ic

.gitignore

@@ -10,5 +10,5 @@ src/test.php
 config-runtime.php
 /config.yaml
 /.idea
-/htdocs/dist-css
+/public/*/dist-css
-/htdocs/dist-js
+/public/*/dist-js

Makefile

@@ -10,13 +10,5 @@ all:
 deploy:
 	./deploy/deploy.sh
 
-static: build-js build-css runtime-config
+static:
-
+	./deploy/static.sh -o "$$(realpath .)"
-build-js:
-	./deploy/build_js.sh -i ./htdocs/js -o ./htdocs/dist-js
-
-build-css:
-	./deploy/build_css.sh -i ./htdocs/scss -o ./htdocs/dist-css
-
-runtime-config:
-	./deploy/gen_runtime_config.php --htdocs-dir ./htdocs --commit-hash $$(git rev-parse --short=8 HEAD) > ./config-runtime.php

data/ic_books.md

@@ -0,0 +1,9 @@
+## Works
+
+- 2011: [The Book of NEWS](https://kniganews.org/navi-g/navi-knmm/) (_rus._)
+- 2012-2013: [There Beyond The Clouds](/tbc/)
+- 2012-…: [Taboos, Dogmas, and Heresies in Science as Religion](https://kniganews.org/navi-g/tabu/) (_rus._)
+- 2014-2015: ["Women, Einstein, and Holography"](https://kniganews.org/navi-g/navi-weh/) (_rus._)
+- 2015-2017: ["Sci-Myst, or the Scientific-Mystical Detective"](https://kniganews.org/navi-g/navi-sm/) (_rus._)
+- 2017-…: [“Here, There, and Everywhere"](https://kniganews.org/navi-g/nav-hte/) (_rus._)
+- 2021-…: [Edward Witten and One Black Bird](https://kniganews.org/navi-g/navi-obb/) (_rus._)

data/tzo/1.md

@@ -0,0 +1,25 @@
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/weather.jpg)</center>
+
+<center>(1)</center>
+
+The unity of matter and consciousness is a very old idea, but to this day it has not yet achieved the status of a universally recognized fact.
+
+Of course, one can try to find out **why this** happens. But it is much more beneficial to ask another question: **what does** science lose by ignoring this inseparable connection?
+
+Since it is most convenient to present the search for an answer to this question in retrospect, let's briefly return to the year 1900 [i1], that separates such different XIX and XX centuries.
+
+The highly influential British scientist William Thomson, also known as Lord Kelvin, delivered a keynote lecture then [o1], dedicated to the triumphant achievements of physical science.
+
+The essence of his speech was that complete clarity about the structure of the surrounding world was almost achieved, except for two small clouds that still darkened the clear scientific sky…
+
+Alas, it soon became clear after this report that the "trifles" that slightly troubled Kelvin were actually harbingers of the most radical changes in science. One of the clouds eventually became quantum physics, and the other became the general theory of relativity.
+
+<center>([Read more](/tbc/21/))</center>
+
+### Inside links
+
+[i1] *Two Worlds* [https://kniganews.org/map/n/00-01/hex10/](https://kniganews.org/map/n/00-01/hex10/) 
+
+### Outside links
+
+[o1] Thomson W. (Lord Kelvin). *19th century clouds over the dynamical theory of heat and light*. Philosophical Magazine and Journal of Science, 2, 1–39; (1901)

data/tzo/21.md

@@ -0,0 +1,25 @@
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc21darkly.jpg)</center>
+
+<center>(2)</center>
+
+If at the dawn of the new 21st century, the global physics community had decided to hold a review lecture similar to Lord Kelvin's report a century ago, today's summary picture would be far less optimistic.
+
+The two small cloudlets on the scientific horizon that worried scientists in 1900 had, by the end of the 20th century, grown not just into gigantic dark clouds of scientific ignorance but had also, one might say, obscured almost the entire universe from humankind.
+
+More precisely, about 96% of the world around us constitutes something about which modern science can say practically nothing substantive. [o2]
+
+<center>(3)</center>
+
+The only thing that has been achieved so far is to give the unknown components their own, not the best names: "dark matter" and "dark energy" (a more appropriate term might be the word "invisible").
+
+Since dark matter, which makes up about 23% of all material in the universe, refers to particles, this ignorance falls under the category of quantum physics. In other words, what the first "cloud" eventually turned into.
+
+Similarly, dark energy, which accounts for about 73% of the universe, turns out to be a direct offspring of another "cloud," known as Einstein's General Theory of Relativity (GTR). [o3]
+
+<center>([Read more](/tbc/22/))</center>
+
+### Outside links
+
+[o2] S. Matarrese, M. Colpi, V. Gorini, U. Moschella (Eds). *«Dark Matter and Dark Energy. A Challenge for Modern Cosmology»*. Springer (2011)
+
+[o3] L. Papantonopoulos (Ed.) *«The Invisible Universe: Dark Matter and Dark Energy»*. Lecture Notes in Physics 720. Springer (2007)

data/tzo/22.md

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+<center>![](https://kniganews.org/wp-content/uploads/2012/12/22foggy.jpg)</center>
+
+<center>(4)</center>
+
+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.
+
+As one of the fundamentally unsolvable problems, it is enough to mention the quantum phenomenon, named by Erwin Schrödinger as **Verschränkung** or "entanglement". [o4]
+
+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]
+
+Quantum physics is not without reason called the most successful and most accurate of all sciences developed by humanity. However, the meaning of its mathematical constructs is practically impossible to explain in everyday language.
+
+Similarly, the equations of General Relativity allow mathematics to justify many non-trivial phenomena observed on macro scales in the 4-dimensional universe. However, no one has been able to clearly explain the strange **nature of time**. [i3]
+
+Time as a fundamentally different dimension of space, where one cannot move independently either forward or backward. You can only always be at one point "now," moving strictly in one direction – from the past to the future. [o5]
+
+And finally, another fundamentally important problem. It remains completely unclear what the **secret of gravity** is, because of which it stubbornly does not fit into the quantum description of the world, continuing to remain a classical interaction. [i4]
+
+<center>(5)</center>
+
+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.
+
+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"…
+
+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.
+
+However, there have been several moments in the history of science when researchers managed to get particularly close to solving the problem, and from different sides. One of the most promising episodes of this kind occurred in the late 1950s.
+
+<center>([Read more](/tbc/31/))</center>
+
+# Inside links
+
+[i2] EPR and relativity, [https://kniganews.org/map/e/01-00/hex4a/](https://kniganews.org/map/e/01-00/hex4a/)
+
+[i3] Science a la Riverbank, [https://kniganews.org/map/e/01-11/hex70/](https://kniganews.org/map/e/01-11/hex70/)
+
+[i4] Loops and networks, [https://kniganews.org/map/w/10-00/hex8c/](https://kniganews.org/map/w/10-00/hex8c/)
+
+# Outside links
+
+[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)
+
+[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)

data/tzo/31.md

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+<center>![](https://kniganews.org/wp-content/uploads/2012/12/31many-worlds.png)</center>
+
+<center>(6)</center>
+
+By 1957, when Princeton University graduate student Hugh Everett III prepared his dissertation [o6] with a completely new perspective on quantum mechanics, this science had already achieved the status of the "queen of physics." Primarily, of course, because of the atomic bomb.
+
+However, successes in military and other practical applications did not assist in resolving the fundamental problem at the core of quantum theory. The world of quantum objects is fundamentally different from the observed classical world, and how to understand this crucial difference wasn't clear in the 1950s and remains unclear today.
+
+The essence of the problem is that Schrödinger's wave function, used to describe quantum objects, operates with complex numbers. But these are quantities that do not suit descriptions in our real-world context.
+
+"In our world," the result of any measurement — be it velocity, position, or spin — can only be a single numerical value. A complex number, not only consists of two parts, but one of them is "imaginary." In other words, there is always a component representing magnitude in a "non-real" dimension associated with the number ***i*** or the square root of (-1).
+
+Thus, a quantum object, when viewed from the classical world, always appears as a simultaneous collection or superposition of incompatible states. Due to this fundamental ambiguity, any measurement of a quantum object's state cannot be predicted precisely and only provides probabilistic values. Yet, the wave function itself is quite deterministic — in terms of complex numbers.
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc31mwsf.jpg)</center>
+
+<center>(7)</center>
+
+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?
+
+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.
+
+Everett essentially suggested simply trusting the formulas. And if the mathematics shows that quantum world objects exist continuously and not as fragmented bits from one measurement to another, then that's likely how it really is.
+
+He proposed that the crucial role of the observer, constantly making measurements, and thus "realizing" the branching quantum world into the more familiar classical world view, be assigned to the universe itself.
+
+In the original, expanded version [o7] of Everett's dissertation, it seems the **formulation of quantum mechanics in the terms** of the then-novel **Shannon's information theory** first appeared in science.
+
+Based on this foundation, Everett suggested that **the particles of the universe as a whole can be likened to a computational system**, or in his terminology, a "complex automaton," with the ability to memorize their previous states and compare them with new states.
+
+<center>(8)</center>
+
+During each particle interaction, i.e., mutual state measurements, they form a single quantum system. Or, in Everett's terminology, they become "correlated" (today usually referred to as "entangled"). The result of each such interaction-measurement is stored, so that deterministic measurement records become the "subjective experience" of observer-particles.
+
+Finally, as Everett demonstrated, based on considering these records, one can compute the same empirical predictions as with the traditional probabilistic approach. But it's correct to consider in this case that all system states are equally real, forming a branched multitude of worlds with different probabilities of realization…
+
+Everett himself believed he clearly demonstrated how his approach generated exactly the same picture of measurement outcome probabilities as the Copenhagen interpretation. [o8]
+
+However, for everyone else — both opponents and supporters — this coincidence of outcome pictures remained entirely unclear. It also remained unclear how the branching mechanism could be realized in nature.
+
+Overall, such a radical revision of traditional scientific views on reality was, as known, entirely disliked by the quantum theory luminaries of the time. Everett's interpretation was dubbed "new theology," and for it to finally be established in the scientific mainstream under the name **multiverse** or **many-worlds**, it took several decades of debates and further developments.
+
+But without the author himself, who was disappointed with his colleagues' reaction to his discovery. Immediately after defending his dissertation, Hugh Everett essentially parted ways with the "queen of physics" forever. [i5]
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc31alice.jpg)</center>
+
+<center>([Read more](/tbc/32/))</center>
+
+### Inside links
+
+[i5] Everett's interpretation, [https://kniganews.org/map/n/00-01/hex1e/](https://kniganews.org/map/n/00-01/hex1e/)
+
+### Outside links
+
+[o6] Hugh Everett. "*‘Relative state' formulation of quantum mechanics*". Reviews of Modern Physics (1957) 29 (3): 454–462. [http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html](http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html)
+
+[o7] Hugh Everett III "*The Theory of the Universal Wavefunction*", Manuscript (1955), pp 3–140 of Bryce DeWitt, R. Neill Graham, eds, "*The Many-Worlds Interpretation of Quantum Mechanics*", Princeton University Press (1973). [http://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf](http://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf)
+
+[o8] Peter Byrne, "*Everett and Wheeler, the Untold Story*", pp 521-541 in Saunders S. et al (Eds) "*Many Worlds? Everett, Quantum Theory, and Reality*", Oxford University Press (2010)

