ic/tzo: fix long dashes

data/tzo/31.md

@@ -18,7 +18,7 @@ Thus, a quantum object, when viewed from the classical world, always appears as
 
 The way the Copenhagen interpretation resolves this discrepancy issue is outlined in all quantum physics textbooks. Within its framework, the idea of wave function collapse, occurring during any measurement and "collapsing" the superposition into a single value with some probability, was invented.
 
-It's no secret that this idea generates only the appearance of explanation, simultaneously raising a host of new questions. The main one being—what does the world look like in between measurements?
+It's no secret that this idea generates only the appearance of explanation, simultaneously raising a host of new questions. The main one being — what does the world look like in between measurements?
 
 Hugh Everett's obvious merit was that he managed to leave the well-functioning mathematics of equations untouched while offering them a significantly different, logical, and far less artificial interpretation.
 

data/tzo/42.md

@@ -18,7 +18,7 @@ Dominating physics of the XIX century, the idea of the ether was necessary for s
 
 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]
 
-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.
+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.
 
 It is also necessary to note that Bjerknes's pulsating spheres were the direct mechanical embodiment of the abstract idea of Maxwell about "displacement current." That is, the idea upon which he built his fundamental equations of electromagnetism, successfully carried over into the physics of the XX century. With the only difference that in new physics, the old-fashioned "displacement current" accompanying oscillations of particles in the ether came to be called the "relativistic correction." In other words, Maxwell, himself not knowing, predicted in his equations the effects of the theory of relativity many decades before its birth…[i16]
 
@@ -26,9 +26,9 @@ It is also necessary to note that Bjerknes's pulsating spheres were the direct m
 
 Another important reason for a unified view of classical and quantum physics is the quite recent discovery made in the mid-1990s of **oscillons** or oscillating solitons. This remarkable phenomenon was discovered by experimental physicists working with granular materials under periodic vibration. [i17]
 
-The still poorly studied physics of granular media [i18] — sand, powders, suspensions, colloids—is particularly interesting because these materials, in a state of vibration, can demonstrate mutually exclusive properties of solid bodies-crystals, flowing liquids, and all-penetrating gases. A similar puzzling set of properties, it can be reminded, had to be assumed for the ether in the old days. Interestingly, the most mathematically advanced, the latest model of the ether was the concept of a granular medium called "Kelvin's vortex sponge." [i19]
+The still poorly studied physics of granular media [i18] — sand, powders, suspensions, colloids — is particularly interesting because these materials, in a state of vibration, can demonstrate mutually exclusive properties of solid bodies-crystals, flowing liquids, and all-penetrating gases. A similar puzzling set of properties, it can be reminded, had to be assumed for the ether in the old days. Interestingly, the most mathematically advanced, the latest model of the ether was the concept of a granular medium called "Kelvin's vortex sponge." [i19]
 
-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.
+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.
 
 ![](https://kniganews.org/wp-content/uploads/2012/12/bc42osc.jpg "Oscillation phases of oscillon")
 
@@ -40,11 +40,11 @@ Putting the facts slightly differently, the new discovery has revealed remarkabl
 
 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]
 
-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.
+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.
 
 Whereas the proton is almost two thousand times larger than the electron. Moreover, all scientific observations show that electrons and protons retain their identity, not transforming into one another.
 
-To overcome this problem, it is time to recall the quantum effect of Zitterbewegung or "trembling motion"—as the zigzag oscillations of particles are otherwise called. And to compare this picture with another phenomenon known as "symmetry breaking," which lies at the foundation of modern quantum field theory.
+To overcome this problem, it is time to recall the quantum effect of Zitterbewegung or "trembling motion" — as the zigzag oscillations of particles are otherwise called. And to compare this picture with another phenomenon known as "symmetry breaking," which lies at the foundation of modern quantum field theory.
 
