ic: tzo minor fixes
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For the four percent of the universe that is considered by science as known and fairly well studied, the level of understanding still remains very far from what is usually called a clear picture. The list of vague, and sometimes completely dark areas can be made very long.
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As one of the fundamentally unsolvable problems, it is enough to mention the quantum phenomenon, named by Erwin Schrödinger as **Verschränkung** or "entanglement". [o4]
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As one of the fundamentally unsolvable problems, it is enough to mention the quantum phenomenon, named by Erwin Schrödinger as **Verschränkung** or "**entanglement**". [o4]
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Essentially, there is an instantaneous interaction of particles, predicted by formulas and confirmed by experiments, occurring completely independently of the distances separating them at any range. However, the nature and mechanism of this interaction are completely unclear… [i2]
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@ -20,7 +20,7 @@ And finally, another fundamentally important problem. It remains completely uncl
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The general essence of all the listed problems is that the colossal array of scientific knowledge accumulated by humans about nature cannot be assembled into a coherent and consistent picture.
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And there is a strong feeling that the reason for constant failures here is the absence of one extremely important connecting component in the description, generally referred to as "consciousness"…
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And there is a strong feeling that the reason for constant failures here is the absence of one extremely important connecting component in the description, generally referred to as "**consciousness**"…
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It cannot be said that scientists categorically refuse to notice and include this essential element in their theories. It is more accurate to say that no one has yet managed to do it nicely and convincingly.
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@ -38,6 +38,6 @@ However, there have been several moments in the history of science when research
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# Outside links
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[o4] Amir D. Aczel, "*Entanglement: the greatest mystery in physics*". Four Walls Eight Windows (2002); A. Bokulich and G. Jaeger (eds), "*Philosophy of **Quantum Information and Entanglement*", Cambridge University Press (2010)
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[o4] Amir D. Aczel, "*Entanglement: the greatest mystery in physics*". Four Walls Eight Windows (2002); A. Bokulich and G. Jaeger (eds), "*Philosophy of Quantum Information and Entanglement*", Cambridge University Press (2010)
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[o5] J. J. Halliwell, J. Pérez-Mercader, W. H. Zurek. "*Physical Origins of Time Asymmetry*". Cambridge University Press (1996); Michael Lockwood, "*The labyrinth of time: introducing the universe*". Oxford University Press (2005)
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@ -8,7 +8,7 @@ However, it happened in such a mysterious way that the breakthrough seemed to be
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All that is known on this matter today can only be gleaned from the memoirs of people who communicated with Pauli during that period. First and foremost, from the recollections of his longtime friend Werner Heisenberg – since it was precisely their joint work on the so-called "world formula" (a unified quantum field equation) that became the impetus for the discovery. [o9]
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There are also a few brief but extremely inspired letters from Pauli, where the essence of his great insight is conveyed by words like: "**Division and reduction of symmetry, this is the kernel of the brute!**… Now we are on the trail!". [o10]
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There are also a few brief but extremely inspired letters from Pauli, where the essence of his great insight is conveyed by words like: "**Division and reduction of symmetry, this then the kernel of the brute!**… Now we are on the trail!". [o10]
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@ -90,4 +90,4 @@ In an ultra-brief formulation, this idea is since some time expressed by the max
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[o17] R. Feynman, "*QED The Strange Theory of Light and Matter*". Princeton University Press(1985)
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[o18] Юрий Манин. "*Не мы выбираем математику своей профессией, а она нас выбирает*". Interview with the newspaper "Троицкий вариант", №13, 30 September 2008
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[o18] Yuri Manin. "*We don't choose mathematics as our profession — it chooses us*". Interview with the newspaper "Troitsky Variant", No. 13, 30 September 2008
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@ -6,9 +6,7 @@ The theoretical construction of the multiverse in Hugh Everett's dissertation wa
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One notable feature of the Dirac equation is that it can be written in a unique form, sometimes referred to as the zigzag representation of a spinor [o19]. In this description, every electron (or another massive fermion with spin 1/2) appears as a particle moving along a zigzag trajectory and is in a state of continuous oscillations between the left-handed "zig" phase and the right-handed "zag" phase. Each of these alternating states, by itself, is massless, and mass arises only when the entire scenario is considered collectively.
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<center>Zigzag representation of an electron (from R. Penrose's book "The Road to Reality")</center>
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In this description, there is an coupling constant, which in Dirac's theory controls the speed of shifts between the "zig" and "zag" parts of the Dirac spinor. In the later Higgs theory, which appeared in the 1960s, this constant turns into a special — Higgs — field, which enters into equations as another interaction that gives fermions mass…
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@ -18,7 +16,7 @@ Describing this field slightly differently, the zigzag oscillations of particles
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Dominating physics of the XIX century, the idea of the ether was necessary for scientists to explain light and other electromagnetic interactions. In the XX century, after rejecting the ether, physicists discovered two other completely different fundamental interactions, strong and weak nuclear ones. However, the general mathematical structure of these mechanisms undoubtedly guides theorists towards the search for a unified construction capable of combining all three (ideally all four, along with gravity) interactions. But at the same time, a model of particle oscillations in a very specific medium — called the "field with nonzero vacuum energy" and possessing properties of a superfluid — clearly emerged.
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Emphasizing the clear parallel between the Higgs field and the ether is useful for several reasons. First of all, to remember the long-forgotten studies of the Norwegian scientist **Carl Bjerknes**. At the end of the XIX century, he mathematically rigourously built, based on the equations of hydrodynamics and the concept of ether as an all-pervasive medium, a "theory of pulsating spheres," explaining practically all known effects of electromagnetism at the time. Moreover, Bjerknes's model was vividly confirmed by his ingenious experiments with liquids and oscillating systems immersed in them. [i14][i15]
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Emphasizing the clear parallel between the Higgs field and the ether is useful for several reasons. First of all, to remember the long-forgotten studies of the Norwegian scientist **Carl Bjerknes**. At the end of the XIX century, he mathematically rigourously built, based on the equations of hydrodynamics and the concept of ether as an all-pervasive medium, a "**theory of pulsating spheres**," explaining practically all known effects of electromagnetism at the time. Moreover, Bjerknes's model was vividly confirmed by his ingenious experiments with liquids and oscillating systems immersed in them. [i14][i15]
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One of the most spectacular results of the theory, in particular, looked like this. Spheres periodically changing their size during pulsations in one phase create waves leading to their mutual repulsion, and during oscillations in antiphase—to attraction. Moreover, the strength of this interaction is inversely proportional to the square of the distance between "charges"—as in Coulomb's law.