data/tzo/32.md

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+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc32mir.jpg)</center>
+
+<center>(9)</center>
+
+It so happened that in the same 1957, but quite independently of the work of the unknown graduate student Hugh Everett, another outstanding discovery occurred in the field of theoretical science. Its author was a much more famous scientist, one of the fathers of quantum physics, Wolfgang Pauli.
+
+However, it happened in such a mysterious way that the breakthrough seemed to be there, yet in the end, it was as if it weren't there at all. Due to some mysterious life circumstances accompanying this discovery, humanity to this day remains in complete ignorance of what specific results were obtained then. [i6][i7]
+
+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]
+
+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]
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc32twow.jpg)</center>
+
+<center>(10)</center>
+
+From Pauli's letters, it is also known that in the remarkable results of a purely physico-mathematical nature that he obtained, there was clearly something else visible. According to the scientist's own words, he was beginning to see that their theory with Heisenberg was forming a bridge allowing to unite the physics of the micro-world and human consciousness… [o11]
+
+To make it clearer what is being discussed here, it should be reminded that for many years Wolfgang Pauli had been associated and collaborated with Carl Gustav Jung, one of the founders of modern psychology. Under the strong influence of Jung's concepts, Pauli was extremely fascinated by the idea of a new description of reality. A strictly scientific picture that would organically include both matter and consciousness, mutually complementing each other in an inseparable unity.
+
+To put it more poetically, the scientist was searching for ways to return to the modern scientific conception of the world the ancient notion of the "soul of matter". A notion commonly accepted in antiquity, but completely lost over the last 300 years. [i8]
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc32alice.jpg)</center>
+
+<center>(11)</center>
+
+Fully understanding the unorthodoxy, so to speak, of these ideas, Wolfgang Pauli was in no hurry to bring them to scientific publication. However, among people close to him, topics about the future merging of matter and consciousness into a single coherent picture were regularly discussed.
+
+Pauli was always very careful in his wording and spoke about it approximately as follows: "In my personal opinion, in the science of the future, reality will be neither mental nor physical, but somehow both of them at once, and at the same time neither one nor the other separately"… [o12]
+
+Alas, a sharp and tragic turn in the scientist's life, that clearly happened in 1958, but still remains an absolute mystery for the historians of science, put an end to everything.
+
+All that is known is that at the beginning of the year, experiencing unprecedented excitement from the achieved successes, Pauli went to the USA for scheduled lectures and work meetings with colleagues. However, from this trip, the scientist returned home in an extremely depressed state. Without any explanations, he completely ceased joint work with Heisenberg and stopped communicating with Jung.
+
+Against the backdrop of deep mental depression, Pauli soon developed significant physical health problems. After an acute pain attack, doctors discovered rapidly progressing cancer in his body. An urgent operation could not help, and in December of the same year, the great physicist was gone… [i7]
+
+<center>([Read more](/tbc/33/))</center>
+
+### Inside links
+
+[i6] World formula, [https://kniganews.org/map/n/00-01/hex1b/](https://kniganews.org/map/n/00-01/hex1b/)
+
+[i7] Something happened, [https://kniganews.org/map/n/00-01/hex1c/](https://kniganews.org/map/n/00-01/hex1c/)
+
+[i8] Something else, [https://kniganews.org/map/n/00-01/hex13/](https://kniganews.org/map/n/00-01/hex13/)
+
+### Outside links
+
+[o9] Werner Heisenberg, *Physics and Beyond: Encounters and Conversations*. London (1971)
+
+[o10] Pauli to Heisenberg, 21 Dec. 1957 [2811] in K. v. Meyenn, ed.: *Wolfgang Pauli: Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg u.a.*, Vol V. Springer-Verlag (1996)
+
+[o11] Pauli to Jaffé, 5 Jan. 1958 [2825], in K. v. Meyenn, ed.: *Wolfgang Pauli: Wissenschaftlicher Briefwechsel*, Vol IV. Springer-Verlag (1996)
+
+[o12] Pauli to Pais, 17 Aug. 1950 [1147], in K. v. Meyenn, ed.: *Wolfgang Pauli, Wissenschaftlicher Briefwechsel*, Vol IV, Springer-Verlag, (1996)
+

data/tzo/33.md

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+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc33bouncejugglin.jpg)</center>
+
+<center>(12)</center>
+
+In the history of science of the late 1950s, there are still a few notable and hard-to-explain losses caused by the disappearance of outstanding scientists from the spheres of fruitful scientific activities. [i9]
+
+This didn't necessarily happen under such tragic circumstances as in the case of Pauli. But in the final outcome — as in the history of Claude Shannon, in particular — it was equivalent to a mysterious and clearly premature scientific death.
+
+Speaking of information theory, no scientist of the 20th century has made a contribution to this field that could be compared to Shannon’s. Without any exaggeration, this man is accepted as the father of information theory and scientific cryptography.
+
+And this same person, at the peak of a brilliant career, for unnamed reasons, left big science, shifting to a quiet and inconspicuous teaching job. Metamorphosis occurred in the same already known interval between 1957 and 1958, when the scientist was barely 40 years old. [i10]
+
+Nothing comparable to his previous masterpieces of scientific creativity was done by Claude Shannon for the rest of his life. At least that’s what is commonly believed.
+
+<center>(13)</center>
+
+But it definitely makes sense to inquire what this clever man, famous not only for his gift as an outstanding theorist but also for his talents as a skilled engineer-designer, was doing in the subsequent years.
+
+It is no secret, for instance, that Shannon turned his large house into something between a library, a workshop, and a museum, where various devices and apparatuses of his own making accumulated.
+
+And an old passion of the scientist for juggling eventually led him, among other things, to create his own theory of this art — based on the fundamental "juggling theorem". [o13]
+
+A particular interest of Shannon's was the technique of manipulating multiple objects "on the bounce" — at moments when they hang in the air before starting to fall.
+
+As a juggler practitioner, he even attempted to master a peculiar juggling technique while hanging upside down. As an engineer-developer, he constructed a robot that confidently juggled three balls, which bounced off a drum membrane when thrown downwards.
+
+Another interesting work by Shannon in the same vein was a "philosophical" sculpture depicting a juggler tossing other, smaller jugglers, who, in turn, juggled even smaller jugglers…
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc33fractaljuggler.jpg)</center>
+
+<center>(14)</center>
+
+Another important amusement among the scientist's "home entertainments" was various experiments with the subtle interconnections between randomness and determinism in our lives.
+
+For example, one of the devices that entertained guests in Shannon's house worked as a coin tosser. The mechanism of this machine was set so precisely that it allowed someone to predetermine the exact number of coin turns in the air. In other words, a seemingly random probabilistic outcome of the classic experiment with a coin landing heads or tails was programmed to be completely deterministic.
+
+Another striking example of the same series was a specialized minicomputer constructed by Shannon, about the size of a pack of cigarettes, which could consistently beat a casino in roulette. More precisely, based on quick measurements for the velocity of the roulette wheel and the speed of the ball's throw by the croupier, this device effectively predicted the most likely "outcome of the experiment" — the diamond, i.e. the one of the eight sectors of the roulette where the ball will stop… [o14]
+
+In short, if you look at all these unserious entertainments of Claude Shannon from a slightly different, physico-theoretical perspective, linking them with the studies of Everett and Pauli, you can discover rather interesting things.
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc33alice.jpg)</center>
+
+<center>([Read more](/tbc/41/))</center>
+
+### Inside links
+
+[i9] Unamusing coincidences, [https://kniganews.org/map/n/00-01/hex1d/](https://kniganews.org/map/n/00-01/hex1d/)
+
+[i10] Juggler on a train, [https://kniganews.org/map/n/00-01/hex1f/](https://kniganews.org/map/n/00-01/hex1f/)
+
+### Outside links
+
+[o13] Claude Shannon, "*Scientific Aspects of Juggling*", in N.J.A. Sloane and A. D. Wyner (eds), "*Claude Elwood Shannon Collected Papers,*" New York, IEEE Press (1993) pp. 850-864; Peter J. Beek and Arthur Lewbel, "*The Science of Juggling*", Scientific American, November 1995, pp 92-97. [https://www2.bc.edu/~lewbel/jugweb/sciamjug.pdf](https://www2.bc.edu/~lewbel/jugweb/sciamjug.pdf)
+
+[o14] Edward O. Thorp, "*The Invention of the First Wearable Computer*", 2nd. International Symposium on Wearable Computers, Pittsburgh, Pennsylvania, October 19-20, 1998. [http://www1.cs.columbia.edu/graphics/courses/mobwear/resources/thorp-iswc98.pdf](http://www1.cs.columbia.edu/graphics/courses/mobwear/resources/thorp-iswc98.pdf)

data/tzo/41.md

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+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc41base.jpg)</center>
+
+<center>(15)</center>
+
+The ideas of scientists who "dropped out" of science for various reasons in the late 1950s are most conveniently compared using the tools of mathematics. This is natural since mathematics is the basic language for describing nature. Why this is so, no one can say for certain. But it is an undisputed fact.
+
+And besides that, mathematics is especially attractive because it allows, quoting well-known specialists [o15], the manipulation of objects without giving them precise definitions. There's a point, there's a straight line, there's a plane – based on these concepts and the relationships between them, it is possible, knowledgeable people assure, to teach geometry even to the blind.
+
+The metaphor of human blindness is particularly apt in the context of comprehending the incomprehensible nature – if one recalls the famous parable of the blind men trying to understand what an elephant is by touching different parts of it. [i11]
+
+Given that we inherently have the concepts of a point, a straight line, and a plane, it is easy to demonstrate how mathematics is inseparably linked to physics through the concept of motion. That is, based on the idea of dynamics – movement – one can derive all subsequent concepts from a single one.
+
+The movement of a point generates a 1-dimensional line, specifically, a straight line and a circle. The movement of a line generates a surface. Thus, a straight line can generate a 2-dimensional plane in two basic ways – parallel translation and rotation around one of its points.
+
+Similarly, 3-dimensional space can be generated by parallel translation of a plane or rotation of a plane around one of its lines. It is clear that this process can be developed further – towards the generation of spaces of higher dimensions.
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc41rotatinplane.jpg)</center>
+
+<center>(16)</center>
+
+The idea of rotation is embedded in the foundations of mechanics and geometry from the outset. Alongside the point, line, and plane, a fundamentally important object in geometry is the circle. The uniform motion of a point along a circle, accordingly, is a fundamentally important system in mechanics.
+
+The equation describing the motion of a point in such a system, as it turned out, is equally suitable for describing the oscillations of a weight on a spring or a pendulum on a suspension, for the sinusoidal propagation of waves, and for describing the modes of string vibrations. Due to obvious connections with music, the system is called a harmonic oscillator.
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/simple_harmonic_motion_orbit.gif)</center>
+
+<center>Simple examples of harmonic motion (Wikipedia animation)</center>
+
+When classical physics was replaced by quantum physics, it quickly became apparent that the harmonic oscillator plays no lesser role there. More precisely, a much greater one. Not only because the strictly discrete natural frequencies of a musical string's sound are a direct mechanical analogy for the allowed orbitals of an electron in an atom. But also because the wave equations of quantum objects are fundamentally built on the idea of oscillations and the mathematics of complex numbers. And this mathematical apparatus is essentially ideally suited for solving problems about the motion of a point in a circle (in the phase space of states).
+
+Another very important geometric feature of oscillating systems is the appearance of additional rotation in them when at least two influences act on the oscillating system. This phenomenon is most often called the **Berry phase** – in honor of the English physicist-mathematician Michael Berry, who rediscovered the phenomenon once again in the 1980s. But in reality, different manifestations of the same effect were known to scientists much earlier.
+
+Thus, in classical mechanics, the "Foucault's pendulum" – the rotation of the plane of oscillations of a plumb line under the influence of Earth's rotation – has been known for centuries. In quantum physics, the rotation of the plane of polarization of photons when passing through a fiber-optic cable is a well-known manifestation of the same effect. It is also possible that quantum spin – the phenomenon of particles rotating around their own axes – can be naturally explained through the peculiarities of system oscillation.
+
+<center>(17)</center>
+
+When – in the 19th century – the tools of multidimensional geometry began to be included in the standard arsenal of mathematics, the most curious researchers began to tackle the problems of perception. In other words, long before the appearance of the concept of 4-dimensional space-time, work began to be devoted to how an observer from, say, a 2-dimensional world would perceive 3-dimensional objects. [o16]
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc41flatland.jpg)</center>
+
+One of the most characteristic examples of this kind is the passage of a 3-dimensional sphere through a flat world. To the inhabitants of the plane, it would initially appear as a tiny point, then a circle of variable – first growing, then decreasing – diameter, and finally again as a vanishingly small point. Using this analogy, it is significantly easier to imagine that a 4-dimensional sphere passing through a 3-dimensional world like ours would appear as a spherical object with a size changing from zero to a maximum diameter.
+
+From this picture, it is logical to move on to constantly oscillating quantum particles and the well-known tunneling effect. That is, the phenomenon of a quantum particle passing through a barrier insurmountable in classical physics. A particle's wave function description shows that its real size (probability amplitude) periodically decreases to zero. So, at these moments, it can slip through barriers as if invisible.
+
+Another important aspect of the quantum world is that particles of matter interact – quantum entangle – not directly but necessarily through a photon or a mediator particle. For the geometric description of this picture, it is essential that a moving photon can be represented by its plane of polarization. Typically, if a photon is reflected by a particle, the plane of the wave propagates without rotation (linear polarization). But if the photon is emitted by a particle, then the plane of polarization rotates around the axis of propagation (circular polarization).
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/photon.jpg)</center>
+
+<center>A twisted ribbon — one way to depict a single photon with circular polarization</center>
+
+Looking at the picture from this perspective, it is easier to imagine the mechanism of forming quantum entanglement. When a photon departs from one particle, they are already entangled, and the photon's plane of polarization already carries information about the quantum state (spin direction) of the particle. When the photon reaches another particle, the plane of polarization makes a "slice" of its current state. If the particle’s diameter is maximum, then the interaction takes place at its maximum. And if the cross-section diameter is zero at that moment, then there is no interaction and, consequently, no entanglement at all.
+
+It's probably not hard to understand that although in this movement and interaction scheme all elements are defined by a deterministic wave function, the final picture of all these oscillating particles-targets and rotating photon's planes is quite intricate and tangled. So the easiest way to describe it is by approximate methods through probability amplitudes. In other words, a general – though very rough – scheme has been constructed for a mechanical description of the quantum world. Moreover, it's a world that, in many significant properties, is very similar to Everett's branching world.
+
+<center>(18)</center>
+
+In the history of science, there is a tradition, probably going back to biblical texts with their meticulous listing of who begot whom since the time of Adam and Eve. In the scientific world, in a similar vein, people also like to record the genealogical connections of generations – who was whose teacher and student. In particular, it has become noted in modern encyclopedias that the most famous students of the patriarch of American physics, John Archibald Wheeler, were Richard Feynman and Hugh Everett.
+
+Enough has been said about the complex history of the unacknowledged-in-life glory of Everett. About the extraordinary personality of the Nobel laureate Feynman, not to mention his more direct and brilliant scientific career, there are so many books published today that it seems almost everything has been said. But it may turn out that actually not all facts and connections are generally known yet. For example, of this kind.
+
+In his lectures and books, Feynman repeatedly emphasized [o17] that the three basic theories of modern physics, describing fundamental forces, are essentially very similar to each other. And they are built on the same basis as the very first of them historically – quantum electrodynamics, or QED (for the development of which Feynman received the Nobel Prize).
+
+All three quantum theories – electromagnetic, strong, and weak nuclear interactions – describe the interaction of spin-1/2 objects (like electrons) with spin-1 objects (like photons, gluons, and W-bosons) in the same terms of probability amplitudes. Naturally, it would be very desirable to know why all physical theories have such a similar structure.
+
+Without having a definitive opinion on this matter, Feynman proposed several possible answers. And one of them, the most promising, looks like this. Perhaps **all these similar phenomena – are actually different sides of one and the same picture, hidden from us**. Such a picture, the parts of which, taken separately, only seem different – like fingers on one hand…
+
+The importance of this very deep idea can be illustrated by the example of the Feynman integral, which is a convenient way to compute events in the quantum world. But first, it is necessary to recall one of the fundamental principles of quantum physics – the superposition of states.
+
+The essence of the principle, in short, is this. In classical physics, for any object moving from point A to point B, a specific and uniquely determined trajectory is implied, but in quantum physics, the same picture looks significantly different. For an object of the micro-world, like an electron, such a trajectory is a superposition or overlay of all possible paths from point A to point B, taking into account the probabilities of each route. If we move to numerical descriptions, the problem is calculated analytically as a "weighted average" using the path integral, proposed by Richard Feynman in the 1940s while developing quantum electrodynamics.
+
+It should be emphasized that this mathematical construct, which has proven itself very well in a variety of different physical applications, far removed from QED, looks extremely strange from the perspective of professional mathematicians. One of the scientific authorities in the mathematical field described the Feynman integral with these words: "Imagine something like the Eiffel Tower hanging in the air – without foundation from the point of view of mathematics. There it all is, all of it works, but it stands on who knows what"… [o18]
+
+However, Feynman's construction – a "weighted average" for the superposition of all possible particle trajectories, considering the probabilities of each route – can naturally be reformulated in Everett's construction terms with its constantly branching worlds. That is, it is logical to assume that both these schemes are based on the same theoretical foundation.
+
+If we recall that Hugh Everett built his concept on Shannon's theory of information, then the subsequent conclusion seems quite amusing. It is possible that the **mathematical foundations of the Feynman integral** are hidden there – **in the depths of information theory**.
+
+In an ultra-brief formulation, this idea is since some time expressed by the maxim "**It from bit**" . And it is unlikely a coincidence that such a beautiful aphorism was invented – at the end of his long life – by John Archibald Wheeler [i12]. The teacher of Feynman and Everett, who managed to outlive his students by several decades.
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc41eiffel.jpg)</center>
+
+<center>([Read more](/tbc/42/))</center>
+
+### Inside links
+
+[i11] Cave and Elephant, [https://kniganews.org/map/w/10-00/hex88/](https://kniganews.org/map/w/10-00/hex88/)
+
+[i12] Juggler on a Train, [https://kniganews.org/map/n/00-01/hex1f/](https://kniganews.org/map/n/00-01/hex1f/)
+
+### Outside links
+
+[o15] Mark Kac and Stanislaw M. Ulam, "*Mathematics and Logic: Retrospect and Prospects*", F.A. Praeger Publishers (1968)
+
+[o16] Abbott, Edwin A. (1884) *Flatland: A romance in Many dimensions*. Dover thrift Edition (1992 unabridged). New York.
+
+[o17] R. Feynman, "*QED The Strange Theory of Light and Matter*". Princeton University Press(1985)
+
+[o18] Юрий Манин. "*Не мы выбираем математику своей профессией, а она нас выбирает*". Interview with the newspaper "Троицкий вариант", №13, 30 September 2008

