⁷ = 3,23606797.. · 10⁷  

 

¹²⁸√1/m_p = ¹²⁸√(1/1,6725 · 10^-27) = ¹²⁸√597907324364723467862481315,39611 =

 

= 1,618797228.. ≈ ɸ_Cheope = 1,61859034.. (+0,0002068..

 

⁸√1/m_p = 2,223715.. · 10³ ≈ 2ħ² = 2,224242.. · 10³

 

¹⁴⁴√1/m_p = 1,534436.. ≈ r_p = 1,535

 

⁴³²√1/m_p = 1,153407.. ≈ 1 + r_p/10 = 1,1535

 

1/r_e = 1/2,81777.. · 10^-15 = 354,890569.. · 10¹² ≈ lunar year · 10¹² =  354,36 · 10¹²

 

√1/r_e = 1,883853.. · 10⁷  ≈ (2/ɸ_Cheope)³ · 10⁷ = 1,886597.. · 10⁷

 

√(2 + lunar year/10³) = √2,35436 = 1,534392.. ≈ r_p = 1,535

 

 

 

These ɸ-π relations between the constants have obvious consequences on the equations regarding the dynamic values ​​of elementary particles in which they are placed. From what we have seen above, we have that the electron mass can be derived from its radius by this simple equation

 

m_e/r_e = 9,1091 : 2,81777 = 3,23273… ≈ 2ɸ

 

so we have that

 

m_e = r_e · 2ɸ

 

As demonstrated, the famous De Broglie’s equation about the wavelength

 

λ = h/m_e v

 

could be transformed in this way

 

λv = h/m_e = (sine π/2° + cosine π/2° + tangent π/2°) x 2π/r_e x 2ɸ

 

But if we put equal to 1 the classic radius of electron, we have that the equation becomes a simple function of π and ɸ

 

λv = h/m_e = (sine π/2° + cosine π/2° + tangent π/2°) x 2π/2ɸ

 

Above we have seen that

 

λ = 2π [1/(1 + 1/ɸ³)³] /n.

 

So we have that we can transform this formula in this way

 

 {2π [1/(1 + 1/ɸ³)³] /n} v = (sine π/2° + cosine π/2° + tangent π/2°) · 2π/2ɸ

 

so v is equal to

 

v = [(sine π/2° + cosine π/2° + tg π/2°) · 2π] : {2ɸ · {2π [1/(1 + 1/ɸ³)³] /n}}

 

Or, the famous uncertainty principle developed by Heisenberg could become

 

Δ_x Δ_p ≥ 1/2 ħ = Δ_x Δ_p ≥ 1/2 sine π/2° + cosine π/2° + tangent π/2°

 

or

 

Δ_x Δ_p ≥ 1/2 ħ = Δ_x Δ_p ≥ 1/2 · ⁹√ɸ

 

With a procedure of this kind we can derive the characteristic number of the constant that  we need to determine the radius of the proton (1,535), and the ratio (1835,791) that binds it to that of the electron. We’ll start again from π, however, in the approximation that we find into the Great Pyramid, which corresponds to the Pythagorean fraction 22/7

 

r_p = (22/7 : 2) : {1 + [(1/ɸ³) : 10]} = (3,142857… : 2) : {1 + [1/0,618033…³] : 10]} =

 

= 1,57142857… : [1 + (0,23606… : 10] = 1,57142857… : 1,023606… = 1,53518…

 

We can derive the constant of the mass from the classic radius, first calculating the diameter and then dividing it by the constant (1,835791..) that establishes (or, we could say: whose meaning is) that the mass is inversely proportional to the dimension of the radius. As the diameter is expressed in meters and the mass is expressed in kilos, we have that this relation seems to allude to an hidden proportion between the meter and the kilo systems based on π and/or ɸ

 

d_p = (r_p · 2) = 1,535 · 2 = 3,07

 

d_p : 1,835791 = 3,07 : 1,835791 = 1,672303.. ≈ m_p = 1,6725

 

We can derive the figure of the unitary charge c_u dividing that same constant (1,835791) by 1 + 1/ɸ⁴

 

1,835791 : (1 + 1/ɸ⁴) = 1,835791.. : 1,145898.. = 1,602054.. ≈ c_u = 1,6022

 

Two possible methods to derive the constant equal to 1,835791 are these that we see below

 

³√(1/ɸ · 10¹⁰) : 10³ = 1,835146..