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@ -32,9 +30,7 @@ The still poorly studied physics of granular media [i18] — sand, powders, susp
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Speaking more specifically about oscillons, the main feature of this variety of waves in a granular medium is their rare stability. Once arisen, this solitary wave can rise and fall, maintaining its identity indefinitely long—as long as the experiment lasts.
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<center>Oscillation phases of oscillon</center>
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Another equally important feature of oscillons is the specificity of their interaction, explicitly referring to the long-standing Bjerknes’ theory of pulsations. Being in the same phase of oscillation, oscillons repel each other, and being in opposite phases, they attract each other.
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@ -42,7 +38,7 @@ Another equally important feature of oscillons is the specificity of their inter
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Putting the facts slightly differently, the new discovery has revealed remarkable possibilities. By combining oscillons with Bjerknes’ theory, a clear and comprehensible explanation emerges — not only for well-known phenomena (which are explained in textbooks rather clumsily), but also for the still-mysterious secrets of electricity and magnetism.
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Like a beautiful and natural resolution of the mystery of the exact equality of charges in such different by their properties electron and proton. Or the mystery of the total correspondence of the number of electrons to the number of protons in the universe.[i13]
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Like a beautiful and natural resolution of the mystery of the exact equality of charges in such different by their properties electron and proton. Or the mystery of the total correspondence of the number of electrons to the number of protons in the universe. [i13]
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Mysteries of this kind would be solved easily and simply if it could be shown that the proton and electron are in fact opposite oscillation phases of the same oscillon. But the big problem with this approach is that the phases of an oscillon in a granular liquid look much the same—as hills and valleys on the surface.
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@ -58,10 +54,10 @@ In the fourth dimension — time — our entire world, as is well known, constan
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In mathematical terminology, a situation when all orientation directions of elements were previously equal — or symmetric — and then became consistently oriented in one direction, is called "symmetry breaking."
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In classical physics, a very fitting example of this phenomenon is provided by the phenomenon of antiferromagnetism. Like other substances with magnetic properties, antiferromagnets consist of molecules with a dipole moment that behave like tiny magnets. At high temperatures, all these little magnets are oriented randomly within the substance, meaning that every direction is equally probable, and the entire system as a whole is symmetrical.
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When the system's temperature drops, at a certain point, spontaneous alignment of the magnets along a single axis occurs. Symmetry of directions in the system turns out to be broken. Moreover, in antiferromagnetic substances, each magnet, during spontaneous ordering, aligns antiparallel to its neighbors. In other words, their common direction's axis is one, but the poles of neighboring molecules are pointed in opposite directions.
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Juxtaposing this picture of spontaneous symmetry breaking with the phenomenon of oscillons and the "trembling" of massive particles along the time axis, there is little left to do. To assume that the particles' zigzag jumps occur not in the same world, but from one membrane-space to another. Then the solution appears almost self-evident. The proton is the broad base of the oscillon on one membrane, and the electron is the almost pointlike peak of the same oscillon on another membrane.
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@ -50,17 +50,15 @@ This is unusual because such transitions were long deemed impossible in both nat
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However, **at the turn of the 2000s, it was established — both theoretically and practically — that smooth reversals of vortices are indeed possible**.
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Initially, in 1997, it was demonstrated by a duet of string theorists, Eva Silverstein and Shamit Kachru [o21]. Based on Hořava-Witten's two-brane model, they showed that **spaces of neighboring branes can be closely interconnected through particle phase transitions from one membrane to another**. The transitions occur through a very specific system state, a nontrivial "moduli space compression point", after passing which the particles reverse their chirality. [i27]
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Initially, in 1997, it was demonstrated by a duet of string theorists, Eva Silverstein and Shamit Kachru [o21]. Based on Hořava-Witten's two-brane model, they showed that **spaces of neighboring branes can be closely interconnected through particle phase transitions from one membrane to another**. The transitions occur through a very specific system state, a nontrivial "**moduli space compression point**", after passing which the particles reverse their chirality. [i27]
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Soon after, in 2001, an essentially similar experimental result emerged. In laser optics, a multinational group from Spain and the USA built a device that not only achieved a helicity reversal in a screw-shaped beam of light but also captured images detailing the mechanism's operation. [o22]
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Studies of nonlinear optics phenomena are vital on their own and particularly interesting for sharing many similarities with the physics of quantum superfluids like Bose-Einstein Condensates. Specifically, the behavior of quantum vortices in BECs and laser optics is described by similar equations.
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<center>Process of the dynamical inversion of the topological charge</center>
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As laser experiments have shown, once a spirally twisted light beam passes through a cylindrical lens, its previously round core starts to flatten into an elongated ellipse, stretching into a thin line that is nearly nonexistent. After the light passes the lens's focus—or "compression point"—this line reshapes into an ellipse, with energy inside circulating in the opposite direction…[i23]
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As laser experiments have shown, once a spirally twisted light beam passes through a cylindrical lens, its previously round core starts to flatten into an elongated ellipse, stretching into a thin line that is nearly nonexistent. After the light passes the lens's focus—or "**compression point**"—this line reshapes into an ellipse, with energy inside circulating in the opposite direction…[i23]
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<center>(26)</center>
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@ -2,7 +2,7 @@
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<center>(27)</center>
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When Albert Einstein developed his theory of gravitation or GTR (General Theory of Relativity) by 1916, quantum mechanics was still about a decade away from being born. In other words, GTR was initially and remains to this day a purely classical theory. However, an unequivocal hint at the unity of gravitation and quantum physics was almost immediately obtained – in the beautiful theoretical work of Theodor Kaluza.[i30]
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When Albert Einstein developed his theory of gravitation or GTR (General Theory of Relativity) by 1916, quantum mechanics was still about a decade away from being born. In other words, GTR was initially and remains to this day a purely classical theory. However, an unequivocal hint at the unity of gravitation and quantum physics was almost immediately obtained – in the beautiful theoretical work of Theodor Kaluza. [i30]
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In 1919, Kaluza showed that if one added another – fifth – extra dimension to the equations of GTR, an astonishing thing happened. It turned out that with this approach, one could elegantly merge Einstein's theory of gravitation and Maxwell's theory of electromagnetism into a unified and homogeneous conceptual system. (Put a bit differently – from the standpoint of modern science – even then a signal came that there is some direct connection between the graviton and the photon.)