data/tzo/42.md

@@ -0,0 +1,99 @@
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc42escher.jpg)</center>
+
+<center>(19)</center>
+
+The theoretical construction of the multiverse in Hugh Everett's dissertation was built on the basis of the Schrödinger wave equation. In other words, his concept did not address the effects of the theory of relativity, which significantly affect the behavior of quantum particles and are accounted for in the fundamental relativistic Dirac equation. It is clear that to develop Everett's ideas to a complete picture, the results of P.A.M. Dirac must also be considered.
+
+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.
+
+<center>![](https://kniganews.org/wp-content/uploads/2011/10/5dzigzag.jpg)</center>
+
+<center>Zigzag representation of an electron (from R. Penrose's book "The Road to Reality")</center>
+
+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…
+
+Describing this field slightly differently, the zigzag oscillations of particles occur in some all-pervasive substance akin to a superfluid that uniformly fills the entire space of the universe. If one thinks deeply about the essence of this concept, it turns out that the currently accepted Higgs mechanism implicitly reincorporated into the description of nature a special fluid previously known to physicists as the ether. [i13]
+
+<center>(20)</center>
+
+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.
+
+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.
+
+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]
+
+<center>(21)</center>
+
+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]
+
+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.
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc42osc.jpg)</center>
+
+<center>Oscillation phases of oscillon</center>
+
+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.
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc42osclls.jpg)</center>
+
+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.
+
+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.
+
+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.
+
+<center>(22)</center>
+
+Relying on Dirac's relativistic equation, it can be stated that both the electron and proton, being in their Zitterbewegung, are constantly making jumps of the type up-down. And these directions "up" and "down" are for each particle their own, arbitrarily set by the orientation of their spin axis. But this consideration is valid only in the 3-dimensional space we observe.
+
+In the fourth dimension — time — our entire world, as is well known, constantly shifts in only one direction: from past to future. In other words, considering the projection of the spin of massive particles on the time axis, one can say that in the 4th dimension, they all experience jumps in the same direction.
+
+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."
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc42antiferromagnet.jpg)</center>
+
+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.
+
+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.
+
+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.
+
+Formulating more precisely, it would be more accurate to speak of the electron not as a "hilltop" but as the lower point of a conical "pit" of the oscillon. Because in conditions of a double membrane, constantly in a state of vibrations, phases of the oscillon like "hill" turn out to be less stable and perform the role of anti-particles. That is, they disappear as a result of annihilation. Such a pair of membranes vibrating in antiphase is commonly named in modern physics as a "brane-antibrane" system.
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc42twobr.png)</center>
+
+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.
+
+Completing the initial description of this model, it remains to remind of the extraordinary enthusiasm experienced by Wolfgang Pauli when he made his "discovery of **division and reduction of symmetry**." Historians of science don’t have any documents explaining the essence of this inspiring discovery. However, now there is an opportunity to show that things remarkably resonant with Pauli's description have been rediscovered in modern physics, and the conclusions that follow from this also appear extremely inspiring.
+
+<center>([Read more](/tbc/43/))</center>
+
+### Inside links
+
+[i13] Forgotten Secrets, [https://kniganews.org/map/e/01-00/hex40/](https://kniganews.org/map/e/01-00/hex40/)
+
+[i14] Water Attractions, [https://kniganews.org/map/e/01-00/hex44/](https://kniganews.org/map/e/01-00/hex44/)
+
+[i15] Family Business, [https://kniganews.org/map/e/01-00/hex45/](https://kniganews.org/map/e/01-00/hex45/)
+
+[i16] Maxwell's Principle of Relativity, [https://kniganews.org/map/e/01-01/hex5d/](https://kniganews.org/map/e/01-01/hex5d/)
+
+[i17] Dancing on Sand, [https://kniganews.org/map/e/01-00/hex43/](https://kniganews.org/map/e/01-00/hex43/)
+
+[i18] Brazilian Nut and Gravity, [https://kniganews.org/map/e/01-00/hex4b/](https://kniganews.org/map/e/01-00/hex4b/)
+
+[i19] Odyssey of the Vortex Sponge, [https://kniganews.org/map/e/01-01/hex51/](https://kniganews.org/map/e/01-01/hex51/)
+
+### Outside links
+
+[o19] Roger Penrose, "*The Road to Reality. A Complete Guide to the Laws of the Universe*", J.Cape (2004)