 <center>(22)</center>
 
@@ -66,7 +66,7 @@ Formulating more precisely, it would be more accurate to speak of the electron n
 
 ![](https://kniganews.org/wp-content/uploads/2012/12/bc42twobr.png)
 
-Thus, on a pair of membranes, only the stable version of oscillons remains — in the form of a conical "pit" (the proton) and its "bottom" in the form of a point-like microvortex (the electron), synchronously jumping from one surface to the other—along the time axis [i16]
+Thus, on a pair of membranes, only the stable version of oscillons remains — in the form of a conical "pit" (the proton) and its "bottom" in the form of a point-like microvortex (the electron), synchronously jumping from one surface to the other — along the time axis [i16]
 
 Accordingly, as a result of this process — spontaneous symmetry breaking — the overall picture of the world turned out bifurcated into two identical halves. Particles of these halves constantly interchange places, and the inhabitants of the world-membranes do not even suspect the existence of their inseparable counterpart.
 

data/tzo/43.md

@@ -4,7 +4,7 @@
 
 One of the most appealing features of the world model as a double membrane is **the possibility of a natural explanation for the phenomenon of quantum entanglement**. That is the otherwise incomprehensible scientific fact according to which quantum particles can instantaneously interact with each other completely independently of the distance separating them.
 
-In terms of doubling the structure of all particles, it is much easier to imagine a situation where particles initially form a single coherent quantum system on both membranes, followed by a delicate evolution of half the system on just one of the membranes. In other words, researchers in one of the worlds can carefully separate the particles—unaware that they are only working with halves of pairs—and move them far apart without collapsing their quantum states.
+In terms of doubling the structure of all particles, it is much easier to imagine a situation where particles initially form a single coherent quantum system on both membranes, followed by a delicate evolution of half the system on just one of the membranes. In other words, researchers in one of the worlds can carefully separate the particles — unaware that they are only working with halves of pairs — and move them far apart without collapsing their quantum states.
 
 Meanwhile, the second halves of the pairs on the other membrane do not change their position and continue to remain a single quantum system. But if someone then measures — i.e. fixes — the state of one of the spatially separated particles, the state of its paired particle on the second membrane will also be fixed or collapsed. This means the entire "quadruple system" collapses as a whole, causing the other particle on the membrane where the experiment is conducted to "sense" the change of state of the first one instantly, regardless of the distance…
 
@@ -12,7 +12,7 @@ This whole scheme, however, can only work if the particle pairs (electron-proton
 
 The sole exception is gravity. The theory allows for the possibility of gravitational interaction between brane-worlds. However, gravitational effects are so minuscule compared to other interactions that quantum experiments in this realm remain exceedingly complex.
 
-Not to mention that, on a theoretical level, no one has yet succeeded in beautifully and convincingly incorporate gravity into quantum physics. Although **the general scheme of unification — through the idea of discrete or granular space-time structure**—has more or less become clear. [i20]
+Not to mention that, on a theoretical level, no one has yet succeeded in beautifully and convincingly incorporate gravity into quantum physics. Although **the general scheme of unification — through the idea of discrete or granular space-time structure** — has more or less become clear. [i20]
 
 <center>(24)</center>
 
@@ -44,7 +44,7 @@ The Möbius strip, however, and other more complex one-sided surfaces, are non-o
 
 Here, however, it’s time to remember that in the model of space under study, the surface is not merely one-sided, but consists of two closely adjacent membranes. It is noteworthy, that this particular – two-brane – model became the subject of deep theoretical development in the 1990s. Primarily thanks to the well-known construction [o20] by Petr Hořava and Edward Witten. Using this model they demonstrated the equivalence of five competing string theories previously considered incompatible. [i26]
 
-Furthermore, the two-brane model "with hopping" is intriguing in that, when applied to the Möbius strip, it can transform a non-orientable surface into the more familiar orientable space. However, this necessitates something quite unusual—the particles and all objects made up of them must switch their rotation direction with each transition from brane to brane.
+Furthermore, the two-brane model "with hopping" is intriguing in that, when applied to the Möbius strip, it can transform a non-orientable surface into the more familiar orientable space. However, this necessitates something quite unusual — the particles and all objects made up of them must switch their rotation direction with each transition from brane to brane.
 
 This is unusual because such transitions were long deemed impossible in both nature and mathematics, which deals with smooth transformations. Figuratively speaking, it was assumed that to change the direction of a vortex's rotation — also it called "chirality reversal" — the vortex first needed to be disrupted.
 