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@ -34,9 +34,7 @@ In other words, at the moment of convergence of the branes, the tube's axis is p
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Here, to complete the picture, it remains to find in the phase of brane convergence also the fermionic partner for each quantum of light or single photon. For this, it is time to recall that unusual particles are emitted from both ends of the vortex tube during the brane convergence. One of them – the tachyon leaving the membrane – should be given a separate section further, while the second particle, eventually having the hallmark of a graviton (spin 2) and consisting of what seems like two parts – with a "longitudinally divided mode" – is exactly what is needed for SUSY. [i33]
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<center>Kelvin Oval (left) and vortex ring in section</center>
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There is reason to believe that at the phase of maximum brane convergence, this particle appears as a pair of flat identical vortices rotating in opposite directions – like a vortex ring "in section". This configuration is known in physics as the "Kelvin Oval" [i34], has soliton properties – a stable solitary wave – and is most famous for propagating strictly in a straight line as a single entity. During the branes convergence the axes of rotation of the vortices in this pair are perpendicular to the membrane, so geometrically they should be considered fermions at this moment.
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@ -20,9 +20,7 @@ The last of the mentioned species of well-known quasiparticles – anyons – de
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The remarkable properties of anyons are important for several reasons. Firstly, because due to relativistic effects impacting the body of a very rapidly rotating proton, there are reasons to believe that a spherical particle can take the shape of a flat disk. And for the particle-components of the proton, rotating inside this energy vortex, unclear quantum properties are characteristic. Quarks are not quite fermions, gluons – not quite bosons.
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<center>Hyde's Vacillation</center>
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Secondly, in the field of hydrodynamics, which often comes to theorists' aid in understanding the mysteries of nuclear physics, there is a phenomenon close in essence and called Hyde's vacillation or wavering. Its essence lies in the fact that in flat rotating systems of nature often observed a phenomenon of self-organization in the form of a specific oscillatory process. The phase of regular waves in a liquid or gas periodically alternates with a phase of turbulent vortices, which then again are replaced by regular waves. And so on. That is, stable vacillation of the system occurs between states of order and chaos. There are reasons to believe that a similar process of vacillation of the system between quark-vortices and gluon-waves occurs in the proton during its rotation. [i42]
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@ -48,7 +46,7 @@ Everything indicates that **the universe itself seems to work like a giant quant
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<center>(34)</center>
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Attempts to comprehend the mysteries of nature through quantum informatics inevitably lead to the conclusion that quantum mechanics and information theory combine with each other almost perfectly. These two theories, as is often said today, seem to have been created for each other.[i43]
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Attempts to comprehend the mysteries of nature through quantum informatics inevitably lead to the conclusion that quantum mechanics and information theory combine with each other almost perfectly. These two theories, as is often said today, seem to have been created for each other. [i43]
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However, it is almost never mentioned that information theory and high-energy physics – the most traditional approach to the study of the microworld – practice diametrically different methods of understanding nature. In high-energy accelerators, where particles are smashed with an increasingly powerful "sledgehammer," researchers are trying to reconstruct the principles of the mechanism from the splatters and fragments.
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@ -26,13 +26,13 @@ It was known for a long time that the appearance of tachyons in a system is the
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For example, the unexpected discovery that tachyons could function in the opposite manner — as a mechanism providing the system additional stability. Interestingly, in this case, the system should have a 2-brane "brane-antibrane" construction in Calabi-Yau spaces.
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This is, in essence, the outcome of the study [o32] by a group of theorists from CERN and the University of Pennsylvania (Yaron Oz, Tony Pantev, Daniel Waldram). Their work shows that systems of the brane-antibrane type can be described using a specific triplet construction (*E*1, *E*2, *T*). Where spaces *E*1 and *E*2 are mathematically represented as vector bundles, and the tachyon field *T* serves as a mapping between these spaces.
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This is, in essence, the outcome of the study [o32] by a group of theorists from CERN and the University of Pennsylvania (Yaron Oz, Tony Pantev, Daniel Waldram). Their work shows that systems of the brane-antibrane type can be described using a specific triplet construction (*E*<sub>1</sub>, *E*<sub>2</sub>, *T*). Where spaces *E*<sub>1</sub> and *E*<sub>2</sub> are mathematically represented as vector bundles, and the tachyon field *T* serves as a mapping between these spaces.
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Under a certain natural condition (holomorphicity or differentiability of the mapping), it is shown that the **brane-antibrane field equations can be transformed into a set of vortex equations**. In more accessible language, this **result is equivalent** to the mathematical **idea of stability of this entire triplet construction as a whole**.
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In the works of other researchers (particularly in the previously mentioned article [o33]), mechanisms of tachyon generation by membrane particles, detachment of tachyons from the brane surface, and their subsequent condensation into a state of energy minimum have been analyzed in detail. Therefore, the next natural question is: what could be the space consisting of tachyons and located beyond the membrane?
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Due to Ashoke Sen, this substance, demonstrating the properties of a pressureless fluid, received the general name "tachyon matter." However, more thorough studies of this form of matter revealed in it not only the signs of a fluid but also distinct crystal properties. From here the beautiful name "tachyonic crystal" naturally emerged (first appeared in an earlier, 1994, work by Joe Polchinski and Larus Thorlacius [o34]).