data/tzo/43.md

@@ -0,0 +1,129 @@
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc43escher.jpg)</center>
+
+<center>(23)</center>
+
+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.
+
+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…
+
+This whole scheme, however, can only work if the particle pairs (electron-proton) inhabiting both membranes easily form a single quantum state with other such pairs. The feasibility of this, unfortunately, is far from obvious. Practically all physical interactions between particles — with one exception — must occur within the confines of a single membrane. Otherwise, the existence of a second parallel world would have been established and confirmed through numerous experiments long ago.
+
+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]
+
+<center>(24)</center>
+
+But before delving into the peculiarities of the mechanism connecting quantum gravity and quantum entanglement in the model, it is useful to consider several important ideas and consequences that arise from the overall two-brane construction. One central idea here is the **concept of the universe as a closed one-sided surface**. The simplest example of one-sided surface is the **Möbius strip**. [i21][i22]
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc43mobius.jpg)</center>
+
+Accordingly, the world as a Möbius strip is the simplest and most natural explanation for why the number of positive and negative electric charges in the universe is always equal. So the total electric charge of the universe remains invariably equal to zero.
+
+In the science of physics, it's worth remembering, this fact is assumed but not proven. In the context of a Möbius strip, this becomes self-evident. Simply because any **positive charge of a proton in one part of the universe is at the same time a negative charge of an electron somewhere at the opposite end of the cosmos**.
+
+Furthermore, the peculiarities of the topology of the Möbius strip actually contain much, much more. Virtually any fact established by mathematicians for this object offers beautiful explanations for well-known but poorly understood phenomena in the structure of nature.
+
+For instance, the Möbius strip is closely related to the spin of quantum particles. The known spin 1/2 value for massive fermion particles in geometrical terms means that to return a rotating particle to its original state, its axis needs a 720-degree twist, not just 360, as usual. Essentially, it requires two full turns.
+
+Initially, this fact appeared rather strange and enigmatic to theorists. Until Paul Dirac showed that such an evolution of the electron on its orbit matches the movement of a particle along a Möbius strip: where a single loop leads to an antiparallel twist in spin direction, requiring two loops for a complete return. [i23]
+
+When combined with the hydrodynamic model of oscillations (as per Bjerknes), an astonishingly simple explanation arises for a number of obscure areas in particle electromagnetic interactions. It's known, for instance, that each atom orbit can host a maximum of two electrons, which share the same charge but do not interfere with each other due to their antiparallel spins.
+
+Another fact. The conventional explanation for superconductivity is based on Cooper pairs — electrons with antiparallel spins that bind in pairs and move without resistance in a conductor. Lastly, experiments with proton collisions in accelerators reveal that if the spins of the projectile proton and the target proton are antiparallel, one particle passes through the other as if it weren't there at all, contrary to theoretical predictions. [i24]
+
+It's worth noting that in all these cases, the spins of particles that don't engage in usual electromagnetic interactions are oriented antiparallel to each other. Which translates to a 180-degree difference, or one-quarter of 720 degrees. For twentieth-century physics, it doesn’t mean anything special. However, in the Bjerknes pulsation theory developed nearly a century and a half ago, it is mathematically demonstrated that **there is no electromagnetic interaction between particles oscillating with a quarter phase difference**. [i25]
+
+<center>(25)</center>
+
+It is quite possible that the tempting idea of the world structure based on the Möbius strip would have long been established in science if not for a fundamental obstacle. In terms of topology, this issue is recognized as the difference between orientable and non-orientable surfaces. Simply put, objects in our world typically feature a very clear distinction between the right and left-hand gloves. Similarly, clock hands always move in one direction. This characteristic is known as the orientability of space.
+
+The Möbius strip, however, and other more complex one-sided surfaces, are non-orientable spaces. Here, a single tour around such a world reveals that right gloves become left, and vice versa. The clock hands can move in the opposite direction around the dial. This evidently doesn't correspond with the reality of our world.
+
+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.
+
+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.
+
+However, **at the turn of the 2000s, it was established — both theoretically and practically — that smooth reversals of vortices are indeed possible**.
+
+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]
+
+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]
+
+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.
+
+<center>![](https://kniganews.org/wp-content/uploads/2011/10/67vortexflip.jpg)</center>
+
+<center>Process of the dynamical inversion of the topological charge</center>
+
+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>
+
+A notable feature in the mechanism of an optical vortex or "topological charge" inversion is the experimentally observed phase where it extends into a thin line or vortex tube.
+
+<center>![](https://kniganews.org/wp-content/uploads/2012/12/bc43spiralgal.jpg)</center>
+
+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.
+
+In the Standard Model — as the pinnacle of modern quantum physics — there are quite a few artificial manipulations, where correct equations arise by adjusting free parameters to fit experimental results. There is an understanding that a new theory is needed, which retains all the strengths of the old one but explains the nature of interactions more naturally.
+
+In many respects, the so-called principle of supersymmetry is well-suited for this role. The basic idea of SUSY is quite simple. If it were possible to find in nature such a symmetry that would associate each fermion with its boson, and each boson, respectively, find its paired fermion, then many of the serious problems of the standard model would disappear by themselves.
+
+Putting the same principle in slightly different words, for each particle with spin 1/2 (fermion) present in the universe, it requires a paired particle with spin 1 (boson). And vice versa.
+
+During the mathematical analysis of this supersymmetric picture, another remarkable thing becomes apparent. Performing two consecutive supersymmetric transformations on a system of such particles leads to the emergence of the same system as was at the beginning, but only with different space-time coordinates. In other words, somehow this supersymmetry transforms space-time. This opens up a path to understanding the quantum nature of gravity…
+
+In short, mathematically this entire picture of full symmetry looks extremely beautiful and enticing. However, there is nothing observed in nature that resembles supersymmetric partners for known particles. But intuition tells scientists to persistently **continue the search for SUSY**. Because – **such beauty cannot be completely useless**.
+
+To smoothly return from SUSY to the phase of the thin vortex tube arising when branes converge, one can recall the story of how the well-known term "superstrings" was born in string theory. When in string theory they learned to combine bosonic and fermionic fields into a single system, supersymmetry arose there automatically – by itself…
+
+And to make a long story short, the specific task of interest was thoroughly examined in 2005 by a group of string theorists, including the already mentioned Eva Silverstein. Thanks to this study [o23] it was revealed, in particular, that the evolution of the vortex tube during the convergence-divergence of membranes is accompanied by radical changes in the topology of surfaces.
+
+At one end of the tube, a tachyon particle breaks away or is emitted, leaving the space of the double membrane (the important, as it turns out, role of these particles will be considered a little later). At the other end of the tube, another particle with unusual properties is formed. The particle has a spin of 2, which is characteristic of the graviton, but at the same time, it is like it’s split, possessing a "longitudinally divided mode"…
+
+Since after this the vortex tube disappears and the membranes diverge with breaking of causal connections between them, the final research result was deemed extremely puzzling by theorists. And what to do with this next remained unclear. [i29]
+
+If, however, one looks at the revealed picture from the perspective of a slightly different model — where fermion particles through the phase of a thin tube with a chirality flip change places at each brane convergence — a whole set of unexpected answers to long-standing questions in physics opens up.
+
+In particular, that the beautiful SUSY really exists in nature in all its glory. And why we do not observe it. And from where to where during SUSY transformations, space-time shifts. And finally, what exactly is a graviton — the elusive particle of quantum gravity.
+
+<center>([Read more](/tbc/44/))</center>
+
+### Inside links
+
+[i20] Loops and nets, [https://kniganews.org/map/w/10-00/hex8c/](https://kniganews.org/map/w/10-00/hex8c/)
+
+[i21] Möbius and electricity, [https://kniganews.org/map/e/01-00/hex49/](https://kniganews.org/map/e/01-00/hex49/)
+
+[i22] Rubber geometry, [https://kniganews.org/map/e/01-10/hex6c/](https://kniganews.org/map/e/01-10/hex6c/)
+
+[i23] Spin on Möbius strip, [https://kniganews.org/map/e/01-10/hex67/](https://kniganews.org/map/e/01-10/hex67/)
+
+[i24] As one through another, [https://kniganews.org/map/e/01-01/hex59/](https://kniganews.org/map/e/01-01/hex59/)
+
+[i25] Family business, [https://kniganews.org/map/e/01-00/hex45/](https://kniganews.org/map/e/01-00/hex45/)
+
+[i26] Doubling matters, [https://kniganews.org/map/w/10-00/hex84/](https://kniganews.org/map/w/10-00/hex84/)
+
+[i27] Phase transitions with flip, [https://kniganews.org/map/w/10-00/hex89/](https://kniganews.org/map/w/10-00/hex89/)
+
+[i28] How does it spin? [https://kniganews.org/map/e/01-01/hex56/](https://kniganews.org/map/e/01-01/hex56/)
+
+[i29] Don’t panic – tachyons, [https://kniganews.org/map/w/10-00/hex8a/](https://kniganews.org/map/w/10-00/hex8a/)
+
+### Outside links
+
+[o20] P. Horava and E. Witten. *Heterotic and Type I String Dynamics from Eleven dimensions.* Nucl. Phys. B460 (1996) 506, [arXiv:hep-th/9510209](http://arxiv.org/abs/hep-th/9510209)
+
+[o21] Sh. Kachru, E. Silverstein. *Chirality Changing Phase Transitions in 4d String Vacua*. 25 Apr 1997, [arXiv:hep-th/9704185](http://arxiv.org/abs/hep-th/9704185)
+
+[o22] Gabriel Molina-Terriza, Jaume Recolons, Juan P. Torres, Lluis Torner, and Ewan M. Wright. *Observation of the Dynamical Inversion of the Topological Charge of an Optical Vortex.* Physical Review Letters, vol 87, 023902 (Issue 2 – June 2001)
+
+[o23] A. Adams, X. Liu, J. McGreevy, A. Saltman, E. Silverstein. *Things Fall Apart: Topology Change from Winding Tachyons*. JHEP 0510, 033 (2005) [arXiv:hep-th/0502021](http://arxiv.org/abs/hep-th/0502021)