@@ -58,7 +58,7 @@ Studies of nonlinear optics phenomena are vital on their own and particularly in
 
 ![](https://kniganews.org/wp-content/uploads/2011/10/67vortexflip.jpg "Process of the dynamical inversion of the topological charge")
 
-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]
+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]
 
 <center>(26)</center>
 
@@ -66,7 +66,7 @@ A notable feature in the mechanism of an optical vortex or "topological charge"
 
 ![](https://kniganews.org/wp-content/uploads/2012/12/bc43spiralgal.jpg)
 
-This result is particularly fascinating for two reasons. First, as the image of this phenomenon evidently resembles astronomical images of spiral galaxies with a bar in the core. This same concept—using the metaphor of a spinning "garden sprinkler"—often appears in popular explanations for a range of physical theories, from nuclear physics to superstrings and quantum gravity. [i28]
+This result is particularly fascinating for two reasons. First, as the image of this phenomenon evidently resembles astronomical images of spiral galaxies with a bar in the core. This same concept — using the metaphor of a spinning "garden sprinkler" — often appears in popular explanations for a range of physical theories, from nuclear physics to superstrings and quantum gravity. [i28]
 
 Secondly, the nontrivial phase of a thin vortex tube arising when two neighboring branes converge may be directly related to resolving the major theoretical problem succinctly named SUSY or SuperSYmmetry. But it is worthwhile to begin by saying at least a few words about supersymmetry itself.
 

data/tzo/53.md

@@ -86,13 +86,13 @@ When the idea of reality as a computer-generated hologram is discussed in debate
 
 Therefore, a far more promising endeavor seems to be something else. Take a closer look at the known aspects of holography and from them attempt to derive useful conclusions for oneself regarding the nature of the "simulated" world and the place we occupy in this simulation.
 
-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.
+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.
 
 ![](https://kniganews.org/wp-content/uploads/2013/02/bc53mandelbrot.jpg "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.")
 
-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]
+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]
 
-A crucial feature of this specific state of matter is the close connection of liquid crystals with biology. The main component of living organisms is water, and organized organic solutions are liquid crystals. **The functioning of cell membranes and DNA molecules**, the transmission of nerve impulses and muscle work, the life of viruses, and the web spun by a spider—**all these processes**, from a physics point of view, **occur in the liquid-crystalline phase**. **With all the features inherent in this phase — the tendency toward self-organization while maintaining high molecular mobility**.
+A crucial feature of this specific state of matter is the close connection of liquid crystals with biology. The main component of living organisms is water, and organized organic solutions are liquid crystals. **The functioning of cell membranes and DNA molecules**, the transmission of nerve impulses and muscle work, the life of viruses, and the web spun by a spider — **all these processes**, from a physics point of view, **occur in the liquid-crystalline phase**. **With all the features inherent in this phase — the tendency toward self-organization while maintaining high molecular mobility**.
 
 Of particular interest are such forms of liquid crystal as biological and cell membranes. The molecules forming them, phospholipids, are arranged perpendicularly to the membrane surface, while the membrane itself demonstrates elastic behavior, allowing for stretchy extensions or compressions. The molecules forming the membrane can easily mix, yet have a tendency not to leave the membrane due to the high energy costs of such processes. But lipid molecules can regularly jump from one side of the membrane to the other.
 

data/tzo/61.md

@@ -10,7 +10,7 @@ Unlike the universal language of mathematics, equally suitable for all people re
 
 However, in the philosophical legacy of these thinkers, there are very important nuances — moreover, mathematical nuances — that, if properly developed, could have not only brought Descartes's and Pascal's philosophies closer together but also done much more. Like laying a rigorous mathematical foundation under the scientific concept of the unified nature of matter and consciousness.
 
-To make it clearer what is being discussed here, it's time to recall **two** remarkable images, or as they are also called, **archetypal symbols**, which fascinated these philosophers immensely. These symbols—**the sphere and the tree**—appear in humanity's ideas about the **structure of the universe** from time immemorial.
+To make it clearer what is being discussed here, it's time to recall **two** remarkable images, or as they are also called, **archetypal symbols**, which fascinated these philosophers immensely. These symbols — **the sphere and the tree** — appear in humanity's ideas about the **structure of the universe** from time immemorial.
 
 The rich history of the sphere image (and quite an unusual design) in this context is vividly recounted in Jorge L. Borges's essay titled "Pascal's Sphere". Without delving into retelling the well-known text, it is sufficient to quote only how precisely Blaise Pascal formulated what he realized: "**Nature is an infinite sphere, the center of which is everywhere, and the circumference nowhere**"…
 
@@ -34,7 +34,7 @@ And most curiously, **another graphical representation — aside from the tree
 
 The theory of *p*-adic numbers emerged at the end of the 19th century. In other words, the scientific world found out about this discovery almost simultaneously with the publications of the revolutionary ideas in physics regarding the quantization of energy and the special theory of relativity.
 