 

Or, using a rather good approximation of π (3,1438, which differs from the actual of π less than 3 thousandths) we could write

 

10^3,1438.. + (10^3,1438../3,1438..) = 1392,51537.. + 442,94019.. = 1835,45557..

 

With the actual figure of π this same formula gives this result

 

10^π + (10^π/π) = 1385,455.. + 441,004.. = 1826,45998..

 

It seems also very meaningful that 1835,791.. is a number that gives very interesting results also if we do the ratio with the round angle or, as we could say, with the number of “pure” days of the Ancient Egyptian and Maya calendar

 

1835,791.. : 360 = 5,0994.. ≈ π_Cheops · ɸ_Cheops = (3,142857.. · 1,61859..) = 5,08699..

 

1835,791.. : 360² = 0,014165.. ≈ (π – 3) : 10 = 0,014159…

 

Anyway, in a more simple but a little less precise way, we can derive the ratio between the classic radius of the electron and which of the proton also by this formula

 

2/ɸ³ – 1/ɸ⁶ = 1,832815…

 

This number – that results a little inexact in relation to the constant which determines the inverse ratio between the mass and the radius of proton and electron – is instead practically perfect to define the ratio between the magnetic force (F_mp e  F_me ) and the gravitational one (F_gp e F_ge)  expressed by a proton and by an electron. For convenience we see again the calculations that we have made above

 

F_me/F_ge = 4,17 · 10⁴²

 

F_mp/ F_gp = 1,24 · 10³⁶

 

4,17 · 10⁴² : 1,24 · 10³⁶ = 3362903,2258

 

If we make the 8^th root of this figure we get very near to the approximation of the Planck constant that was calculated by the same Planck at the beginning of the last century. A result that we can achieve also by means of the ratio between the fourth and the fifth number of the Fibonacci series as

 

⁸√3362903,2258 = 6,543.. ≈ h_Planck = 6,55 ≈ (8/5)⁴ = 6,5536

 

But making the square root we have seen that

 

√3362903,2258 = 1833,822…

 

A number that  corresponds in a way that appears very meaningful with which we have just seen above (2/ɸ³ – 1/ɸ⁶ = 1,832815..). Curiously, this figure could be obtained also on the basis of the number of elemental particles known by the Dogon culture, that is 266 as

 

266 · (2π + 1/ɸ) = 266 · 6,901219… = 1835,724.

 

Anyway, also forgetting this last archaeo-scientific  curiosity, now we know that we can transform all the equations of the “old” quantum mechanics in functions of ɸ and π. And just this – mathematical functions of ɸ and π – could be the ones that Plato called “elements”. As in his thinking – as indeed in the Ancient Egyptian one – there was no difference between abstract theory and geometrical-mathematical reality, a totally abstract mathematical function could represent as well an element of microscopic reality, or a cosmic cycle, etc.

 

 

 

But we will treat this subject in a successive work, as in this moment it seems more important to underline that the reverse proportion between the radius and the mass of electron and proton could be the starting point to get to that theory of the unified fields that probably Ancient Egyptians had already conquered at the time of the construction of the Pyramids of the so called IV Dynasty.

Into this theory the gravitational field would result a sort of emanation of a particular distribution in the space of the magnetic field; or, vice versa, as the measurements are connected by means of the radius, the magnetic field would result a particular distribution in the space of the gravitational field (and so of the mass). This is not – in an absolute sense – a novelty, as the relativity theory had already affirmed that the energy could be thought as a state of the matter, and the matter as a state of the energy. This way, we would have explain also the origin of the monophysism as a religious theory: if these hypothesis would correspond to reality, we would have that each entity is at the same time the others, and that all of them are One.