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Due to Ashoke Sen, this substance, demonstrating the properties of a pressureless fluid, received the general name "tachyon matter." However, more thorough studies of this form of matter revealed in it not only the signs of a fluid but also distinct crystal properties. From here the beautiful name "**tachyonic crystal**" naturally emerged (first appeared in an earlier, 1994, work by Joe Polchinski and Larus Thorlacius [o34]).
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<center>(38)</center>
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@ -48,10 +48,10 @@ According to theoretical estimates, this layered structure of a stable tachyonic
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This skeleton, formed by "fibers of the soul," looks like one-dimensional only locally. However, in general, it is organized into a single global structure. On the one hand, this **giant network penetrates and encompasses all space-time**. On the other hand, it somewhat **resembles the structure formed by neurons in the human brain**…
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Completely independently of these works, a renowned theorist and Nobel laureate Frank Wilczek put forward his own set of substantive ideas in early 2012 about a specific physics-mathematics framework, one that continuously generates threads of matter’s memory in the form of crystalline structures. In particular, Wilczek demonstrated that both in classical and quantum mechanical descriptions of our world, it is possible — as it turns out — to construct crystal structures in the 4th dimension, that is, in time, in a consistent and mathematically grounded way. [o36]
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These kinds of crystals turn out to be as stable as crystals in 3-dimensional space, as they are generated in cycles of oscillations of rotating systems in their most stable state of energy minimum. Particularly interesting results were achieved by Wilczek when analyzing "time crystals," as he called them, in conditions of quantum mechanical systems — where twisted elongated spiral structures form in imaginary time…
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<center>(39)</center>
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@ -66,7 +66,7 @@ Demonstrating in just a few sentences that all these things are actually inextri
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It has been known at least since the early 1980s that the characteristic structure of DNA may have the most direct relation to music and acoustics— as the physics of harmonious tones, chords, and their combinations-melodies. In 1982, the prominent American psychologist Roger Shepard successfully generalized the musical "Drobisch Spiral" known since the 19th century for modeling pitch relations and showed that a double spiral with independent cycles for octaves and fifths provides the optimal compact representation of chords and harmonies. [i49]
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Around the same time, at the turn of the 1970s and 1980s, the theory of numbers ceased to be viewed as "one of the most beautiful but at the same time most useless branches of mathematics." Public key cryptography, directly relying on the mathematical apparatus of number theory, was discovered in the field of information security. And in quantum physics, clear interconnections between the regularities in the spectra of frequencies-energies (or "music") of quantum objects and the regularities in the distribution of prime numbers (divisible only by 1 and themselves) began to be discovered.
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Around the same time, at the turn of the 1970s and 1980s, **the theory of numbers ceased to be viewed as "one of the most beautiful but at the same time most useless branches of mathematics."** Public key cryptography, directly relying on the mathematical apparatus of number theory, was discovered in the field of information security. And in quantum physics, clear interconnections between the regularities in the spectra of frequencies-energies (or "music") of quantum objects and the regularities in the distribution of prime numbers (divisible only by 1 and themselves) began to be discovered.
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<center>(40)</center>
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@ -124,4 +124,4 @@ And there are already distinct signs that if the newly discovered interconnectio
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[o37] Yu. Matiyasevich (2007) "*Hidden Life of Riemann's Zeta Function*", [[arXiv:0709.0028](http://arxiv.org/abs/0709.0028); [arXiv:0707.1983](http://arxiv.org/abs/0707.1983)]
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[o38] Alain Connes, Matilde Marcolli (2007) "[Noncommutative Geometry, Quantum Fields and Motives](http://www.alainconnes.org/en/downloads.php)". American Mathematical Society, 2007
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[o38] Alain Connes, Matilde Marcolli (2007) "[_Noncommutative Geometry, Quantum Fields and Motives_](http://www.alainconnes.org/en/downloads.php)". American Mathematical Society, 2007
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@ -18,9 +18,7 @@ The strange "paradoxes of duality" in the physics of quantum objects, which beha
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Since the 19th century, hydrodynamics has known the so-called solitary waves (solitons), whose behavior largely corresponds to the nature of particles [i50]. Why this happened is a different long story [i51], but scientists began seriously studying the physics of wave solitons only a century later, starting in the 1960s. In other words, when quantum physics, based on an alternative concept of particles, had long been in a state of maturity and triumphant success.
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<center>Train of solitons in a Bose-Einstein condensate</center>
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In this way, the "incomprehensible," supposedly, wave-particle duality ended up being embedded in the foundation of a grand scientific edifice. It became a kind of basis for the subsequent construction of an entire tower of new paradoxes and difficult-to-explain dual descriptions of nature. Rebuilding the entire structure on the basis of purely wave representations for the sake of conceptual integrity and harmony of the theory seemed, to say the least, irrelevant for the scientific majority…
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@ -34,7 +32,7 @@ Perhaps it is for this reason that "improper" soliton waves were ignored for so
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Secondly – for effectively resolving paradoxes – it is useful to remember that a false dogma at the basis of reasoning leading to contradiction, is far from always explicitly stated and often appears as a self-evident assumption. Specifically, the judgment that "solid" objects and "liquid" waves are essentially different in their properties has never been put forward as a dogma. Since for reasonable people, it has always been considered obvious.
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There is very serious evidence that for another most important "duality paradox" in modern physics – the two incompatible descriptions of nature for the micro world of particles and the macro world of the cosmos – the cause of the irresolvable contradictions is a incorrect assumption accepted by default. Namely, the presupposition of the continuous nature of space-time. And there are clear signs that **the theory of quantum gravity** – as a holistic and consistent description of nature – **must necessarily rely on the idea of discrete time and granular space**.[i52]
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There is very serious evidence that for another most important "duality paradox" in modern physics – the two incompatible descriptions of nature for the micro world of particles and the macro world of the cosmos – the cause of the irresolvable contradictions is a incorrect assumption accepted by default. Namely, the presupposition of the continuous nature of space-time. And there are clear signs that **the theory of quantum gravity** – as a holistic and consistent description of nature – **must necessarily rely on the idea of discrete time and granular space**. [i52]
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Thirdly, finally, what else useful does the resolution of paradoxes with dual descriptions of nature show? If both of two pictures, that look like the correct correct ones, stubbornly do not combine with each other, then there must necessarily be another, different form of representation of the same phenomenon. A form for which the first two – difficult-to-combine – projections turn out to be only partial, "flat," representations of different sides of the same "volumetric" structure.