-How deep the connection is between these greatest discoveries in physics and the apparatus of *p-*adic numbers becomes much clearer much, much later. So much so that initially, and even almost a century after the discovery—nearly until the end of the 20th century*, p*-adic numbers existed in the understanding of scientists completely separately from physics.
+How deep the connection is between these greatest discoveries in physics and the apparatus of *p-*adic numbers becomes much clearer much, much later. So much so that initially, and even almost a century after the discovery — nearly until the end of the 20th century*, p*-adic numbers existed in the understanding of scientists completely separately from physics.
 
 In other words, the unusual arithmetic construct, created by the German algebraist Kurt Hensel [o44], was long considered by the scientific world as theoretically useful, yet a completely abstract mathematical structure. One with absolutely no connection to reality, nor any applicable practical usage.
 
@@ -46,7 +46,7 @@ But noting how beautifully the structure and characteristics of unusual *p-*adic
 
 The peculiar essence of the *p*-adic construct lies in the fact that an abstract mathematical idea of continuity can, as it turns out, be derived consistently and non-contradictorily based on a model very different from the familiar real numbers. If, for real numbers, it is self-evident that all of them are orderly arranged on the number line, and any segment on this line can be divided (to infinity) into two smaller segments with a common boundary, for* p*-adic numbers, the picture looks substantially different.
 
-It should begin with the fact that the set of *p-*adic numbers is unordered. That is, for any pair of such numbers, it is impossible to say that one is "greater" and the other "less." Consequently, between these numbers, there's no interval where other numbers might be found—like "less than the first and greater than the second." Yet, with their purely discrete nature, they densely fill all the "numerical space."
+It should begin with the fact that the set of *p-*adic numbers is unordered. That is, for any pair of such numbers, it is impossible to say that one is "greater" and the other "less." Consequently, between these numbers, there's no interval where other numbers might be found — like "less than the first and greater than the second." Yet, with their purely discrete nature, they densely fill all the "numerical space."
 
 For illustration, *p*-adic numbers can be likened to the branches and leaves of a vast sprawling tree. If we imagine that such a tree grew from some specific point on the number line, we will discover an astonishing correspondence between these sets. There are so many branches and leaves on this mathematical tree that for any point on the number line, a corresponding value can be found on the tree structure by moving along the branches according to strictly defined rules.
 
@@ -66,7 +66,7 @@ Against the backdrop of these explanations, the important successes of physics a
 
 In other words, **the mathematical bridge for an organic transition from classical physics to quantum theory existed, essentially, from the very beginning**. Moreover, a decade and a half later (in 1916, simultaneously with the birth of Einstein's General Theory of Relativity), a fundamentally important mathematical result for both physics was proved in the theory of numbers.
 
-A student of Hensel, the then-very-young Russian mathematician Alexander M. Ostrowski proved a theorem (now known under his name) according to which rational numbers can be completed to a continuous set in only two alternative ways—either by the apparatus of real numbers or *p-*adic. There are no other options and cannot be in principle…
+A student of Hensel, the then-very-young Russian mathematician Alexander M. Ostrowski proved a theorem (now known under his name) according to which rational numbers can be completed to a continuous set in only two alternative ways — either by the apparatus of real numbers or *p-*adic. There are no other options and cannot be in principle…
 
 <center>(48)</center>
 
@@ -120,7 +120,7 @@ In fact, this axiom describes the standard procedure of measurement — we essen
 
 Here a fundamental contradiction between traditional, Archimedean mathematics of space and the structure of the real world described by quantum physics is revealed.
 
-In quantum theory—the most advanced of all human physical sciences — there is a fundamentally important result. According to which, with any conceivable accuracy of instruments, there is no way to measure a distance with an error less than a certain constant, known as the "Planck length."
+In quantum theory — the most advanced of all human physical sciences — there is a fundamentally important result. According to which, with any conceivable accuracy of instruments, there is no way to measure a distance with an error less than a certain constant, known as the "Planck length."
 
 This minimum length of scale is derived as a ratio of the most fundamental constants that describe the physics of our world — the Planck constant, the speed of light, and the gravitational interaction constant. The Planck length is very small, 10⁻³⁵ meters, but it indicates that at these scales, all the physics-mathematics known to us ceases to operate. For the reason that the geometry of ordinary Euclidean and, even more generally, Riemannian space inadequately describes the properties of the real physical world at very small distances.
 