In a theoretical scenario of this kind, the space itself should be considered as a force: this way, the meaning of d² into a formula like the one  of Newton would change completely. This value would no more to be intended as the passive effect of an amorphous entity (the distance) but as the action of a force that contrasts the effects of the mass on other mass. So, a sort of force of gravity with a minus sign (and this could be the base of a kind of dynamo capable to wheel transforming the gravitational field in a magnetic one).

This fact, on the moment, could be shocking, or seem completely incomprehensible. But, actually, this is no more than the relativity theory carried on at its extreme conclusions: if mass can have an effect on the space-time, why space-time should not have an effect on the mass?

We realize that in this moment the argument could appear premature, but in a later work we will demonstrate that the ratio between the meter of the Great Pyramid and the one currently in use in the West is almost identical to G/h. This way we will also demonstrate that the Ancient Egyptians possessed both of these units, as well as the cubit , the medium cubit , etc. (the source of all their units of measure for the length seems to be a millimeter equal to ≈ 1,0066 of our millimeters). We recall that the magnetic charge of an electron expresses a force equal to 4,17 · 10⁴² in relation to the one that is expressed by its gravitational field, and that its mass is about 1/1836 the one  of the proton. Doing  x = 4,17/1836 and then 1/x we obtain 440,27.., a number that at a numerological level corresponds in an almost perfect way to the length of one side of the Big Pyramid. We can obtain a very good approximation to this constant also via cosmological, by the duration of a Precessional Day expressed in solar years

as

 

 ³√(26000 : 360) = ³√72,222… = 4,1644..

 

If instead we divide 1835,791.. by one of the two typical numbers that in the Ancient Egyptian culture were the symbols of the Dog Star cycle (1460 and 1461), and then we do the square of the result, and at the end we multiply it by 2, we got another time to a very meaningful scientific and mathematical result, as

 

1835,791 : 1460 = 1,257391…² · 2 = 3,16206473.. ≈ ħ · c =3,161526.. ≈ √10 = 3,162277..

 

This kind of relations seems to indicate that also into the structure and the more important dates of the ancient calendar we can find a scientific meaning. One of most important religious feast was celebrated the seventeenth day of the first month. This means that we can write this date 1,17. Well, this figure is the one through which the measurements of the Djedefre sarcophagus were determined, and if we divide  the round angle by this figure we get to the diameter of the proton multiplied by 10²

 

360 : 1,17 = 307°,692.. ≈ d_p · 10² = 307

 

The inverse of the tangent of this angle corresponds to √π – 1 (the value of the tangent is negative: to make simpler the formula, we will consider directly it as positive)

 

(1 + 1/tg 307°,692..) = (1 + 1/1,294207878..)² = (1 + 0,772673..)² = 1,772673..² =

 

= 3,142370.. ≈ π  = 3,141592..

 

This means that we can get both to the diameter of the proton and to the date of the Ancient Egyptian feast starting from π, as

 

tg x = -1/(√π – 1) = -1,294575..;       x = 307°,684.. ≈ d_p · 10² = 307

 

360° : 307°,684.. = 1,170029.. ≈ date of Ancient Egyptian feast

 

We have to notice that we could get to a very similar result by means of ɸ in the way that we see below

 

1/(3/ɸ – 1) = 1/0,854101966.. = 1,170820..

 

 

 

The scientific investigation expected to understand the meaning of the Great Pyramid is, therefore, about this kind of concepts and theories. We can assume that it will be much, much more difficult than what we would expect from a culture which from the point of view of our official archeology had a mathematics and an astronomy at the level of our elementary schools, or little more.

Furthermore, we have to consider that already in this moment the results of this research drives us to put problems that were completely unimaginable.

In the Graham Hancock book “The Sign and the Seal. A quest of the lost Ark of the Covenant” (Chapter Six) we read about a fact that at first sight appears rather insignificant.