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@ -90,9 +88,7 @@ Therefore, a far more promising endeavor seems to be something else. Take a clos
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An aspect of holography, which is quite significant but has been practically untouched so far, is the principle of self-similarity. Due to the peculiarities of recording wave information in a hologram, any fragment of a holographic snapshot — in contrast to a photograph—reproduces the entire image as a whole, only with possibly fewer details.
|
||||
|
||||
|
||||
|
||||
<center>The boundary of the Mandelbrot set with successive magnification of image fragments serves as an example of the holographic principle in the geometry of complex numbers.</center>
|
||||
|
||||
|
||||
Manifestations of this principle of self-similarity can be seen everywhere: from the Mandelbrot fractal in mathematics and fractal geometry in nature to obvious analogies in the structure of the atom, solar system, and galaxy. Here, however, it is especially useful to consider a less known example of constructive analogies of nature—based on liquid crystals. [i57]
|
||||
|
||||
@ -134,7 +130,7 @@ And it is surely not a coincidence that in the last few decades, a very powerful
|
||||
|
||||
[o40] Jacob D. Bekenstein, "*Information in the Holographic Universe*". Scientific American, August 2003.
|
||||
|
||||
[o41] L. Susskind, "*The World As A Hologram*,*" J. Math. Phys. 36, 6377 (1995), [*[*arXiv:hep-th/9409089*](http://arxiv.org/abs/hep-th/9409089)*]; R. Bousso, "*The holographic principle*,*" Rev. Mod. Phys. 74, 825 (2002), [[arXiv:hep-th/0203101](http://arxiv.org/abs/hep-th/0203101)]
|
||||
[o41] L. Susskind, "*The World As A Hologram*," J. Math. Phys. 36, 6377 (1995), [[arXiv:hep-th/9409089](http://arxiv.org/abs/hep-th/9409089)]; R. Bousso, "*The holographic principle*," Rev. Mod. Phys. 74, 825 (2002), [[arXiv:hep-th/0203101](http://arxiv.org/abs/hep-th/0203101)]
|
||||
|
||||
[o42] Juan Maldacena, "*The Illusion of Gravity.*" Scientific American, November 2005.
|
||||
|
||||
|
||||
@ -98,9 +98,7 @@ Well, the direct relevance of this entire construction to the mathematics of *p-
|
||||
|
||||
So from the very beginning and up to this day, *p-*adic numbers have been although not the only, but undoubtedly the most important example of ultrametric spaces. Or a system of infinitely nested spheres "whose center is everywhere and the circumference nowhere."
|
||||
|
||||
|
||||
|
||||
<center>Conventional depiction of 3-, 5-, 7-adic numbers (in reality, there are no gaps between circles)</center>
|
||||
|
||||
|
||||
<center>(49)</center>
|
||||
|
||||
@ -138,7 +136,7 @@ Because **in any physical experience, any needed magnitude can truly be measured
|
||||
|
||||
The description of natural-scientific models using real numbers — as one of the possible extensions of rational numbers — progressed for several centuries and hit a dead end on the micro scale. According to Ostrowski's theorem, another logically justified option for describing the world is *p-*adic numbers, in whose space the Archimedean axiom is violated.
|
||||
|
||||
Since there are no other options for expanding rational numbers to the concept of continuity in mathematics, it is natural to assume that the time has most likely come to describe the world in terms of *p-*adic arithmetic and non-Archimedean geometry.
|
||||
Since there are no other options for expanding rational numbers to the concept of continuity in mathematics, it is natural to assume that the **time has most likely come to describe the world in terms of *p-*adic arithmetic and non-Archimedean geometry**.
|
||||
|
||||
For some unexplained historical reasons, the key role in reformulating physics into the language of *p-*adic numbers and ultrametric analysis was taken up by scientists from the Russian mathematical school. And what is remarkable, real progress in this direction began only after the passing of Marc Krasner and Alexander Ostrowski in the mid-1980s.
|
||||
|
||||
@ -210,7 +208,7 @@ Pauli began to develop his ideas on a unified mathematical description of matter
|
||||
|
||||
In those same years, in 1944, Carl Jung began additional work as a professor at the University of Basel. Another professor at this university was Alexander M. Ostrowski. Furthermore, in 1949, this *p-*adic specialist married a specialist in analytical psychology, Margaret Sachs, a disciple and associate of Carl Gustav Jung. Finally, in 1958, Ostrowski himself became a visiting professor at ETH in Zurich, where Pauli worked permanently…
|
||||
|
||||
In short, nearly everything was ready for Pauli and Ostrowski to come closer together. The great physicist would surely have learned more about *p-*adic numbers, adeles, and their remarkable features. And, of course, Pauli would have noticed how beautifully the structure of adeles fit his ideas of the mutual complementarity of matter and consciousness… But none of this, alas, happened in reality.[i67]
|
||||
In short, nearly everything was ready for Pauli and Ostrowski to come closer together. The great physicist would surely have learned more about *p-*adic numbers, adeles, and their remarkable features. And, of course, Pauli would have noticed how beautifully the structure of adeles fit his ideas of the mutual complementarity of matter and consciousness… But none of this, alas, happened in reality. [i67]
|
||||
|
||||
As it turned out, it took another half s century to wait. And what we could have known about a unified mathematical model for physics and the soul back then is only slowly coming to light now.
|
||||
|
||||
|
||||
@ -132,7 +132,7 @@ Regarding existence on the "divine" level, in this phase, according to Empedocle
|
||||
|
||||
Regrettably, the extraordinarily distinctive teaching of Empedocles did not take root in ancient Greek culture. After the philosopher's death, no disciples remained capable of continuing his work, nor was there a school to develop and spread Empedoclean ideas.