@@ -204,7 +204,7 @@ These ideas of Manin look particularly remarkable when compared with Wolfgang Pa
 
 It is exceedingly difficult to miss the obvious parallels in the ideas of Pauli and Manin. And to make it clearer how close Wolfgang Pauli was to the most significant physical-mathematical discoveries only happening now, it is enough to provide such biographical facts.
 
-Pauli began to develop his ideas on a unified mathematical description of matter and consciousness under the great influence of the theories of Carl G. Jung, with whom he was closely acquainted since the early 1930s and maintained regular contact for the rest of his life. During the war years, i.e., the first half of the 1940s, Pauli worked in Princeton, USA—where in the same period worked the "father of all adeles" Claude Chevalley.
+Pauli began to develop his ideas on a unified mathematical description of matter and consciousness under the great influence of the theories of Carl G. Jung, with whom he was closely acquainted since the early 1930s and maintained regular contact for the rest of his life. During the war years, i.e., the first half of the 1940s, Pauli worked in Princeton, USA — where in the same period worked the "father of all adeles" Claude Chevalley.
 
 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…
 
@@ -226,7 +226,7 @@ It cannot be said that these innovative and profound works went entirely unnotic
 
 The principal question among these is the problem of the connection between spirit and matter. Scientists had no clarity on this issue in the times of Descartes and Pascal, and they still don't today. Relying on the available body of knowledge, science is still faced with an "explanatory gap," with no clear understanding of the mechanisms that enable the interaction between matter and consciousness.
 
-Another question closely related to the first is where exactly is consciousness located? In the brain? Or somewhere else—perhaps in a "space above the head"? Or maybe consciousness is distributed everywhere there is energy and space?
+Another question closely related to the first is where exactly is consciousness located? In the brain? Or somewhere else — perhaps in a "space above the head"? Or maybe consciousness is distributed everywhere there is energy and space?
 
 No one today is capable of providing clear and convincing answers to these questions.
 

data/tzo/62.md

@@ -116,9 +116,9 @@ To clarify that this significant (but for some reason hushed-up) scientific disc
 
 The all-pervading "Higgs field," according to contemporary scientific views, can be likened to a superfluid. An important feature of such superfluids, as known, is the spontaneous formation of discrete vortex cells when the medium rotates.
 
-And if on one side of the sphere 12 dodecahedral structure cells form, on the other side—where the 20 vertices of the polyhedron become centers of vortex convection—an icosahedron naturally forms out of 20 cells. Namely, a regular polyhedron that is the dual of the dodecahedron.
+And if on one side of the sphere 12 dodecahedral structure cells form, on the other side — where the 20 vertices of the polyhedron become centers of vortex convection — an icosahedron naturally forms out of 20 cells. Namely, a regular polyhedron that is the dual of the dodecahedron.
 
-In the end, when this entire configuration stabilizes to a minimum-energy state, on each side of the sphere—inside and outside—there are identical grids of 32 soccer ball cells, shifted relative to each other by convective processes. These vortex processes effectively "cut off" the energy-costly vertices of the dodecahedron and the icosahedron, overlaying both structures shifted onto each other and ultimately generating a symmetrical, energetically optimal construction.
+In the end, when this entire configuration stabilizes to a minimum-energy state, on each side of the sphere — inside and outside — there are identical grids of 32 soccer ball cells, shifted relative to each other by convective processes. These vortex processes effectively "cut off" the energy-costly vertices of the dodecahedron and the icosahedron, overlaying both structures shifted onto each other and ultimately generating a symmetrical, energetically optimal construction.
 
 ![](https://kniganews.org/wp-content/uploads/2013/05/bc62futbol.jpg)
 
@@ -148,7 +148,7 @@ In this research, calculations demonstrated that a graphene Möbius strip behave
 
 Three years later, in May 2012, theoretical work from the Institute for Nuclear Theory in Seattle, USA, showed that if the known physical properties of a topological insulator are assumed for the space-time of the entire universe, then it is possible to discern a completely natural topological mechanism that generates precisely three generations of fermion particles. [o57]
 
-To briefly explain the essence of the discovery made by David Kaplan and Sichun Sun, their calculations indicate that our universe possesses an additional, fifth dimension, which due to insurmountable mathematical circumstances is "prohibited" for the particles of our world—similar to how the interior spaces of materials known as topological insulators are beyond reach for conduction electrons on their surfaces.
+To briefly explain the essence of the discovery made by David Kaplan and Sichun Sun, their calculations indicate that our universe possesses an additional, fifth dimension, which due to insurmountable mathematical circumstances is "prohibited" for the particles of our world — similar to how the interior spaces of materials known as topological insulators are beyond reach for conduction electrons on their surfaces.
 