In the middle of the XIX century a delegate of the Fathers of Armenia went to visit Abyssinia. His intention was to prove wrong the idea that in the whole nation people firmly believed,  that the Ark of Alliance had been transported to Axum, and that it was still kept there. After having questioned for long time the Axumitas priests, the delegate, which name was Dimotheos, convinced them to show him a reddish marble table. Its length was circa 24 cm, its width 22 cm and its thickness 3 cm. According to the Axumitas priests this was one of the two marble boards that were contained into the Ark. So, the whole volume of these two table is equal to

 

(24 · 22 · 3) · 2 = 3168 cm³

 

If we divide this number by 10⁴ we have a result of 0,3168, that is the cosine of an angle very near to that which tangent is identical to the constant from which we get the speed of light as

 

cos x = 0,3168 ≈ √10/10 = 0,3162277..;          x = 71°,5304..;     

 

tg 71°,5304.. = 2,9939784.. ≈ c = 2,9979246 (-0,0039462

 

Instead, if we divide 3168 by 3 · 10³, we get to a result very near to the Dirac constant as

 

3168 : 3000 = 1,056 ≈ ħ = 1,054571..

 

To get to measures capable to give us the constants of our more fundamental physical laws, it is sufficient to imagine that they were taken with a (very) little imprecision. On the other side, given the proximity of the Israeli and Ancient Egyptian culture at that time, it’s reasonable to think that the two board were conformed in a similar way and with a similar purpose as the plate that was found at the end of the Southern Shaft of the King Chamber. It is useful to notice that the cosine of the angle that we have be numerologically obtained through the volume of the Ark, corresponds with good approximation to 1/10 of the constant from which we can obtain the Newton constant from ħ. And The formula is 2 · 3,1626501.. · ħ = 6,67, so that the difference with the cosine of 71°,5304.. is

 

3,1626501.. – cos 71°,5304.. · 10 = 3,1626501.. – 3,1680145.. = -0,005364..

 

We can get to a better result directly by ħ and c, as

 

ħ · (ħ · c) · 2 = ħ² · c · 2 = 1,112121.. · 2,9979246 · 2 = 6,668112.. ≈ G = 6,672

 

Now, if we recall that 10 raised to 3,1646… gives a result equal to 1461, the length of the cycle of Sirius, we get to the conclusion that we have find a numerological connection between the volume of the Ark, the plate found at the end of the shaft of the Great Pyramid, and two very important physical constants, that is ħ and c. This connection is not perfectly exact. But we know that in the ancient times the possibility to establish a symbolic relation was more important than the exactness of the numbers involved: a Precessional Day has a duration of 72,222.. years, but in the myth always appears the 72, because, for example, it was impossible for Jesus too to send in mission 72,222.. apostle, or to Seth to kill Osiris with the help of 72,222..conspirators. Nevertheless, no reasonable historian has any doubt about the fact that the 72 alludes to the duration of a Precessional Day.

 

 

11.

 

Following the Old Testament, the Ark that contained the two stone boards measured 2,5 cubits of length, 1,5 cubits of width and of height. These measures appear very meaningful. The length divided by the width gives a result of 1,666.., very similar to the golden number (1,618033988..) and identical to the constant that we use to transform the sixtieths of a degree in hundredths of a degree and vice versa. But it is not impossible that these measures were transcript with a slight error, to avoid to reveal an hermetic secret, represented by more meaningful numbers. After what we have seen, it is spontaneous to imagine that the Ark could be 2,618033988… cubits (ɸ²) of length, with a width and a height of 1,618033988.. (ɸ). We have to recall that ɸ/π = 0,515036…: numerologically this cipher is very similar to the inclination of the Cheops Pyramid that, measured in degrees and sixtieths of degree, is more or less 51° 51’, that’s to say ɸ/π · 10².