|
||||
|
||||
<center># # #</center>
|
||||
<center>#</center>
|
||||
|
||||
However, it is worth noting that in the very same historical period when the extraordinary thinker Empedocles was living and teaching in the Mediterranean, another sage was teaching a new perspective on the world in a completely different region of the planet, on the Indian subcontinent, known by the names Siddhartha Gautama, Shakyamuni, or simply Buddha.
|
||||
|
||||
@ -156,7 +156,7 @@ However, for all living beings, who in the process of reincarnation receive —
|
||||
|
||||
For the Buddhist universe is arranged such that only humans have the capability to fully control their consciousness, achieve enlightenment, and, if desired, leave the realms of rebirth entirely, becoming a Buddha and entering nirvana—the highest level of existence in a state of complete freedom and blissful union with the void of unity. And if desired, one can live on, but now as enlightened beings — bodhisattvas, saints helping all others to attain enlightenment.
|
||||
|
||||
<center># # #</center>
|
||||
<center>#</center>
|
||||
|
||||
If we attempt to translate the Buddhist worldview into the language of contemporary physics-mathematics, one of the first — evidently useful for this matter — constructs appears to be the Randall-Sundrum model or RS (see [TBC section 4.4, chapter 29](/tbc/44/#chapter29)).
|
||||
|
||||
@ -176,7 +176,7 @@ It's understood that animals, whose bodies consist of the same basic elements as
|
||||
|
||||
As for the inhabitants of all other Buddhist worlds (devas and asuras, pretas and hellish beings), they, as entities not registered in our world by physical observations, naturally end up as constant inhabitants of other so-called "subtle" layers of the universe.
|
||||
|
||||
<center># # #</center>
|
||||
<center>#</center>
|
||||
|
||||
One idea of Buddhists deserves special consideration, namely that human consciousness — with its vast range of layer coverage — in its different states of emotional and mental activity, exists at different levels of the multi-tiered universe.
|
||||
|
||||
@ -204,7 +204,7 @@ But as all beings go through purification in reincarnation processes on differen
|
||||
|
||||
As Empedocles stated about this process, driven by the power of Love, all living beings strive for unity in "venerable harmony." In the Buddhist universe's cylindrical structure, however, a place for nirvana is not very visible and is vaguely named as "the other shore." Yet, if one relies on Empedocles' idea of Sphairos and imagines a multi-dimensional sphere in a modern fashion, in the form of a Hopf fibration, the picture of the future for humanity and the world becomes much clearer.
|
||||
|
||||
<center># # #</center>
|
||||
<center>#</center>
|
||||
|
||||
From the above discussions, it can be understood that the structure of subtle human bodies and the multi-dimensional construction of the universe's space-time is convenient (and beneficial) to view collectively as a unified whole. Additionally, when transitioning to representing both in the form of a set of nested tori, it is again convenient to interpret image (b) in application to different vertical axes—time and frequency vibrations.
|
||||
|
||||
@ -222,7 +222,7 @@ Delving further into this mechanic, it's not difficult to figure out how bad kar
|
||||
|
||||
Here, however, it's much more interesting to examine not the mechanics of reincarnations and karma cleansing in the Buddhist worldview (as thoroughly described in countless books), but the geometric, so to speak, aspects of human evolution towards the highest level of consciousness, otherwise known as "enlightenment" or "reaching the other shore."
|
||||
|
||||
<center># # #</center>
|
||||
<center>#</center>
|
||||
|
||||
One of the most remarkable features of the Hopf fibration is that important details of this specific geometric construction were well-known to people earlier, in various contexts: mathematically, philosophically-mystically, and religiously-practically.
|
||||
|
||||
@ -410,7 +410,7 @@ For a more objective perception of this tirade, it's worth noting that Lev Landa
|
||||
|
||||
It is clear, of course, that from such positions, finding the key to this enigma is unlikely. By enclosing themselves, like a fence, from reality with simplistic formulas like "The afterlife is complete nonsense," researchers willingly deny themselves access to the full picture.
|
||||
|
||||
<center># #</center>
|
||||
<center>#</center>
|
||||
|
||||
Now that the historical context has been outlined more clearly, it's time to proceed to the story of the recent journey of American neurosurgeon Eben Alexander [o64]. This refers to his quite unusual personal experience, which fundamentally altered not only the doctor's attitude towards death but also the general perception of the universe and life as a whole.
|
||||
|
||||
@ -500,7 +500,7 @@ The brightest example of this unpreparedness is demonstrated by a recent publica
|
||||
|
||||
From the very title of this review, "Proof of Hallucination," it becomes clear that the exceedingly rich and extraordinary near-death experience of the neurosurgeon appears to contemporary science as an entirely ordinary delusion of a sick person. And nothing more…
|
||||
|
||||
<center># # #</center>
|
||||
<center>#</center>
|
||||
|
||||
The sad but quite understandable consequence of such a reaction to the doctor's report from the scientific community became this: almost the only place — besides the circle of close relatives — where Alexander's stories were taken seriously and without skeptical smirks was the church.
|
||||
|
||||
@ -564,7 +564,7 @@ In the collective consciousness of humanity, for conveying and comprehending thi
|
||||
|
||||
|
||||
|
||||
In the memorable dream of Wolfgang Pauli, known as the "Great Vision of the World Clock" [i82], there is one important detail which, for some reasons, has not been mentioned much here before.
|
||||
In the memorable dream of Wolfgang Pauli, known as the "Great Vision of the World Clock" [i80], there is one important detail which, for some reasons, has not been mentioned much here before.
|
||||
|
||||
The previously omitted element is the "large black bird" that supports all that intricate construction, which simultaneously powerfully inspired and greatly puzzled the dreamer. Moreover, the intricate clock mechanism remained an unfathomed mystery not only for Pauli himself but also for his much more experienced in such matters friend, Carl Gustav Jung.
|
||||
|
||||
@ -792,7 +792,7 @@ It is well known that Richard Feynman, due to his character, paid extremely grea
|
||||
|
||||
Therefore, there's no need to doubt that if Feynman decided to place an unusual drawing on the cover of his monumental work, he did it not by chance. But we will probably never know why the scientist not only accepted when his wish was ignored but also never attempted to realize his idea again — despite reissues and the enormous popularity of the "Feynman Lectures" worldwide.