data/tzo/44.md

@@ -0,0 +1,159 @@
+<center>![](https://kniganews.org/wp-content/uploads/2013/01/bc44pf.jpg)</center>
+
+<center>(27)</center>
+
+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]
+
+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.)
+
+In particular, Kaluza demonstrated that the equations of GTR for the case of five dimensions could be transformed in such a way that they decomposed into the description of three interconnected subsystems: (1) regular four-dimensional Einsteinian gravity; plus (2) a set corresponding to Maxwell's equations for the electromagnetic field; and plus (3) another obscure field of scalar nature.
+
+A scalar field, it can be explained, in physics is a force field that has only one component, which affects every point in space regardless of the reference frame rotations. An illustrative example of such a field is often given as ocean tides – when the level of the ocean rises and falls at a point on the water surface all around at once. Unlike wind or river flow, which have direction and are described in terms of vector fields.
+
+The example with the oscillating scalar field of tides is particularly good because using visual hydrodynamic analogies it allows illustrating the depth of Kaluza's discovery, which was far ahead of its time. (Moreover, it provides a fairly transparent analogy for the mechanism that ensures the vibration of the system in the physics of oscillons.)
+
+Already in Maxwell's theory of electromagnetism, constructed on the concept of "displacement current" or otherwise pulsating charges, there is nothing said about what energy constantly fuels these continuous oscillations. They simply exist. Later, with the emergence of quantum physics, such things as the continuous spin of particles and their constant emission of virtual photons – with clear violations of the law of the conservation of energy – also began to be accepted as a given. It's simply there, although it's not clear where it comes from.
+
+On the other hand, evident interconnections – through the Bjerknes theory of pulsations – between Maxwell's electromagnetism and the newly discovered phenomenon of oscillons clearly point to the source of this hidden energy. At the core of all the aforementioned phenomena – particle oscillations, their spins, virtual photon emissions – there must be an (oscillating) scalar field. And it is precisely this field that serves as an essential component in the long-known equations of Theodor Kaluza.
+
+Of course, in modern physics, particularly in string theory, Kaluza's hypothetical scalar field has been studied thoroughly and extensively. Its quanta-particles are known by various names such as dilaton, graviscalar, or radion. Moreover, relying on the dilaton, attempts are now being made to explain some of the toughest problems – both dark energy and the inflationary expansion of the universe and the challenges in searching for SUSY.
+
+But it seems no one has yet put forward the idea to which the unity of the scalar field, electromagnetism, and gravitation in Kaluza's equations transparently hints. The idea that **photons and gravitons might actually be different manifestations of the same phenomenon**.
+
+<center>(28)</center>
+
+To clearly and succinctly explain the essence of the idea "graviton as a pair of photons", it is convenient to start from SUSY and the geometric meaning of spin. Naturally, in the context of a constantly vibrating double membrane, the two sides of which continually separate and converge again for particle hoppings from brane to brane.
+
+The spin value of 1/2 for a fermion particle – a proton and electron – on such a brane (having the shape of a Möbius strip) geometrically means that its axis of rotation is directed perpendicular or "across" the plane of the brane. Or, otherwise, coincides with the axis of time, along which the membrane shifts in each cycle of brane convergence-divergence.
+
+Correspondingly, the spin value of 1 for a boson particle – a photon of light – geometrically means that its rotation axis is directed "along" the membrane or perpendicular to the time axis. Figuratively speaking, **a photon "does not feel" the dimension of time, always existing in the present without past and future**. [i31]
+
+Earlier it was shown that during the mutual convergence of branes, a fermionic pair of proton-electron particles makes a rather tricky flip, accompanied by the phase of a thin tube and emission of a complex of particles. This is a very important moment because the ends of the vortex tube – in terms of the entire system – denote the proton and electron, and the axis of the tube makes a turn, providing the fermions with a chirality flip when jumping from brane to brane. [i32]
+
+In other words, at the moment of convergence of the branes, the tube's axis is perpendicular to the time axis. And this means that from a geometric point of view, the spin values of the proton and electron at this moment become equal to 1. That is, each of the initial fermions obtains a bosonic partner during this phase. Yet, from our world, the triumph of SUSY is impossible to witness. But more on this a little later.
+
+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]
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/01/bc44kelvinvrtx.jpg)</center>
+
+<center>Kelvin Oval (left) and vortex ring in section</center>
+
+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.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/01/bc44doublefot.jpg)</center>
+
+And remarkably, the total spin of this pair of vortices with an antiparallel combination of rotation axes sums up from the values (+1/2) and (–1/2). That is, equal to zero – as with the **Higgs boson**, whose influence is presumed in the Standard Model to be responsible for **generating the inert mass of quantum particles**…
+
+But when the branes begin to diverge, these flat vortices move in pairs along a straight trajectory twisted like a screw – like a screw dislocation in a crystal [i35]. At this – until the next convergence of branes – the vortices appear as divided across different worlds. Since each moves within the body of its membrane.
+
+And similarly, as the zigzag representation of fermion particles in Dirac's equation requires necessarily considering two successive phases of jumps – "zig" and "zag" – analogously here, each half of the oval becomes a full-fledged particle after one half-turn of the screw ("tick") has passed in one membrane, and the second ("tock") – after the brane convergence – in the other membrane.
+
+In other words, each of the vortex parts of the oval in this double-phase "tick-tock" – observed and in our world – appears as a single circularly polarized photon. Or, otherwise, a boson with spin 1. However, if we take into account the fact that actually it's only a half of a composite particle, its overall – **resultant – spin turns out to be 2. As it should be for a graviton, carrying gravitational interactions**…
+
+Thus, in the model, a whole bouquet of hidden properties of bosons is revealed. It turns out that **both particles, responsible for the inert and gravitational mass of objects – the heavy Higgs and the massless graviton – are actually different phases of the same particle**, consisting of a pair of vortices.
+
+And since this pair is made up of two photons of our world, and in the phase of brane convergence they correspond to two fermions forming the Higgs, a full supersymmetry of particles distinctly emerged. But observing the existence of SUSY partners for any particle of our world is extremely difficult. **Because our world at those moments doesn't actually exist.**
+
+Investigating the mechanism of brane convergence-divergence step by step, one can also see the hidden trick that the double SUSY transformation pulls off with changing the position of particles in space-time. In fact, after the first SUSY move, all particles of our world disappear, transforming into their superpartners. A repeat action of SUSY returns all particles of the world back – but already on another brane, that shifted by a cycle along the time axis…
+
+<center>(29)</center>
+
+Of course, such a condensed picture requires additional explanations and justifications. For instance, from this description, it remains completely unclear what mechanism ensures that photons – even paired ones – provide the actual gravitational interaction or "mutual attraction".
+
+To give a simple and clear answer to this question immediately is not possible. Primarily because it still remains unclear what gravity actually is. Clarity here is expected after answering a more specifically posed question: why is gravitational interaction by such a large order of magnitude weaker than electromagnetism? In physics, this vague place is known as the **mass and energy hierarchy problem**.
+
+By the late 1990s, however, a promising work [o24] by Lisa Randall and Raman Sundrum appeared in this area, securing its place among colleagues under the name "RS model". And although it has not been possible to develop the success of this result as thoroughly as desired, it needs to be mentioned here necessarily. For the very reason that the RS model is also based on the concept of the world as a double membrane. [i36]
+
+Other substantial details in Randall and Sundrum, however, look different. But here the interest is in the general mathematics of the scheme. And the mathematical calculations there are such that if the existence of yet another, fifth dimension for our 4-dimensional universe, which separates our world from another 4-dimensional universe, is allowed, then the mass hierarchy problem is solved easily and beautifully.
+
+In the RS model, it is assumed that only the 3 known interactions of quantum physics operate on our brane, while all gravity is concentrated on the second membrane, called the "gravitybrane." Calculations of the model based on General Relativity showed that the energy of the branes in this situation curves the fifth dimension extremely strongly, giving the entire structure very specific features.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/01/bc44grbran.jpg)</center>
+
+In essence, the strongest changes in sizes, masses, and even the flow of time that occur in this two-brane configuration when shifting through the fifth dimension are very reminiscent of the powerful space-time deformations near cosmic black holes. However, if we assume that particles from the Standard Model physics are located on one of the branes, then according to calculations, they inevitably must have a small mass. This result means that, in principle, the hierarchy problem could be solved in a completely natural and automatic way…
+
+The only problem is that, in this case, it's solved by replacing one mystery with another. Because answering the question of the nature of the mysterious "gravitybrane" turned out to be no easier than unraveling the hierarchy mystery.
+
+But if we assume that there is actually no other gravitational brane, and instead there is a one-sided surface of the universe in the form of a double membrane, then it turns out the following.
+
+The mathematical results of the RS model distinctly indicate that **the vast space of one side of reality – like the solar system – narrows on the other side of the membrane into a very small**, by cosmic standards, **area with strong gravity**. In other words, **focused into a star**.
+
+In this highly asymmetric picture, which establishes a one-to-one correspondence between macro objects on both sides of the membrane, it's quite difficult not to notice an analogy with the geometry of the micro world. Where in a very similar way a "huge" proton on one side of the universe turns out to be a tiny, almost point-like electron on the other brane.
+
+Moreover, the Randall-Sundrum model also contains – albeit implicitly – an indication of what exactly should be understood under the mysterious fifth dimension separating the membranes (and fundamentally necessary for the overall construction of Theodor Kaluza).
+
+Each of the two branes at the edges of the RS model is similar to the world familiar to humans – flat space without any special gravitational curvature effects. Moreover, the same picture is characteristic of any layer given by a slice of space through any point along the fifth dimension axis. All layers also have flat geometry.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/01/bc44slices.jpg)</center>
+
+However, as a whole all these 4d-layers are glued to each other so that the five-dimensional space is very strongly curved. That is, **when transitioning in the fifth dimension from one layer to another, the scales of sizes, locations, time, mass, and energy change significantly**. But although the values of masses for particles vary greatly depending on the position in the fifth dimension, all physics invariably continues to appear 4-dimensional…
+
+<center>(30)</center>
+
+The multi-layered structure of space-time across the fifth dimension, revealed in the RS model, is important for the following reasons.
+
+It is time to remind that one of the specific features of matter in the currently accepted view of the world is, according to the Standard Model, three generations of particles. In each generation are observed the same sets of particles with increasing levels of mass-energy.
+
+In our world, only particles of the lowest energy level are stably observed, and the other generations appear only momentarily in high-energy physics experiments. Why nature needs other generations of particles besides ours is another unresolved problem of theoretical science.
+
+But if we look at "generations of particles" as practically non-overlapping layers of reality differing in particle energy, it is not difficult to notice the similarity of this structure with the layers in the RS model.
+
+Further, this similarity can be naturally developed by referring to the wave properties of particles and the well-known phenomenon in wave physics called the generation of additional harmonics. This mechanism allows us to see not so much "different" particles, but essentially the same basic elements of our world – but with sequential stepwise increases in their mass-energy as they transition from one layer of reality to another. [i37]
+
+In passing it should be recalled that in the physics of vibrating granular media, a phenomenon such as the spontaneous stratification of an initially heterogeneous material into fractions is well known. During such self-organization, elements with approximately the same scale of sizes and mass accumulate in each layer. [i38]
+
+In other words, **the fifth dimension of space-time can quite naturally be considered as the spontaneous stratification of particles by energy levels**. Or, we can also say, the distribution of reality across different vibration frequencies – like channels on a TV… [i39]
+
+(The question of exactly how many "TV channels" there are is much more complex than it might seem. However, under the conditions of 3 generations of particles on each of the branes, and also considering the very special phase of the merging of the two branes into one, we can always speak of at least 7 different layers of reality, i.e., 3×2+1.)
+
+When touching on such an exciting topic as the nature of the fifth dimension, it is also important to note the deep geometrical kinship between the structure considered here and the ten-dimensional space of string theory.
+
+Due to the unquestionable presence of a frequency layer structure in each of the branes, the number of dimensions of the brane turns out to be 5. The number of branes in the system is 2, and any particle simultaneously exists on both branes. In other words, the total number of dimensions turns out to be (2×5), that is, 10. Exactly as many as needed for the minimal number of dimensions of space-time in string theory.
+
+All other description details, of course, have much less resemblance. At first glance. But it depends on how you view the comparison. You can, for example, view it like this.
+
+In string theory, a rich mathematical toolbox based on the geometric structure known as Calabi-Yau manifolds has been developed for analyzing physics in hidden dimensions. The dimension of these spaces is 6, and thus they very suitably complement the known 4 dimensions of space-time to the 10 needed in string theory.
+
+But it makes sense to look at the construction of Calabi-Yau manifolds in a more expanded, historical context. And recall that initially, they appeared in mathematics as objects of a specific 3-dimensional space in which each dimension is described by a complex number. In other words, in this space, there are 3 real coordinates and three imaginary coordinates. Or – we can also say – three "hidden" dimensions.
+
+In the 4-dimensional world observed by humans, 3 space coordinates are real, and one – time – is "hidden." When moving to the extended – double-brane -- model, it is important to note one crucial detail. The second world complementing our world to the 10-dimensional in a double membrane universe is actually also "ours". That is, although remote, it is also with three real coordinates. And plus, to complete the picture, two more "hidden" dimensions: time and two layer-frequency dimensions.
+
+That is, by looking at the picture slightly differently, we get that the **world complementing** our model **is pure Calabi-Yau space in its original configuration of 3+3 dimensions**.
+
+And if the extremely non-trivial geometry at the core of this model and string theory is the same, then reformulating one into the other is already a technical matter.
+
+And since the compactified, in principle unattainable micro-spaces of string theory now turn out to be the same as our macrouniverse, only with a previously hidden structure, very interesting prospects open up.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/01/bc44calabiyau.jpg)</center>
+
+Calabi-Yau spaces are famous for extremely intricate configurations of geometry with many holes and transitions. And **in topology, any hole means an alternative shortest path from one point of space to another**. In other words, along with the new map of the universe, the perspective of fast travels to previously unthinkable distances simultaneously appears. We just need to learn how to move along frequency layers…
+
+There is evidence that this is done relying on information theory, quantum calculations, and… Shannon's juggling theorem.
+
+<center>([Read more](/tbc/51/))</center>
+
+### Inside links
+
+[i30] Closing the Circle, [https://kniganews.org/map/w/10-00/hex85/](https://kniganews.org/map/w/10-00/hex85/)
+
+[i31] Spin on the Möbius Strip, [https://kniganews.org/map/e/01-10/hex67/](https://kniganews.org/map/e/01-10/hex67/)
+
+[i32] Phase Transitions with Flip, [https://kniganews.org/map/w/10-00/hex89/](https://kniganews.org/map/w/10-00/hex89/)
+
+[i33] Don't Panic – Tachyons, [https://kniganews.org/map/w/10-00/hex8a/](https://kniganews.org/map/w/10-00/hex8a/)
+
+[i34] Forks of History, [https://kniganews.org/map/e/01-10/hex69/](https://kniganews.org/map/e/01-10/hex69/)
+
+[i35] Light as a Dislocation, [https://kniganews.org/map/e/01-10/hex6a/](https://kniganews.org/map/e/01-10/hex6a/)
+
+[i36] Bipartition with Deformed Geometry, [https://kniganews.org/map/w/10-00/hex86/](https://kniganews.org/map/w/10-00/hex86/)
+
+[i37] Granulated Geometry, [https://kniganews.org/map/e/01-10/hex6e/](https://kniganews.org/map/e/01-10/hex6e/)
+
+[i38] Brazilian Nut and Gravity, [https://kniganews.org/map/e/01-00/hex4b/](https://kniganews.org/map/e/01-00/hex4b/)
+
+[i39] Multidimensional Geometry, [https://kniganews.org/map/e/01-10/hex6f/](https://kniganews.org/map/e/01-10/hex6f/)
+
+### Outside links
+
+[o24] Randall L, Sundrum R. "*A Large Mass Hierarchy from a Small Extra Dimension*". Phys. Rev. Lett. 83 3370 (1999); arXiv:[hep-ph/9905221](http://arxiv.org/abs/hep-ph/9905221). See also: Lisa Randall. "*Warped Passages: Unraveling the Universe's Hidden Dimensions*". ECCO Press (2005)