At any rate, this way of doing the measures of the Ark conserves some very clear allusions as to ɸ as to π. We can assume that the unity of measure was one half of a cubit. This way its length is equal to 0,5 multiplied by 5,  its width and height to 0,5 multiplied by 3. So we can construct this proportion, characterized by 5 and 3, the fifth and fourth numbers of the series of Fibonacci:

 

(2,5 · 1,5 · 0,5) : 3 = 0,625 ≈ 1/ɸ = 0,618033988..

 

This fact seems very important as above we have seen that we can reconstruct the constant of Planck by the sixth and the seventh numbers of the Fibonacci series (8 and 13) in this way

 

(13 – 8) + 13/8 = 5 + 1,625 = 6,625 ≈ h = 6,626

 

So, we can reconstruct the same constant also by the measurements of the Ark, adding 1 to its volume

 

1 + (2,5 · 1,5²) = 6,625 ≈ h = 6,626

 

Multiplying 0,625 this number by 5 we have that

 

0,625 · 5 = 3,125

 

a number very near to the approximation to π that we find in the sarcophagus of Djedefre. Furthermore, the tangent of an angle of 3°,125 is equal to 0,054595…, a number practically identical to ħ – 1; obviously the same it is true also for an angle equal to π, as the angle of π° has a tangent equal to 0,054886..

The 2,5 cubits of length result meaningful in connection with the round angle (and so also in connection with the number of the “pure” days of the Ancient Egyptian solar calendar) because

360 : 2,5 = 144, a number that corresponds to 2 Precessional Days in round figures (72 · 2 = 144) and also to the 12° number of the series of Fibonacci. Furthermore, the square root of 144 is 12, the number of months of the Ancient Egyptian solar calendar (we notice that this numerological connections, that to us are nothing, in ancient time were seen almost as the notes of that divine harmony that was thought to be the secret Law of the universe).

The cycle of Sirius, divided two times by c² and then by 10² gives a result equal to

 

1461 : (2,9979246²) : 100 = 1,625581 ≈ 13/8 = 1,625

 

So it is spontaneous to hypothesize that what was called “Ark of the Covenant” or in much later times “Graal”, was the star Sirius – heavenly correspondent  of the goddess Isis – and the numbers associated with its cycle, which in turn contained the numbers of those fundamental physical laws that give man power over nature (so it seems to become clear that the stories that tell about the Ark that goes from  mount Sinai to Israel, and then from Israel to Ethiopia, are more than an hermetic way to allude to astronomical observations that first are possible in a place and then in another). This hypothesis is strengthened by the fact that some centuries later the Christianity called the  Virgin Mary “Ark of the Covenant”. And the links between the figure of the Virgin and that of Isis-Sirius are clear from the Apocalypse. Among the many other things that we could say to prove this historical fact, it seems very meaningful that in Egypt it has been found a figure representing Isis standing on the Moon and crowned with 12 stars, exactly like the woman persecuted by the dragoon of which it is told about in  the Apocalypse (it is easy to hypothesize that the Apocalypse dragoon could be a transfiguration of  Seth).

This way, we would have given a satisfying explanation to the mystery of Flegetanis, the character of the Wolfram von Eschenbach Parzival that was capable «to see the secrets hidden into the constellations (and that) declared that there was a thing called Graal, of which he clearly read the name in the stars».

 

 

12.

 

The ties between the Jewish culture and the Ancient Egyptian were until now ignored or radically underestimated. It is therefore very useful in this context to remember that, according to the biblical law, it is considered Jew who was born from a Jewish mother, not from a Jewish father. But we should note that the wife of Abraham was barren (also if miraculously she had a son in a very hold age). Hence, the first Eva of the Jewish people was an Egyptian woman, that was a wife servant. So, if we follow the testimony of the Old Testament, we must think that the Egyptian people and the Jew one are nearly the same blood, because, following the matrilineal ideas, Israeli descends for one half from an Egyptian mother (at least if we have to consider the descendants of the first Abraham son as a part of the Israeli people).
So it is not surprising that even in the numbers connected with the Deluge and the Ark of Noah probably we can find some hermetic allusions  to an Ancient Egyptian wisdom that could have been absorbed by Israel with the mediation of Moses that – as we all know – following the Israeli tradition was adopted by the daughter of the Pharaoh and brought-up as an Egyptian noble.