 Viewing space-time as a 4D surface, scientists likened it to a conducting surface bounding the bulk "insulator" of a higher dimensionality (5D). Subsequently, by reasonably assuming a specific topology for such a 5D space composed of discrete energy layers, the authors showed it is possible to generate exactly three families of particles — bound to their four-dimensional surfaces.
 
@@ -238,7 +238,7 @@ There are many testimonies in the history of astrophysical observations that the
 
 On the other hand, all these facts and evidence are commonly ignored in mainstream cosmology as they do not fit the dominant theoretical model based on the "big bang" and inflationary expansion.
 
-However, the degree of uncertainty in current theoretical physics is such that over the past decade, the idea of a "cyclic universe" has been steadily gaining more and more supporters. It cannot be said that this idea is particularly new. Even at the dawn of the "big bang" theory, the concept of a quasi-stationary—that is, cyclically expanding and contracting—universe was actively advocated by the renowned astrophysicist Fred Hoyle.
+However, the degree of uncertainty in current theoretical physics is such that over the past decade, the idea of a "cyclic universe" has been steadily gaining more and more supporters. It cannot be said that this idea is particularly new. Even at the dawn of the "big bang" theory, the concept of a quasi-stationary — that is, cyclically expanding and contracting — universe was actively advocated by the renowned astrophysicist Fred Hoyle.
 
 Now, it is being noticeably revived in a new guise by respected scientists such as Paul Steinhardt, Neil Turok, or for instance, Roger Penrose. Attempting to overcome the limitations of GR equations, which reduce space-time to "singularity points" under extreme conditions — about which physics still has nothing substantial to say —Steinhardt and Turok have created a cyclic model of the "ekpyrotic universe." According to this concept, two membrane worlds periodically come together and drift apart, cyclically creating and destroying the universe without encountering any singularities. [o59]
 

data/tzo/7.md

@@ -78,15 +78,15 @@ So mechanical clocks with 12-hour dials, which appeared in Europe only in the Re
 
 Modern science has no reliable evidence that the number 12 for astronomical segmentation of the sky was chosen because of the 12 faces of a dodecahedron — a regular polyhedron, laid, according to the views of ancient mystics, as the foundation of the universe's structure. [i81]
 
-However, it is precisely this fact that is clearly indicated by the ancient tradition preserved till today, originating from the civilizations of Sumer and Babylon, whereby the clock face is divided into 60 minutes. Thus, each of the 12 equal hourly sectors comprises 5 minute sectors. This is, undeniably, a direct description of the construction of a dodecahedron—twelve equal faces, each with 5 equal sides.
+However, it is precisely this fact that is clearly indicated by the ancient tradition preserved till today, originating from the civilizations of Sumer and Babylon, whereby the clock face is divided into 60 minutes. Thus, each of the 12 equal hourly sectors comprises 5 minute sectors. This is, undeniably, a direct description of the construction of a dodecahedron — twelve equal faces, each with 5 equal sides.
 
 Considering all these observations, along with the newly clarified — more detailed — geometric structure that forms the basis of the universe, we can point out such evident correspondences.
 
-The basic form of a spherical dodecahedron, as now established, has a split design of two spheres nested within each other. For the second sphere—due to the geometric concept of duality—it is initially considered a spherical icosahedron, i.e., 20 identical faces shaped as equilateral triangles. In terms of the clock face, this is also 60 minutes (20x3), which is interesting.
+The basic form of a spherical dodecahedron, as now established, has a split design of two spheres nested within each other. For the second sphere — due to the geometric concept of duality — it is initially considered a spherical icosahedron, i.e., 20 identical faces shaped as equilateral triangles. In terms of the clock face, this is also 60 minutes (20x3), which is interesting.
 