data/tzo/51.md

@@ -0,0 +1,120 @@
+<center>![](https://kniganews.org/wp-content/uploads/2013/02/bc51esch.jpg)</center>
+
+<center>(31)</center>
+
+Any reader, minimally familiar with modern physics, has undoubtedly already noticed that throughout the entire previous material, only electromagnetism and gravity were considered. And almost nothing was said about other fundamental interactions – strong and weak nuclear forces. Accordingly, nothing has been mentioned about the particles characteristic of them: quarks, gluons, heavy bosons. **Naturally, this is not accidental**.
+
+The basic elements of electromagnetism – proton, electron, photon – are stable particles and usually do not provoke any reservations about their reality. With strong interaction particles, everything is fundamentally different. They are not observed directly in experiments, but rather indirect indications of their supposed properties are noted. Meanwhile, the basic characteristics of these objects occasionally violate the rules firmly established for "true," i.e., stably observed quantum particles. [i40]
+
+Taken together, all of this seems not so much like "real things," but rather a convenient and well-functioning mathematical abstraction. One that gradually became familiar and was perceived as "reality."
+
+Approximately the same can be said for the heavy bosons of weak interactions. Extremely short-lived particles, quickly decaying into stable components but very needed for the elegance of mathematical theory. [i41]
+
+Rephrasing the thought, it may turn out that with the emergence of a more elegant and consistent theory, retaining all the advantages but devoid of the shortcomings and constraints of the old model, the overall picture will simplify itself. And the fundamental necessity for all these artificial objects will fall away naturally.
+
+This, of course, does not at all negate the important processes occurring with particles and the products of their decay in accelerators. But in the future descriptions of the physics of these processes, objects like quarks and gluons will likely occupy roughly the same position that all other quasiparticles currently hold in science. That is, mathematically useful but essentially abstract constructions like excitons, polarons, phonons, and other anyons.
+
+<center>(32)</center>
+
+The last of the mentioned species of well-known quasiparticles – anyons – deserves special consideration. The construction ANYon – that is, "any" particle – was introduced into quantum theory as a micro-vortex object capable of simultaneously demonstrating the mutually exclusive properties of fermions and bosons. In the space of a three-dimensional universe, this is impossible, but in a flat two-dimensional world – quite possible. [i40]
+
+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.
+
+<center>![](https://kniganews.org/wp-content/uploads/2011/10/46vacillation-840.jpg)</center>
+
+<center>Hyde's Vacillation</center>
+
+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]
+
+Thirdly, finally, it has been established that anyon particles, thanks to their rare topological features, provide a highly promising toolkit for implementing error correction systems in quantum computers.
+
+<center>(33)</center>
+
+To more convincingly highlight the non-coincidental connection between these things, it makes sense to quote John Archibald Wheeler. This prominent theoretical physicist, among other things famous for inventing the term "black holes" and for an unusually long creative life, described in the late 20th century the evolution of scientists' views on the structure of the universe in approximately the following words.
+
+In the first period of his life in physics, Wheeler wrote in his final autobiographical book, he was captivated by the idea that "everything in the world is particles". In the second period, starting in the early 1950s, he adhered to the view of the world as consisting of fields. And closer to the finale [mid-1990s] he was enthralled by a new idea "everything is information"… [o25]
+
+The depth and importance of this man's judgments, linking in his scientific fate the past and future of 20th-century physics, may become clearer if a few such facts are mentioned. John Wheeler was a disciple of Niels Bohr, the father of quantum physics. Subsequently, John Wheeler's graduate students in different eras were Richard Feynman, Hugh Everett, and David Deutsch. That is, people who played a key role in the emergence and establishment of a new field of scientific research called quantum computing.
+
+Richard Feynman is considered the first of those who analyzed and justified in the early 1980s the possibility of constructing fundamentally new computers based on quantum effects – as a natural way to cheaply model phenomena of the quantum world. [o26]
+
+Although Hugh Everett had already passed away by that time and had long ceased to engage in physics, it was his interpretation of quantum mechanics that later served as the theoretical basis for the practical implementation of quantum computers.
+
+And David Deutsch – now one of the most prominent ideologists of quantum computing and the Everett multiverse – on the basis of this platform first advanced in 1985 the concept of a quantum computer as a universal quantum simulator of reality. [o27]
+
+In the 1990s – a time of rapid flourishing in the field of quantum computing – one of the most unexpected discoveries was made, perhaps. Delving into the details of quantum computing algorithms, nuances of practical qubit implementation, and quantum error correction technologies, researchers became increasingly convinced that they were dealing with **a task of the "reverse engineering" recovery type**.
+
+Everything indicates that **the universe itself seems to work like a giant quantum computer**.
+
+<center>(34)</center>
+
+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]
+
+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.
+
+Conversely, Shannon's information theory deals with the problem of guaranteed preservation and integrity of the object – despite all external noise, distortion, and interference. In terms of quantum mechanics, this task is particularly relevant, given the extremely fragile states of coherent quantum systems, easily collapsing from the slightest external influences.
+
+With this – informational – perspective on the objects of the microworld, well-known phenomena of strong nuclear interactions, say, begin to look significantly different than in conventional quantum chromodynamics. In particular, the three quarks (two UPs and one DOWN), stubbornly maintaining their identity amidst the raging vortex of energy in the proton, can be viewed as a natural mechanism for quantum error correction. That is, a mechanism that allows the proton to stably retain all its familial properties under practically any natural circumstances and collisions. [i44]
+
+It is also appropriate to recall another – not yet demanded in particle physics – Shannon juggling theorem [o28]. Thanks to such – fundamentally also informational – approach, a new way of viewing the theory of weak nuclear interactions might emerge, which describes the mutual transformations of nuclear particles into one another.
+
+The closest relative of the proton, the neutron, is known to differ significantly in its key properties from its super-stable and essentially eternal sibling. In a free state, a neutron lives only about 15 minutes. Within the nucleus, however, the neutron is not only stable but also causes fundamental changes even in protons. According to modern concepts of nuclear physics, protons and neutrons inside the nucleus constantly exchange places and properties with each other, coexisting as a kind of intermediate resonances, transforming nucleons into each other. [i41]
+
+There are reasons to believe that these constant intertransformations provide the nucleus with stability. When at certain moments the nucleus manages to remain electrically neutral to hold all nucleons together even with a significant concentration of repelling protons. At other moments, it displays its full charge to compensate for the negative charges of electrons.
+
+And the Shannon juggling theorem, it can be reminded, is focused on a very similar essence. On the rules that ensure the infinitely long tossing of an arbitrary number of objects with a knowingly smaller number of hands. Or, put differently, when some objects are "at work," and others are flying somewhere in space, waiting for their turn…
+
+<center>(35)</center>
+
+Returning to ideas about creating a practical quantum computer, it is important to particularly highlight the most significant obstacle on this path. While in principle the possibility of creating a functional device of this type has long been demonstrated, a quantum computer with a large number of qubits – necessary for solving real problems – remains an extremely complex challenge to resolve.
+
+But it is indicative that the most ingenious and effective solutions in this area are sought from nature. This is, in fact, why the opinion is gradually strengthening that the universe itself functions as a quantum computer. Moreover, a computer exceptionally reliable and long having realized optimal solutions for all accompanying construction problems.
+
+In 1997, reasoning along similar lines, Alexei Kitaev invented an innovative concept called a "topological quantum computer" [o29]. The idea arose when Kitaev noticed the astounding stability of natural quantum systems, possessing something like an innate resistance to noise. In other words, the extremely high resistance to decoherence essentially appears as their inherent feature.
+
+Developing this idea, Kitaev and other researchers embarked on creating such a computer, in which delicate quantum states depend on the topological properties of a physical system. Topological characteristics, it can be reminded, are considered the most stable properties of objects because they do not change with smooth deformations like stretching, squeezing, and bending.
+
+And a topological quantum computer, consequently, is envisioned as performing calculations on hypothetical threads representing world lines of quantum particles' motion in space-time. It can be considered that the length of such a thread depicts the particle's movement through time, and its thickness – the physical size of the particle in space.
+
+As theorists have shown, if quasiparticles of a special type – the already familiar anyons – are used to implement a topological computer, it is possible to move pairs of neighboring particles around each other in a strictly defined sequence. As a result, the trajectories of anyons in space-time are intertwined into a braid, the topological structure of which contains fault-tolerant quantum computation. In other words, the final states of the particles, containing the results of the computation, are determined by the intertwining of threads in the braid and do not depend on electrical or magnetic interference…
+
+At this point, it's timely to recall the two-brane model of the universe and the mechanism by which SUSY is implemented there. When the branes are in the phase of maximum convergence, space becomes flat, and all particles transform into their opposites. Fermions become bosons, bosons vice versa into fermions, and as a whole, it turns out that all the micro-components of our world, in a certain sense, are anyons.
+
+Moreover, the famous theoretical result of Rolf Landauer [o30], the leading scientist of IBM, fits very organically into this model. Long before the birth of the quantum computer concept, as early as 1961, Landauer demonstrated the possibility of creating a device in which computations occur entirely without energy expenditure. The main condition for the operation of such a scheme turned out to be the complete reversibility of computations or the memorization of not only the output but all input data. [i45]
+
+Later this result, of course, began to be regarded as very important for the development of quantum information theory – as the laws of quantum mechanics are reversible in time. Now the picture emerges that the ideas of Kitaev and Landauer, apparently, have long been united in nature into a single simple mechanism.
+
+It will further be shown that topological braids trailing in time behind quantum particles are seemingly not only real objects. But also, in these very braids, all previous states of the system are constantly memorized. Which is necessary for the reversibility of computations, for reducing overall energy consumption, and much more.
+
+For everything that constitutes the "**soul of matter**"…
+
+<center>([Read more](/tbc/52/))</center>
+
+### Inside links
+
+[i40] Hyde's duality principle, [https://kniganews.org/map/e/01-01/hex5e/](https://kniganews.org/map/e/01-01/hex5e/)
+
+[i41] Helmholtz uncertainty principle, [https://kniganews.org/map/e/01-01/hex5f/](https://kniganews.org/map/e/01-01/hex5f/)
+
+[i42] Looks like an atmosphere, [https://kniganews.org/map/e/01-00/hex46/](https://kniganews.org/map/e/01-00/hex46/)
+
+[i43] Physics of Information, [https://kniganews.org/map/e/01-11/hex78/](https://kniganews.org/map/e/01-11/hex78/)
+
+[i44] Coherence without errors, [https://kniganews.org/map/e/01-11/hex7a/](https://kniganews.org/map/e/01-11/hex7a/)
+
+[i45] Reversibility involving intelligence, [https://kniganews.org/map/e/01-11/hex79/](https://kniganews.org/map/e/01-11/hex79/)
+
+### Outside links
+
+[o25] Wheeler J.A. (1998) "*Geons, Black Holes & Quantum Foam: A Life in Physics*". New York, W.W. Norton & Company, pp. 63-64.
+
+[o26] Feynman R.P. (1982) "*Simulating physics with computers*", Int. J. Theor. Phys. 21 467-488 ; Feynman R.P. (1986) "*Quantum mechanical computers*", Found. Phys. 16 507-531.
+
+[o27] Deutsch D. (1985) "*Quantum theory, the Church-Turing principle and the universal quantum computer*", Proc.Roy. Soc. Lond. A 400 97-117
+
+[o28] Shannon С., "*Scientific Aspects of Juggling*". In "*Claude Elwood Shannon: Collected Papers*". Eds. N.J.A. Sloane and A. D. Wyner. IEEE Press (1993)
+
+[o29] Kitaev A. Yu. (1997) "*Fault-tolerant quantum computation by anyons*". [arXiv: quant-ph/9707021](http://arxiv.org/abs/quant-ph/9707021)
+
+[o30] R. Landauer (1961) "*Irreversibility and heat generation in the computing process,*" IBM Journal of Research and Development, vol. 5, pp. 183-191, 1961
+