For instance, let’s take the numbers connected with the dates of the Deluge

 

17° day of the 2° month

17° day of the 7° month

1° day of the 10° month

1° day of the 1° month

27° day of the 2° month

 

Now, if we make the summation of the numbers referred to the months (= 22) and of those referred to the days (= 63) and then we make the multiplication we get to 22 · 63 = 1386, a number that at first sight seems rather insignificant. But if we make the ratio with the typical number of the cycle of the Dog Star, so important to the Ancient Egyptians, we have

 

1461 : 1386 = 1,054112.. ≈ ħ = 1,054571..

 

A number very similar comes up also in the Timaeus, when Plato says that the minimum harmonic  interval used by the Creator to generate the Universe was 256/243. This ratio gives a result of 1,053497, a number that is one more time rather near to ħ. This number comes out also from the ratio between the number of days of a solar year and which of a so called “year of eclipses”, or also doing the (346,6 : π) root of 346,6, as

 

365,25 : 346,6 = 1,053808.. ≈ ħ = 1,054571..

 

 ^{346,6 : π}√346,6 = ^110,32…√346,6 = 1,05448.. ≈ ħ = 1,054571..

 

It seems worthy of note also the fact that

 

[(346,6 : 100) : e]² = (3,466 : 2,718281828459..)² = 1,275070..² = 1,625803…,

 

a number that reminds us anew  the measures of the Ark.

And in the Big Pyramid too, we find something similar. If we consider that we can derive its fundamental measures in cubits from the pure days of the solar year (360) adding and subtracting 80, we can construct the proportion

 

(360 : 280) : (440 : 360) = 1,051948.. ≈ ħ = 1,054571..

 

We can obtain a number very similar to this using one of the typical numbers of the Dog Star cycle, as

 

 ^{1460 : 10}√1460 = ¹⁴⁶√1460 = 1,05117

 

We note on passing that the height of the Big Pyramid expressed in meters is equal to 146,56: if we divide the typical Dog Star Cycle number by 10 we immediately see the a numerologic connection between 146,5 and 146,1 or 146. It seems remarkable also the fact that dividing the typical number of the Dog Star cycle by one half of the Big Pyramid perimeter we get to

 

(1461 : 440) : 2 = 1,6602..

 

this is the same result to which we arrive dividing it by the height and then by π, as

 

(1461 : 280) : π = 1,6608..

 

We can get an  even much interesting result, dividing the other typical number of the Dog star cycle, 1460, by the height of the Khefren Pyramid as

 

1460 : 143,5 = 10,1742…≈ 2ɸπ = 10,1664..

 

Dividing the number of days of the year of lunar phases by this same number we get to

 

354,36 : 143,5 = 2,4694.. ≈ π/2² = 2,4674..

 

Repeating the same operation with the duration of the solar year we get instead to

 

365,25 : 143,5 = 2,5452…≈ πɸ/2 = 2,5416..

 

Utilizing the “pure” days of the solar year we can obtain

 

360 : 143,5 = 2,5087 ≈ 3,16/2² = 2,4964.

 

In addition to this, we can’t avoid to notice that the Dog star cycle – divided by the number of days of a “Year of Eclipses” – gives another time a very interesting result, as

 

³√1461 : 346,6 = 1,61537.. ≈ ɸ = 1,618033..

 

Instead, divided by a year of lunar phases, the result is

 

1460 : 354,36 = 4,1201 ≈ (ɸ_Cheops²/2) · π_Cheops = 4,1168..

 

With our research we would then come to the point to understand the meaning of those strange legends that go about the Ark of Alliance. If for instance, it contained symbolically scientific secrets about light and radioactivity, here is the explication of the strange fact that Moses face became intolerably bright when descending from the mountain where he received it from God himself. This would be not a real fact, but a mythical allusion to the scientific power that was hermetically contained in the measurements and therefore in the numbers that define the Ark. As we have seen above, an ordinary iron plate can contain the fundamental numbers of an entire science. This way, the brightness of Moses face can become the symbol of the powers that can be obtained from science.