 Consequently, the clocks of the world in fact have two dials. Since it is impossible to see the second sphere when you are on one, in clocks, this idea is conveyed as mutually perpendicular dials having practically no projection onto each other. (Or, in terms of wave physics, oscillations in mutually perpendicular planes have almost no influence on each other.)
 
-Furthermore, since the construction is by definition unified and integral, some energy exchange between the spheres does occur. Thus, due to convective processes, the energetically more favorable structure turns out not to be a pure dodecahedron or a pure icosahedron, but a form combining both, akin to a soccer ball—with 12 pentagons and 20 hexagons. Hence, two spheres, each formed by 32 regular polygons.
+Furthermore, since the construction is by definition unified and integral, some energy exchange between the spheres does occur. Thus, due to convective processes, the energetically more favorable structure turns out not to be a pure dodecahedron or a pure icosahedron, but a form combining both, akin to a soccer ball — with 12 pentagons and 20 hexagons. Hence, two spheres, each formed by 32 regular polygons.
 
 In other words, in terms of the "clocks of the world," these are two dials with 32 divisions each. Remarkably, there is peculiar confirmation of the naturalness of this rather unconventional construction in a very ancient mathematical tradition — dividing a circle into 360 degree sectors in a somewhat strange way.
 
@@ -104,7 +104,7 @@ Equally significant seems another — hitherto unmentioned — feature of the "c
 
 Within the European philosophic-religious tradition, the emergence of ideas about the evolution of nature and humans, occurring alongside the cycles of the universe's development, is generally associated with the teachings of the ancient Greek thinker Empedocles of Acragas.
 
-Since Empedocles lived two and a half thousand years ago, precise dates of his life and death have not been preserved. However, it is quite reliably established that this was the 5th century BC—thus, somewhat later than Pythagoras and slightly before Socrates.
+Since Empedocles lived two and a half thousand years ago, precise dates of his life and death have not been preserved. However, it is quite reliably established that this was the 5th century BC — thus, somewhat later than Pythagoras and slightly before Socrates.
 
 Thanks to Socrates, it is considered, there was a turn in ancient Greek philosophy, roughly speaking, away from cosmology and the physics of the universe towards human matters, primarily ethical issues. Accordingly, the pre-Socratic thinker Empedocles and his teachings occupy an entirely special place in the history of European culture.
 
@@ -154,7 +154,7 @@ And finally, if consciousness is engulfed by emotions, doubts, and constant chan
 
 However, for all living beings, who in the process of reincarnation receive — depending on previously accumulated karma — a birth at some level of existence, landing in the human world is considered a great fortune. Because this level is the most favorable or even the only one from the perspective of self-realization and release from the chain of multifold sufferings (from the boredom of overindulgent devas to the hellish torments of naraka).
 
-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.
+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.
 
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@@ -190,13 +190,13 @@ To make the general dynamics of the development of this geometric structure in t
 
 By a non-accidental, naturally occurring coincidence, these two images in the simplified (a) and more intricate — but also more adequate — view (b) reflect the process of the evolution of the world and humanity as envisioned by ancient Buddhists and Empedocles. To put it differently, we can say that these are two different projections that display a unified multi-dimensional structure as an easier-to-understand three-dimensional image for us.
 
-To explain image (a), one could refer to the "Abhidharma Encyclopedia," the most authoritative compilation of cosmological information in Buddhism, compiled in the 5th century AD. According to this source, in the Buddhist model of the world, the foundation of the universe is a dense vortex of air. Above this vortex is a very thick layer of water, and on top of it — the uppermost layer of "our" dense world, once made of iron, now of gold. (For comparison—in Pauli's world clock, the outer rim of the dial was dark, and now it is golden.)
+To explain image (a), one could refer to the "Abhidharma Encyclopedia," the most authoritative compilation of cosmological information in Buddhism, compiled in the 5th century AD. According to this source, in the Buddhist model of the world, the foundation of the universe is a dense vortex of air. Above this vortex is a very thick layer of water, and on top of it — the uppermost layer of "our" dense world, once made of iron, now of gold. (For comparison — in Pauli's world clock, the outer rim of the dial was dark, and now it is golden.)
 