data/tzo/52.md

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+<center>![](https://kniganews.org/wp-content/uploads/2013/01/bc52escher.jpg)</center>
+
+<center>(36)</center>
+
+The entire history of quantum physics is, in a sense, a history of endless attempts to get rid of tachyons. Or, put differently, attempts to ignore mathematics based on human notions of common sense and a rational view of the world. [i46]
+
+Due to the astonishing effectiveness with which mathematics describes physical reality, scientists have long concluded that it is the most reliable guide on the paths of understanding nature. Accordingly, there is a persistent tradition of treating discovered solutions to obviously correct physical equations with proper attention and respect.
+
+And if a phenomenon described by the solution of the equations is not yet observed in nature, it is pre-accepted as a "scientific prediction." Historians know a very long list of such predictions, successfully confirmed by further searches, observations, and experiments. In essence, this is how science works.
+
+However, the situation with tachyons has always been fundamentally different. Already at the very beginning of the path of quantum physics, when it became clear that to work successfully in this area, it was necessary to operate with complex numbers, there appeared a prediction of an extremely unusual particle. A particle that theorists immediately wanted to forget and never remember again.
+
+That is, the equations allowed for a solution when, along with the square root of (–1), a strange object with imaginary mass, imaginary energy, and in imaginary time appeared in nature. And most unpleasantly, this particle moved at superluminal speed, contradicting the fundamental principles of the theory of relativity and, in fact, moving backward in time. By its very presence, it violated the foundations of the universe as a whole and the principle of causality in particular…
+
+Over time, this inconvenient particle became known as "tachyon." Throughout the 20th century, there were very few enthusiasts who dared to study these objects. And although their efforts gradually led to more knowledge about tachyons, these results brought neither honors nor scientific fame to researchers.
+
+At least not yet. Because until recently, physicists remained unclear about how to treat these tachyons and why nature might need them at all…
+
+<center>(37)</center>
+
+A true breakthrough in tachyon research occurred at the turn of the 1990s and 2000s, mainly thanks to a large series of works by string theorist Ashoke Sen. It was after Sen's detailed publications that the scientific mainstream seemed to stop pretending that tachyons do not exist. [o31]
+
+Consequently, there finally appeared a serious interest in the place these objects might occupy in nature and how to integrate them into the overall picture of the world without contradictions. When the matter was taken seriously, substantial progress soon followed.
+
+It was known for a long time that the appearance of tachyons in a system is the first major signal of a model's instability. But when this problem was learned to be effectively treated by "condensing" tachyons to a state of energy minimum, rather unexpected results began to appear.
+
+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.
+
+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.
+
+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**.
+
+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?
+
+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]).
+
+<center>(38)</center>
+
+Although progress in tachyon research is undoubtedly provided predominantly by the efforts of string theorists, noticeable successes in this area have also been achieved through significantly different approaches to the problem. And most pleasantly, the beautiful results of other researchers not only harmoniously blend with the results of string theory but also effectively complement them towards a fuller picture. [i47]
+
+Among remarkable features already identified by theorists in the structure and organization of a tachyonic crystal, such can particularly be noted. In general, the tachyon matter fluid consists of closed string-loops. When the membrane surface is periodically excited or "shaken," the structure of tachyons detaching from it becomes more orderly. If the shaking frequency becomes equal to a specific critical value, the description of the system's physics takes a particularly simple form.
+
+The tachyon matter fluid structures into a layered or "laminated" array of branes overlapping each other in imaginary time. In this case, **the loops of tachyons — closed strings — in the layers of the liquid crystal behave in such a way that their physics becomes an exact dual representation of the open string physics characteristic of the brane surface** (where the ends of the particles as "open strings" are attached to the brane and antibrane). [o35]
+
+Restating the essence of this discovery in more familiar terms, distinct signs of particle memory have been identified, which not only provide the reversibility of quantum physics but also form the foundation of the "soul of matter."
+
+According to theoretical estimates, this layered structure of a stable tachyonic crystal fills about 80% of all space in the universe. Interestingly, within the foundation of this layered vacuum construction, there is also a kind of "skeleton," threading the layers of the sandwich with filaments or fibers consisting of the energetically most intense points of space-time.
+
+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**…
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/01/bc52timecrystal.jpg)</center>
+
+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]
+
+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…
+
+<center>(39)</center>
+
+Wilczek's time crystals are a completely new thing and have yet to achieve any significant theoretical or practical development. Nevertheless — for the sake of capturing significance — it is appropriate to mention such a nuance of this discovery. In the early 1980s, Frank Wilczek was one of the theorists who described a new class of curious particles known as anyons (in fact, they got their name from him). [i48]
+
+How important anyons are for understanding the mechanisms of the microcosm and the structure of a topological quantum computer will become known much later. But already at the moment of the discovery of anyons, Wilczek experienced very strong emotional excitement. And he felt the same emotion again upon discovering time crystals: "It's as I had found a new logical possibility for how matter might behave that opened up a new world with many possible directions"…
+
+Already recognizable signs suggest that developing these directions promises, in particular, to converge into a single harmonious picture such seemingly different things as the structure of DNA molecules and the theory of music, the fundamental Riemann Hypothesis in number theory, and a fully quantum description of nature including gravity.
+
+Demonstrating in just a few sentences that all these things are actually inextricably linked is probably a hopeless task. But nothing prevents at least outlining the paths along which scientists are now advancing to restore the unified picture.
+
+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]
+
+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.
+
+<center>(40)</center>
+
+The giant scientific problem is that all tasks about the distribution of prime numbers one way or another close in on the **Riemann Hypothesis**. That is, on the hypothesis formulated in the mid-19th century but to this day not yet proven by anyone about a very beautiful regularity for the zeros of the complex zeta function (all nontrivial zeros of the function lie on a single line parallel to the imaginary axis and passing through the point 1/2 on the real axis).
+
+Prime numbers are a kind of "atoms of mathematics." Any integer can be decomposed into a product of primes, in a unique way. Meanwhile, the **distribution of prime numbers** on the real axis is, in essence, the **simplest model of random events** in our life. Having found another prime number, it is impossible to predict exactly what the next one will be.
+
+However, there is a **deterministic Riemann zeta function**, which, among many other things, allows for accurate estimation of the number of prime numbers less than any given quantity. Interestingly, the zeta function operates not with real numbers but with complex numbers — **like the deterministic Schrödinger wave equation governing the random behavior of quantum objects**.
+
+To vividly demonstrate the connections between the Riemann Hypothesis and the mysteries of quantum physics, it is particularly apt to mention quite a recent result by Russian mathematician Yuri Matiyasevich. In 2007, he published a research paper intriguingly titled "The Secret Life of Riemann's Zeta Function," where he included quite remarkable graphic images. [o37]
+
+By carefully reformulating the Riemann Hypothesis into a series of weaker statements, Matiyasevich used a computer program to calculate and plot on the complex plane the trajectories of certain characteristics-iterations, collectively painting a picture of the "hidden life of the Riemann function."
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/01/bc52matiyas.jpg)</center>
+
+In these graphs, two classes of objects are distinctly visible, located on different sides of the critical line-divider passing parallel to the imaginary axis through the point 1/2. The objects on the left were named "electrons" by the author since their trajectories resemble those of particles colliding and diverging. The objects on the right behave differently, resembling twisted double spirals, and were named "trains" by Matiyasevich.
+
+Looking at this picture, it is hard to miss the transparent analogies in its components with long-known quantum particles forming the "body" of matter, and tachyon spirals (time crystals), now found at the core of the "soul" of matter.
+
+Finally, another very important aspect that cannot be ignored is the connection of the Riemann zeta function to the problem of quantizing gravity.
+
+In the same year 2007, when Yuri Matiyasevich discovered the secret life of the Riemann zeta function, a book was published by prominent French mathematician and Fields medalist Alain Connes, in collaboration with Matilde Marcolli, titled "Noncommutative Geometry, Quantum Fields, and Motives." [o38]
+
+Explaining the purpose of writing this book, the authors state that it is dedicated to the very close intertwining of challenges in the field of number theory and space-time geometry. The most significant, fundamentally important problems in these fields are, as known, the proof of the Riemann Hypothesis (RH) and the construction of a theory of quantum gravity (QG).
+
+Thus, initially studying each of these problems separately from the positions of noncommutative geometry — to the creation of which Alain Connes has the most direct relation — the authors of the book discovered, to their great surprise, that there are very deep analogies between the two given problems.
+
+And there are already distinct signs that if the newly discovered interconnections between RH and QG are correctly explored, then it provides a much clearer and deeper understanding of the picture in both fundamental areas at once…
+
+<center>([Read more](/tbc/53/))</center>
+
+### Inside links
+
+[i46] Don't Panic – Tachyons, [https://kniganews.org/map/w/10-00/hex8a/](https://kniganews.org/map/w/10-00/hex8a/)
+
+[i47] Tachyonic Crystal, [https://kniganews.org/map/w/10-00/hex8b/](https://kniganews.org/map/w/10-00/hex8b/)
+
+[i48] The Hyde Dualism Principle, [https://kniganews.org/map/e/01-01/hex5e/](https://kniganews.org/map/e/01-01/hex5e/)
+
+[i49] Evolution of Spirals, [https://kniganews.org/map/e/01-11/hex72/](https://kniganews.org/map/e/01-11/hex72/)
+
+### Outside links
+
+[o31] A. Sen (1998) "*Tachyon Condensation on the Brane Antibrane System*" [[arXiv:hep-th/9805170](http://arxiv.org/abs/hep-th/9805170)]; A. Sen, "*Rolling tachyon*," JHEP 0204, 048 (2002) [[arXiv:hep-th/0203211](http://arxiv.org/abs/hep-th/0203211)]; A. Sen, "*Tachyon matter*," JHEP 0207, 065 (2002) [[arXiv:hep-th/0203265](http://arxiv.org/abs/hep-th/0203265)]
+
+[o32] Y. Oz, T. Pantev and D. Waldram (2000) "*Brane-Antibrane Systems on Calabi-Yau Spaces*", [[arXiv:hep-th/0009112](http://arxiv.org/abs/hep-th/0009112)]
+
+[o33] A. Adams, X. Liu, J. McGreevy, A. Saltman, E. Silverstein (2005) "*Things Fall Apart: Topology Change from Winding Tachyons*". JHEP 0510, 033 [[arXiv:hep-th/0502021](http://arxiv.org/abs/hep-th/0502021)]
+
+[o34] J. Polchinski, L. Thorlacius (1994) "*Free Fermion Representation of a Boundary Conformal Field Theory*". Phys.Rev.D50:622-626, 1994. [[arXiv:hep-th/9404008](http://arxiv.org/abs/hep-th/9404008)]
+
+[o35] Davide Gaiotto, Nissan Itzhaki, Leonardo Rastelli. "*Closed Strings as Imaginary D-branes*". Nucl. Phys. B688: 70 (2004). [[arXiv:hep-th/0304192](http://arxiv.org/abs/hep-th/0304192)]
+
+[o36] F. Wilczek. "*Quantum time crystals*".[[arXiv:1202.2539](http://arxiv.org/abs/1202.2539)]; A. Shapere and F. Wilczek. "*Classical time crystals*". [[arXiv:1202.2537](http://arxiv.org/abs/1202.2537)].
+
+[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)]
+
+[o38] Alain Connes, Matilde Marcolli (2007) "[Noncommutative Geometry, Quantum Fields and Motives](http://www.alainconnes.org/en/downloads.php)". American Mathematical Society, 2007