That means, for instance, that to knock down the walls of Jericho was not the Ark itself, but the power of the wisdom that was codified in it, that in the myth it is symbolically ascribed to the Ark in an immediate,  direct way. This is a way to conceive things that could  appear at first sight a little strange to us, but, with a little effort, we can understand it. It would be as if we said that it was Einstein to destroy Hiroshima and Nagasaki, or that actually it is him that made the nuclear power stations work. In a literal sense these descriptions are surely misleading. But, if we speak in a moral or symbolic way, these are surely a kind of truth. At the end, Einstein himself felt morally (and so symbolically) responsible for the destruction power that was obtained from his theory.

 

 

13.

 

In conclusion, we can say that that wonderful and almost miraculous system of congruences of astronomical-physical and metrological-trigonometric kind that we have found in these pages cannot be a case. That there is a decimal system in which ¹³⁰√10³ has as a result the fundamental constant of quantum mechanics (that is ħ, that in this approximation is ¹³⁰√10³ = 1,054573..), which is in turn coded in the angle corresponding to the division between the exponent of the root and that of the power, which in turn corresponds to one of those angles which lie in the range of variation of the inclination of the polar axis of the earth in relation to the ecliptic: how can we define all this as a case?

It is enough to take a trigonometry in which the round angle is divided into any number of parts different from 360, or a different metrology, and here that this incredible system of correspondences blows up altogether. So it seems clear that the metric decimal system – and all that came as a result by its adoption – comes through hermetic traditions from unfathomable depths of time in which it was invented as a mathematical-musical instrument capable to create a miraculous harmony from the numbers of pure trigonometry, those of classical and quantum physics and those relating to the specific cosmic cycles of the Earth.

We cannot even exclude that in the distant past travelers coming from deep space – after a long pilgrimage – have chosen to settle in this planet because it was the only – or at least the first found – where the numbers of physics and geometry coincided with those of cosmic cycles (Percival’s arrival at the Castle of the Fisher King could allude to an event of this kind). No hypothesis now is too risky, given the impossibility that what we have seen in these pages can be attributed to chance.

Henceforth, studying geometry of Pythagorean tradition, we must ask ourselves: who was able to develop an abstract system that could match in so meticulous way with the quantities detected by the microscopic physics and with cosmology? In fact, if we make the sum of tangent, sine and cosine of an angle equal to π/2 we see that it corresponds to ħ; doing 1/x with x equal to the cosine of an angle whose sine is equal to 1/π (this is the angle of 18°,560744..), we find again ħ; if we raise to the second power the sum of sine and cosine of the same angle, we find a value very close to the elementary charge c_u = 1,6022 ; adding sine, cosine and tangent of that angle, we find the value of the elementary charge in person:

 

sin + cos + tg 18°,560744.. = 0,318309.. + 0,947986.. + 0,335774.. = 1,602071.. ≈ c_u = 1,6022

 

How w can we even dare to imagine that this is a system of coincidences? How can the coincidences form a system? A system of signs is always a sign of intelligence!

In an angle equal to 20ɸ = 32°,36.. the sum of sine and cosine is 1,3799 … , that is practically identical to the constant of Boltzmann, 1,380054 (and very near to 1 + 1/ɸ² = 1,381966..). Instead , in an angle equal to 100π the tangent is equal to -1,029788, that to say the sign minus of the ratio between the days of a solar year with which of one of lunar phases, that’s to say to 2ɸ/π. In an angle of 10π = 31,41592.. the tangent is equal to 0.61078 … , that is, once again a very good approximation of 1/ɸ. How can anyone believe that this is a miracle of chance? On the contrary, here it seems that we can prove – through these examples and through all the others that we have already done – that trigonometry mysteriously turns around ɸ and π, and that this happens because the trigonometric system was realized this way because reality itself revolves around these numbers.