 It is hardly reasonable to make hasty judgments about the "non-physical" nature of this strange worldview. For it is easy to see that contemporary astrophysics reliably establishes precisely such a path of evolution for the matter of the universe: from the lightest elements, hydrogen and helium (air), further to the heavier oxygen (i.e., to water, as its compound with hydrogen), and then to the synthesis of heavier elements like iron and gold…
 
 In other words, there is reason to view the Buddhists' cylindrical picture of the world as the universe's evolutionary process along the time axis T. But importantly, this same axis can also be interpreted as "frequency of vibrations" 1/T, that is, a physical quantity inverse to time. Or a parameter that in a 5-dimensional picture of the world acts as yet another, fifth dimension of space-time.
 
-With such a "frequency" view of the same picture, one can also see the complex of chakras strung along the human spinal column, and the agglomeration of the universe into parallel level-worlds, named "lokas" in Buddhism. Crucially, when considering the world in such a projection, the universe's process of evolution appears somewhat differently than with Empedocles—as phases of creation and growth of level-lokas, replaced by phases of their reduction and complete destruction. After which the cycle repeats.
+With such a "frequency" view of the same picture, one can also see the complex of chakras strung along the human spinal column, and the agglomeration of the universe into parallel level-worlds, named "lokas" in Buddhism. Crucially, when considering the world in such a projection, the universe's process of evolution appears somewhat differently than with Empedocles — as phases of creation and growth of level-lokas, replaced by phases of their reduction and complete destruction. After which the cycle repeats.
 
 The growth of each world (narakaloka, devaloka, etc.) is directly related to the increasing number of living beings inhabiting these levels. In any of the six worlds of Buddhism, existence is not permanent, but is associated with the cleansing of the soul from various actions burdening its fate, committed in the past and recorded in karma.
 
@@ -206,7 +206,7 @@ As Empedocles stated about this process, driven by the power of Love, all living
 
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-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.
+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.
 
 Previously (in [TBC section 6.2](/tbc/62/)) it was already demonstrated that on the torus surface, the outer horizontal circle, when moving along the time axis, well conveys the evolution of the space of the observable universe: emergence from the vortex funnel at the base, expansion to maximum size, and then contraction in the area of the top torus funnel.
 
@@ -238,9 +238,9 @@ For the constructed correspondences picture, these 4 circles intrinsic to each p
 
 Recalling that the core concept here is about two sides of one universe, and every particle of our world is simultaneously a particle of the world on the other side, one can also comprehend this: **Beings consisting of particles shared with us have consciousness common with ours**.
 
-And although from a geometrical viewpoint, we jointly represent one point on the torus surface as an oversimplified universe map, in reality, we live as entirely different entities—in absolutely different physical conditions of reality, essentially not noticing each other's existence. This is reflected by the skew circles of the "world lines," situated in completely different planes.
+And although from a geometrical viewpoint, we jointly represent one point on the torus surface as an oversimplified universe map, in reality, we live as entirely different entities — in absolutely different physical conditions of reality, essentially not noticing each other's existence. This is reflected by the skew circles of the "world lines," situated in completely different planes.
 
-Yet, geometry allows for situations where both circles end up in one plane or become coplanar, as mathematicians say. This special case reflects the Villarceau circles—when the perimeters of the paired circles precisely pass through each other's centers.
+Yet, geometry allows for situations where both circles end up in one plane or become coplanar, as mathematicians say. This special case reflects the Villarceau circles — when the perimeters of the paired circles precisely pass through each other's centers.
 
 Naturally, it's no accident that such a configuration was known in the so-called "sacred geometry" of various Eastern and Western cultures for many centuries and even millennia before Yvon Villarceau's discovery. This figure appears under different names but is most frequently called Vesica Piscis in mystical literature of the European tradition of the last 3-4 centuries, which translates as "fish bladder" from Latin.
 
@@ -681,7 +681,7 @@ Having constructed with the help of a computer the final fractal drawing – the
 
 ![](https://kniganews.org/wp-content/uploads/2013/09/bc7indrapearl-limit.jpg)
 
-Every part of any such fractal structure contains the essence of the whole. Based on Mumford’s popularly written book, any literate computer user today can write a program that allows for increasingly magnified views of any chosen fragment of an image, and observe the same lace-like structure repeating itself on ever finer levels—revealing worlds within worlds within worlds, and so on…
+Every part of any such fractal structure contains the essence of the whole. Based on Mumford’s popularly written book, any literate computer user today can write a program that allows for increasingly magnified views of any chosen fragment of an image, and observe the same lace-like structure repeating itself on ever finer levels — revealing worlds within worlds within worlds, and so on…
 
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