|
||||
|
||||
Drawing an unexpected parallel, perhaps, for some, we almost certainly will never know the reason why another Nobel Prize-winning physicist, Wolfgang Pauli, suddenly abandoned work on the greatest discovery of his life, fell into a severe depression, and soon died of rapid cancer [i83]. (Incidentally, Feynman also developed cancer during that period, but fortunately, the disease was successfully treated for a while.)
|
||||
Drawing an unexpected parallel, perhaps, for some, we almost certainly will never know the reason why another Nobel Prize-winning physicist, Wolfgang Pauli, suddenly abandoned work on the greatest discovery of his life, fell into a severe depression, and soon died of rapid cancer [i82]. (Incidentally, Feynman also developed cancer during that period, but fortunately, the disease was successfully treated for a while.)
|
||||
|
||||
It's pointless to guess what dramas were unfolding in the minds and hearts of great scientists at those moments in their lives. But in this regard, it's certainly worth recalling one of Wolfgang Pauli's friends, an outstanding mathematician named Heinz Hopf.
|
||||
|
||||
@ -804,7 +804,7 @@ For Hopf personally, as known from his surroundings, the answer to such a questi
|
||||
|
||||
<center>#</center>
|
||||
|
||||
A crucial key to the mystery surrounding Wolfgang Pauli's main and undisclosed discovery is a phrase from his postcard to his old friend Werner Heisenberg: "Division and reduction of symmetry, this is the kernel of the brute!"
|
||||
A crucial key to the mystery surrounding Wolfgang Pauli's main and undisclosed discovery is a phrase from his postcard to his old friend Werner Heisenberg: "Division and reduction of symmetry, this then the kernel of the brute!"
|
||||
|
||||
Returning to the rich symbolism of Shiva Nataraja, it's time to note that besides the distinctly expressed "doubling of the universe" in the image of the two-membrane damaru drum, the entire image of the Cosmic Dance clearly emphasizes the asymmetry of the composition.
|
||||
|
||||
@ -826,7 +826,7 @@ First of all, this means that all of us are literally sitting on a source of fre
|
||||
|
||||
Secondly, to start receiving it at any point in space, it is enough to take a closer look at how particles of matter draw this energy for their dance. All the answers are already provided by nature — it's just about asking the right questions.
|
||||
|
||||
And thirdly — judging from the deafening silence surrounding some curious physical phenomena like the Hyde vacillation — it can be assumed that some secret scientific laboratories has long been in possession of such sources of free energy. Only it seems they absolutely do not want to share this happiness with the rest of humanity… (details see here: [i84][i85][i86][i87][i88]).
|
||||
And thirdly — judging from the deafening silence surrounding some curious physical phenomena like the Hyde vacillation — it can be assumed that some secret scientific laboratories has long been in possession of such sources of free energy. Only it seems they absolutely do not want to share this happiness with the rest of humanity… (details see here: [i83][i84][i85][i86][i87]).
|
||||
|
||||
<center>#</center>
|
||||
|
||||
@ -844,7 +844,7 @@ The image of another god, named Tezcatlipoca or "Smoking Mirror," is directly re
|
||||
|
||||
|
||||
|
||||
One of the most important features of the image of Tezcatlipoca is his pronounced asymmetry: the god has only a left leg, while in place of the second, right leg, he is depicted either with a mirror or a serpent. The significant cosmic role of the mirror and the general notion of the universe as a “hall of mirrors” are, it is worth noting, characteristic of the Hua-yen school of Buddhism [i89], and in modern science — of the dodecahedral model by Jean-Pierre Luminet and Jeffrey Weeks. [i90]
|
||||
One of the most important features of the image of Tezcatlipoca is his pronounced asymmetry: the god has only a left leg, while in place of the second, right leg, he is depicted either with a mirror or a serpent. The significant cosmic role of the mirror and the general notion of the universe as a “hall of mirrors” are, it is worth noting, characteristic of the Hua-yen school of Buddhism [i88], and in modern science — of the dodecahedral model by Jean-Pierre Luminet and Jeffrey Weeks. [i89]
|
||||
|
||||
Another brother and often the twin companion of Tezcatlipoca is the god Huitzilopochtli, whose rather unexpected name translates to "Left-Handed Hummingbird." That is, already in the very name of the deity, coded are both the left asymmetry of nature, a general reference to the two-winged bird, and the unique ability of the hummingbird to hover in the air, in particular.
|
||||
|
||||
@ -852,11 +852,11 @@ Although there was also a fourth brother, Xipe Totec (whose name is better decip
|
||||
|
||||
A characteristic feature in the image of all four brothers, who created the world, was that each had a round ring, or "symbol of eternity" and the closed nature of space-time, suspended from their chest with a ribbon.
|
||||
|
||||
In this regard, to clearly correlate the symbolism of the ancient religion with the history of modern physics, one can recall the "Great Vision of the World Clock" by Wolfgang Pauli [i82]. And at the same time, decode the last unsolved detail of this dream.
|
||||
In this regard, to clearly correlate the symbolism of the ancient religion with the history of modern physics, one can recall the "Great Vision of the World Clock" by Wolfgang Pauli [i80]. And at the same time, decode the last unsolved detail of this dream.
|
||||
|
||||
The horizontal circle of the dial in the clocks of the universe was divided into four sectors, each of which had its own color. In each sector stood a human figure holding a pendulum — the symbol of the eternal movement of the clocks of the world…
|
||||
|
||||
And one more — topological — nuance on the same theme. In the developed dodecahedral model of the universe, representing the construction of the cosmos in the form of a twin soccer ball, there is one specific feature. Two surfaces of the Riemann sphere, nested within one another, are topologically equivalent to one surface of a torus because the "ball" structure has four pinched holes — "four cardinal directions" or four corners of the globe — ensuring the unity (meaning a single surface) of the doubled world… [i91]
|
||||
And one more — topological — nuance on the same theme. In the developed dodecahedral model of the universe, representing the construction of the cosmos in the form of a twin soccer ball, there is one specific feature. Two surfaces of the Riemann sphere, nested within one another, are topologically equivalent to one surface of a torus because the "ball" structure has four pinched holes — "four cardinal directions" or four corners of the globe — ensuring the unity (meaning a single surface) of the doubled world… [i90]
|
||||
|
||||
<center>#</center>
|
||||
|
||||
@ -978,11 +978,11 @@ Well, if your immediate "lower self" is not yet ready for such a convergence of
|
||||
|
||||
This whole subject — about the rather intricate, in reality, internal structure of our self — requires, of course, very meticulous and comprehensive research. Because it's not just about the many layers of our consciousness, but also about how these levels relate to each other — in a "hierarchical" sense.