This finding seems to demonstrate unequivocally that the man – if he descended from something – this is certainly not from the ape. And now it seems beyond doubt too that the wisdom that has come up with this mathematical wonder has roots in unfathomable areas of time and maybe even of space – of which perhaps we cannot even vaguely imagine the depth.

Perhaps the ultimate destiny of our dying civilization – the last destiny that is left to who is left without any destiny – is to discover the land in which these roots deepens. And it is good to hurry, because the time we still have is not so much.

 

Appendix 2 : THE PYTHAGOREAN TRIPLE OBTAINED FROM THE TYPICAL NUMBERS OF THE MAYA CALENDAR SYSTEM HAAB’-TZOLKIN IN COMPARISON WITH THE IRON PLATE FOUND AT THE END OF THE SOUTH STELLAR SHAFT OF THE KING CHAMBER

 

The typical numbers of the Maya calendar system Haab’-Tzolkin are, as we all know, the 18 and the 13. From these numbers – as from whatever couple of integers – we can obtain a Pythagorean triple, to which  a rectangular triangle corresponds, which has the following  dimensions

 

13² + 18² = 169 + 324 = 493 hypotenuse

 

18² – 13² = 324 -169 = 155 minor cathetus

 

2 x 13 x 18 = 468 major cathetus

 

sin α = 155 : 493 = 0,314401.. ≈ π/10 = 0,314159…

 

angle α = 18°,324694..

 

angle β = 71°,675305…

 

Here it seems important to notice that the summation of sine, cosine and tangent of this angle is equal to  4,28304…, while 2π – 2 = 4,28318…

 

Instead

 

1/(sin α + cos α)² = (0,31440162.. + 0,949290..)² = 1,263691..² = 1/1,596916..  = 0,626206.. ≈

 

≈ h – 6 = 0,626

 

Furthermore, if to this number we subtract 1 we get to 0,596916…, a figure very near to the result of the ratio between the constants of the magnetic momentum of the proton 2,793 and which of its rest mass, as 1,6726231 : 2,793  = 0,598862

 

The tangent of the angle β = 71°,675305.. is 3,019354.. The tangent of the angle β of the iron plate found at the end of the South Stellar Shaft of the King Chamber – corresponding to an angle of 71°,55315 – is equal to 2,9979246. The difference between these figures is equal to 0,021430.., and

 

⁸√0,021430.. = 0,618554498.. ≈ ɸ_Cheops – 1 = 0,61859034..

 

The ratio between the hypotenuse and the major cathetus is equal to

 

493 : 468 = 1,053418.. ≈ ħ = 1,054571..

 

This same ratio, in the case of the Ancient Egyptian iron plate, is equal to 1,05416554.., with a difference equal to 0,00074674. The difference with ħ = 1,054571.. is equal to 0,00115, this is a little more than 11 tenth thousands.

 

A very similar number comes out also in the Timaeus, when Plato reveals the minimum harmonic interval used by the Creator to generate the world, that is 256/243 = 1,053497.. In this case the difference with the Mayan number is equal to 0,0000782.

 

Another cosmic cycle, very important to the Maya, was the one of Venus. First thing, we can notice that Venus completes 13 revolutions around the Sun in the time in which Earth completes 8 of them. This ratio comes out from the fact that while Earth takes 365,25 days to finish his orbit, Venus takes only 225 days. This is the reason why the ratio between these cycles is equal to 365,25 : 225 = 1,62333…, that’s to say a figure very near to which that comes out from the two successive element of the Fibonacci series 13 and 8 (13 : 8 = 1,625). This result reminds us the other one that comes out from the Dog star cycle divided 2 times by the constant we need to calculate the speed of light and then by 100. Indeed, as we have already seen 1461 : (2,9979246) : 100 = 1,625 and also the measures of the Ark, which are characterized by a ratio of 0,625.

Putting in relation the cycle of Sirius with that of Venus we get again the same number, since

 

(1461 : 225) : 4 = 1,623333.. ≈ 13/8 = 1,625