|
||||
|
||||
In the most accessible and simplified form, the essence of this rather nontrivial issue is well conveyed in one of Wolfgang Pauli's dreams. In which the scientist converses with a regular guest in his dreams — a character with a distinctly Eastern appearance and the symbolic name of the Persian. [i92]
|
||||
In the most accessible and simplified form, the essence of this rather nontrivial issue is well conveyed in one of Wolfgang Pauli's dreams. In which the scientist converses with a regular guest in his dreams — a character with a distinctly Eastern appearance and the symbolic name of the Persian. [i91]
|
||||
|
||||
Judging by his behavior, this Persian is far more knowledgeable than Wolfgang Pauli in matters of the structure of consciousness and the part of world that hidden from us. That's why he confidently declares: "It is me who stand between you and the Light, so you are my shadow, and not the other way around." For Pauli, however, this hardly sounds convincing, as he is sure that Persian in his dreams is just one of the aspects of his own consciousness.
|
||||
|
||||
Interestingly, around the same time (a few years later), Pauli's friend and fellow dream researcher, Carl Gustav Jung, had a dream quite resonant with this theme, but linking "shadows and projections" not so much with inhabitants of our consciousness, but directly with aliens. [i92]
|
||||
Interestingly, around the same time (a few years later), Pauli's friend and fellow dream researcher, Carl Gustav Jung, had a dream quite resonant with this theme, but linking "shadows and projections" not so much with inhabitants of our consciousness, but directly with aliens. [i91]
|
||||
|
||||
What is remarkable is that in this dream, the guests tried to demonstrate clearly to the scholar that it is "they" who project "us," and not the other way around (as Jung publicly declared UFOs to be "projections" of our own restless mind).
|
||||
|
||||
@ -1064,27 +1064,25 @@ There are quite a few ways to wake up. One of the simplest recipes has been form
|
||||
|
||||
[i81] Mysteries of the dodecahedron, [https://kniganews.org/map/e/01-10/hex60/](https://kniganews.org/map/e/01-10/hex60/)
|
||||
|
||||
[i82] Highest harmony, https://kniganews.org/map/n/00-01/hex14/
|
||||
[i82] Something happened, [https://kniganews.org/map/n/00-01/hex1c/](https://kniganews.org/map/n/00-01/hex1c/)
|
||||
|
||||
[i83] Something happened, [https://kniganews.org/map/n/00-01/hex1c/](https://kniganews.org/map/n/00-01/hex1c/)
|
||||
[i83] Dancing on Sand, [https://kniganews.org/map/e/01-00/hex43/](https://kniganews.org/map/e/01-00/hex43/)
|
||||
|
||||
[i84] Dancing on Sand, [https://kniganews.org/map/e/01-00/hex43/](https://kniganews.org/map/e/01-00/hex43/)
|
||||
[i84] Looks like an atmosphere, [https://kniganews.org/map/e/01-00/hex46/](https://kniganews.org/map/e/01-00/hex46/)
|
||||
|
||||
[i85] Looks like an atmosphere, [https://kniganews.org/map/e/01-00/hex46/](https://kniganews.org/map/e/01-00/hex46/)
|
||||
[i85] Oscillon identification, [https://kniganews.org/map/e/01-01/hex53/](https://kniganews.org/map/e/01-01/hex53/)
|
||||
|
||||
[i86] Oscillon identification, [https://kniganews.org/map/e/01-01/hex53/](https://kniganews.org/map/e/01-01/hex53/)
|
||||
[i86] How does it spin? [https://kniganews.org/map/e/01-01/hex56/](https://kniganews.org/map/e/01-01/hex56/)
|
||||
|
||||
[i87] How does it spin? [https://kniganews.org/map/e/01-01/hex56/](https://kniganews.org/map/e/01-01/hex56/)
|
||||
[i87] Spin on the Möbius Strip, [https://kniganews.org/map/e/01-10/hex67/](https://kniganews.org/map/e/01-10/hex67/)
|
||||
|
||||
[i88] Spin on the Möbius Strip, [https://kniganews.org/map/e/01-10/hex67/](https://kniganews.org/map/e/01-10/hex67/)
|
||||
[i88] Looking back, [https://kniganews.org/map/e/01-10/hex61/](https://kniganews.org/map/e/01-10/hex61/)
|
||||
|
||||
[i89] Looking back, [https://kniganews.org/map/e/01-10/hex61/](https://kniganews.org/map/e/01-10/hex61/)
|
||||
[i89] Cosmos as a Hall of Mirrors, [https://kniganews.org/map/e/01-10/hex62/](https://kniganews.org/map/e/01-10/hex62/)
|
||||
|
||||
[i90] Cosmos as a Hall of Mirrors, [https://kniganews.org/map/e/01-10/hex62/](https://kniganews.org/map/e/01-10/hex62/)
|
||||
[i90] Convective Geometry , [https://kniganews.org/map/e/01-10/hex6d/](https://kniganews.org/map/e/01-10/hex6d/)
|
||||
|
||||
[i91] Convective Geometry , [https://kniganews.org/map/e/01-10/hex6d/](https://kniganews.org/map/e/01-10/hex6d/)
|
||||
|
||||
[i92] You are my shadow, [https://kniganews.org/map/n/00-01/hex16/](https://kniganews.org/map/n/00-01/hex16/)
|
||||
[i91] You are my shadow, [https://kniganews.org/map/n/00-01/hex16/](https://kniganews.org/map/n/00-01/hex16/)
|
||||
|
||||
### Outside links
|
||||
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user