data/tzo/53.md

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+<center>![](https://kniganews.org/wp-content/uploads/2013/02/bc53escher1.jpg)</center>
+
+<center>(41)</center>
+
+In any attempts by science to grasp the nature of reality, there inevitably remains the feeling that something extremely important has been missed again. This something is precisely what prevents the entire picture from becoming complete and at least roughly understandable.
+
+One of the very old signs of this problem can be considered the phenomenon known in many manifestations and under different names – like the principle of duality or complementarity. The essence of all these terms generally boils down to the following.
+
+For the same phenomenon or object, there are several significantly different descriptions, each of which seems true in its own way. However, the differences in descriptions are such that the subject appears to be endowed with incompatible, mutually exclusive properties. This creates the impression that completely different things are being described, not one and the same.
+
+A fundamentally important detail of this problem is the intentional words "appears to be" and "impression." The importance of this nuance can be illustrated by the example of the so-called "wave-particle duality" of quantum particles – perhaps the most famous natural phenomenon with a dual description of its physical properties.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/02/bc53-wave-particle.jpg)</center>
+
+If we look more closely at the birth and establishment of this fundamental "duality" in science, it's not too difficult to notice the following. Had historical circumstances been slightly different, and if the wave (de Broglie and Schrödinger) views on quantum mechanics had gained a dominant role, the overall picture might have turned out to be far more coherent and comprehensible.
+
+The strange "paradoxes of duality" in the physics of quantum objects, which behave like waves in some experiments, and like particles in others, arise because particles and waves have long been considered fundamentally different entities by tradition. However, the true strangeness here is something else. It has long been established that there is actually no significant difference between them – except that this is usually mentioned in passing or not at all in school textbooks.
+
+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.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/02/bc53-solitontrain.jpg)</center>
+
+<center>Train of solitons in a Bose-Einstein condensate</center>
+
+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…
+
+<center>(42)</center>
+
+The example of naturally eliminating the paradoxical contradiction in wave-particle duality is especially good and instructive due to its, so to speak, methodological aspects.
+
+Firstly, it demonstrates that when constructing any theoretical frameworks, it is extremely undesirable to lay down any immutable dogmas in the foundation. Because **any dogma is a sign of the limitation of human knowledge**. And among the new reliable facts constantly discovered by science, there are always those that refute established dogmas. These facts are usually ignored or, as it's often said, "swept under the rug." However, for the sake of truth, it seems more useful to abandon compromised dogmas.
+
+Perhaps it is for this reason that "improper" soliton waves were ignored for so long in science, and their degree of importance remained misunderstood. And oscillons, or oscillating solitons, particularly close in properties to quantum particles, in the foundations of quantum theory they still seem to not exist at all.
+
+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.
+
+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]
+
+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.
+
+The metaphor of flat and volumetric images of physical phenomena can, as it turns out, be interpreted concerning the nature of reality in the literal sense as well. As physics is increasingly approaching research based on the so-called "holographic principle," an amazing thing is happening.
+
+Previously purely applied **holography technology** [i53] unexpectedly **becomes a conceptual basis for** grand theoretical discoveries regarding **the structure of the universe**. Discoveries that not only lead to a completely new picture of reality but also unite matter and consciousness into an inseparable whole.
+
+<center>(43)</center>
+
+Before moving on to consider the key features of the holographic principle, it is necessary to emphasize the following. We are talking about a direction of research that so far cannot be called influential or, moreover, dominating in modern science.
+
+It is more correct, perhaps, to speak of it as one of the quite exotic scientific approaches in theoretical physics, which in its fifteen- to twenty-year history has managed to gather quite a few supporters among highly respected scientists. And every year, it continues to steadily gain more and more. Because along this path, it is possible not only to elegantly unify quantum theory and gravity with thermodynamics and information theory but also, in passing, find new interesting solutions in other related areas of physics.
+
+The reason for the emergence of this unusual approach can be considered one of those complex paradoxes that abundantly fill modern theoretical science. By the early 1990s, researchers had accumulated such an impressive array of data for the hypothetical cosmological phenomenon known as "black holes" that the reality of these objects, fundamentally inaccessible for direct observation, practically left no doubt. However, the physics inside these objects turns out to be so different that the previously developed theoretical tools are completely unsuitable.
+
+To clarify where such an acute interest of scientists in this topic arises, it should be noted that black holes, as it turned out, not only absorb but also emit energy. In other words, they behave in such a way that their behavior very much resembles elementary quantum particles – other fundamentally important objects of nature with an unclear and paradoxical internal structure. [i54]
+
+From this arise natural questions. Are quantum particles microscopic black holes? And conversely, are cosmological black holes macroscopic "elementary particles" of nature?
+
+When the prominent Dutch theorist Gerard ‘t Hooft [o39] (later a Nobel laureate in 1999 for earlier work in another area of physics) seriously pondered these questions, he sensed, instinctively, in this riddle the depth and potential for a great discovery. Such a discovery could play a role in 21st-century physics similar in significance to what the idea of quantizing energy played for 20th-century science.
+
+As a basis for starting research, ‘t Hooft chose the attractive insights of the Israeli theoretician Jacob Bekenstein regarding the thermodynamic and informational properties of black holes. In the 1970s-80s, Bekenstein managed to elegantly demonstrate how physical concepts such as energy of matter and geometry of space can be combined with previously abstract ideas of information theory. He achieved this through the concept of entropy, which in physics serves as a measure of lost energy or measure of randomness in a thermodynamic system, and in mathematics, as a measure of informational capacity. [o40]
+
+<center>(44)</center>
+
+By postulating the discretely-granulated nature of space-time and generalizing Bekenstein's results, obtained for black holes, onto arbitrary regions of the universe, Gerard ‘t Hooft, in collaboration with Leonard Susskind, reached a very unexpected conclusion. It turned out that all information contained in a given 3D volume of space can be encoded on the 2D surface that bounds this volume.
+
+In much the same way, as is known, the mechanism of holography works – when a flat plate with an encoded hologram, when properly illuminated, reproduces a full three-dimensional image of the object. From this analogy, ‘t Hooft and Susskind proposed the corresponding name for the discovered phenomenon: **the holographic principle**. [o41]
+
+Initially, the unusual ideas of the two theorists about the universe as a hologram were shared by only a rather small group of like-minded scientists. However, soon, as development in string theory and varying-dimensionality membranes progressed, it became apparent that the approaches of the holographic principle are extremely convenient and applicable to research of a variety of physical phenomena in space-time with any number of dimensions.
+
+The essence of the holographic principle in this context can be summarized as the possibility for physics of a non-trivial process or phenomenon, being studied by researchers, to find two equivalent descriptions in spaces of different dimensionsionality. For the number of dimensions *N*, the nature of the phenomenon may appear significantly different than at dimensionality (*N*+1), but in reality, as evidenced by the solutions to equations, these turn out to be different theoretical descriptions of the same thing.
+
+And most pleasantly, due to the revealed duality of descriptions, it is now often possible – by transitioning to a space of a different dimensionality – to find ways to solve problems that were previously considered either too complex or too "obscure" on a conceptual level. With reliance on the holographic principle, it became possible, for example, to approach the longtime problems in the physics of condensed matter – such as quantum phase transitions, superfluidity, and high-temperature superconductivity – in fundamentally new ways.
+
+Speaking of the universality of this approach, it is worth noting the following fact. Initially, the holographic principle was conceived by Gerard 't Hooft as a kind of conceptual alternative to string theory. However, in practice, it has turned out that the most famous work in the holographic spirit was carried out by the string theorist Juan Maldacena [o42] and is now known as the **AdS/CFT correspondence**.
+
+In Maldacena's study, it is shown that the very unusual — in our terms — physics in a hypothetical universe with 5 dimensions and a hyperbolically concave geometry of space (the so-called anti-de Sitter universe or AdS) from a mathematical point of view turns out to be the same as the physics on its spherical 4-dimensional boundary. This 4D boundary physics is described by the so-called conformal field theory (CFT) and corresponds to a world suspiciously similar in nature to the universe we all live in… [o43]
+
+<center>(45)</center>
+
+Summing up the the story about the holographic principle, one can say this. The ever-increasing number of studies in various fields of physics clearly shows that this idea leads to very rich and interesting results. For this reason, as is customary in science, the concept of "the universe as a hologram" should likely be considered true. The big problem, however, is that based on traditional notions of nature (considering matter separately from consciousness), science unable to explain why this principle works.
+
+Although many physicists today generally acknowledge the validity of the holographic idea — that information on surfaces contains information about everything in the world — they still don't know fundamentally important things. Not what specifically should be considered surfaces encoding information. Not how exactly this information is encoded. Not how nature processes these "ones and zeros" bits, as if in a giant quantum computer. And not, finally, how, as a result of this processing, the world-hologram around us generated…
+
+The trick to understanding all these mysteries, as is now not hard to guess, lies in a holistic view of reality, where the "body" of matter does not exist separately from its "soul." That is, memory and consciousness.
+
+Or, more specifically, where the membrane of the cosmos in each cycle of its "biorhythm" generates another layer of tachyon crystal with a record of everything happening in the world. Where the scalar-dilaton in the 5-dimensional equations of Einstein-Kaluza's General Relativity is an acoustic field [i55], not only providing energy to the vibrations of oscillons but also creating a coherent background for the universe as an acousto-optical hologram [i56]. And the 5-dimensional hyperbolic anti-de Sitter space — it’s a world of "black holes," concealing within itself the unified consciousness of the universe…
+
+When the idea of reality as a computer-generated hologram is discussed in debates, the topic of who and why could have arranged all this inevitably arises. As in any other (quasi)religious metaphysical disputes, it is fundamentally impossible to prove anything to opponents here.
+
+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.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/02/bc53mandelbrot.jpg)</center>
+
+<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]
+
+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.
+
+Even in such a brief description of the structure and physics of a biological membrane system, it is quite difficult not to see the obvious similarity with the physics of the world as a membrane described a little earlier. In other words, the design of the smallest living unit — a biological cell — in general terms seems to replicate the structure of the universe. From which, based on the holographic principle, it is naturally presumed that the entire universe as a whole can be considered as a single living organism. Just like the cosmic structures forming it, fractally nested within each other…
+
+In this new, much broader spectrum of self-similar living organisms— from the cell to the universe — humans occupy, at first glance, a fairly modest place. If judged by the ratio of physical sizes. However, humans can also be viewed differently — as a self-aware element of the universe, realizing the creative potential of evolution within a separately isolated body. In such a view, our scale is significantly altered — in accordance with the horizons of our awareness. To the level, one might say, of creators, who meaningfully (more often, however, still clumsily) attempt to transform self-organizing nature.
+
+And it is surely not a coincidence that in the last few decades, a very powerful apparatus has been developed in several areas of mathematics, which reinforces the validity of this idea with rigorous calculations. Only the mathematician-developers themselves largely seem to be unaware of this… [i58]
+
+<center>([Read more](/tbc/61/))</center>
+
+### Inside links
+
+[i50] Forks in history, [https://kniganews.org/map/e/01-10/hex69/](https://kniganews.org/map/e/01-10/hex69/)
+
+[i51] How does it spin? [https://kniganews.org/map/e/01-01/hex56/](https://kniganews.org/map/e/01-01/hex56/)
+
+[i52] Loops and networks, [https://kniganews.org/map/w/10-00/hex8c/](https://kniganews.org/map/w/10-00/hex8c/)
+
+[i53] Full record, [https://kniganews.org/map/e/01-11/hex74/](https://kniganews.org/map/e/01-11/hex74/)
+
+[i54] Almost mysticism, [https://kniganews.org/map/e/01-01/hex5b/](https://kniganews.org/map/e/01-01/hex5b/)
+
+[i55] Levitation and sound, [https://kniganews.org/map/e/01-11/hex71/](https://kniganews.org/map/e/01-11/hex71/)
+
+[i56] Structure of the system, [https://kniganews.org/map/e/01-11/hex7c/](https://kniganews.org/map/e/01-11/hex7c/)
+
+[i57] Between liquid and crystal, [https://kniganews.org/map/e/01-11/hex75/](https://kniganews.org/map/e/01-11/hex75/)
+
+[i58] Missing idea, [https://kniganews.org/2012/11/17/langlands-plus/](https://kniganews.org/2012/11/17/langlands-plus/)
+
+### Outside links
+
+[o39] G. ‘t Hooft, "*Dimensional reduction in quantum gravity,*" in "*Conference on Particle and Condensed Matter Physics (Salamfest)*", edited by A. Ali, J. Ellis, and S. Randjbar-Daemi (World Scientific, Singapore, 1993), [[arXiv:gr-qc/9310026](http://arxiv.org/abs/gr-qc/9310026)]
+
+[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)]
+
+[o42] Juan Maldacena, "*The Illusion of Gravity.*" Scientific American, November 2005.
+
+[o43] Edward Witten, "*Anti–de Sitter Space and Holography.*" Advances in Theoretical and Mathematical Physics, Vol. 2, pp 253–291; 1998, [[arXiv:hep-th/9802150](http://arxiv.org/abs/hep-th/9802150)]
+

data/tzo/61.md

@@ -0,0 +1,277 @@
+<center>![](https://kniganews.org/wp-content/uploads/2013/03/bc61mathevolut.jpg)</center>
+
+<center>(46)</center>
+
+It so happened that René Descartes [i59] and Blaise Pascal [i60], two of the most significant thinkers gifted to the world by France in the 17th century, left a notable mark in history not only as philosophers but also as first-rate mathematicians.
+
+As for the genius Pascal, his contribution to the exact sciences is well-known. However, Descartes – the "father of modern European philosophy," as he is often called – is also renowned as the founder of analytic geometry. Thanks to him, in particular, the mathematical toolkit of science was enhanced with an innovative and extremely effective approach to solving problems based on a coordinate system, which eventually became known as "Cartesian."
+
+Unlike the universal language of mathematics, equally suitable for all people regardless of their worldview and beliefs, different philosophies can lead scientists to diametrically opposed conclusions. Thus, it's not surprising that Descartes's and Pascal's philosophical views on nature differed significantly. Especially in the issues concerning the relationships between the spiritual and the physical world.
+
+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.
+
+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**"…
+
+For Descartes's worldview, it seems, the symbol of the tree appeared more relatable and significant. This image, found in the oldest cosmogonic myths of many of the world's peoples under the common name "tree of life," is reflected in Descartes's "Principles of Philosophy."
+
+The hierarchical **structure for the general complex of human knowledge** about the world — i.e., for "philosophy" in Descartes's terminology — should, in his opinion, look as follows: "All philosophy is **like a tree**, of which Metaphysics is the root, Physics the trunk, and all other sciences the branches that grow out of this trunk, which are reduced to three principals, namely, Medicine, Mechanics, and Ethics."
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/03/bc61desctree.jpg)</center>
+
+Let us ignore the obvious archaism, so to speak, of Descartes's classification of sciences, and focus only on the tree-like structure of knowledge itself. And also recall — for a complete picture — the famous legend about the circumstances under which Descartes invented his coordinate system.
+
+Once, looking at a sprawling tree through a window protected by grid bars, the philosopher is said to have realized that using the squares of the grid, one could assign numbers to identify the positions of parts of the oak — trunk, branches, and leaves. And by reducing the size of the grid cells, one could get descriptions (or "digitizations," as it is now said) of the oak with more and more details.
+
+The rectangular Cartesian coordinate system, as is well-known, became an immensely significant discovery for subsequent constructions of the mathematical foundations of physics. Much less known is that if Descartes' thought had gone slightly differently, and if he had tried to describe the picture in the window using another, new number system — capable of directly describing the tree due to its own tree-like structure — the science today could appear fundamentally different.
+
+That is, essentially even then, at the dawn of the scientific revolution, humanity had the chance to receive a significantly different numbering system. Which, as was recently discovered, is also extremely useful for physics and other branches of scientific knowledge but was discovered only several centuries later under the name ***p*-adic numbers**.
+
+And most curiously, **another graphical representation — aside from the tree — of this mathematical construction is made **with the help of "**a sphere, the center of which is everywhere**"…
+
+<center>(47)</center>
+
+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.
+
+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.
+
+However, from the vantage point of today's complex of knowledge, it's easy to see that the trajectory of scientific development in the 20th century did not necessarily have to be the way it turned out. And if the titans of the scientific revolution had had a bit more desire and time to look around rather than just pushing their own theories, the coherence of the scientific picture would only have benefited.
+
+And this is by no means about fantasies disconnected from reality. For example, the simultaneous emergence [i61] in 1900 of Planck's quantum hypothesis, which opened the path to the micro-world for the scientists, and the publication of Freud's "Interpretation of Dreams", which opened for science the world of the subconscious, could hardly have been immediately perceived as a clear signal to merge physics and psychology into a single stream of mutually agreed research (this understanding hasn't been achieved even to this day).
+
+But noting how beautifully the structure and characteristics of unusual *p-*adic numbers align with the latest discoveries in physical science was quite within the power of the outstanding mathematicians of the era. Especially since there were quite a few such scientists and the tasks of mathematical physics always played a primary role. Despite all of this, alas, neither a unification nor even significant intersections for physics and* p*-adics occurred then…
+
+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."
+
+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.
+
+To understand these rules generally, it's helpful to draw a close analogy with the decomposition of real numbers in different bases. That is, you must imagine how each number is equivalently recorded as a sum of powers of the same base number — as this is done in decimal, binary, hexadecimal notation, and so on.
+
+In constructing *p-*adic numbers, something similar is done, but as the base, a prime number is taken — divisible only by itself and 1 (in the German language, such an object is called *Primzahl*, which suggested to Kurt Hensel naming his discovery *p-adischen Zahlen*). Hensel found that if rational numbers, i.e., fractions, are expressed in a specific mathematical way (using modular arithmetic) through the powers of a prime number, a special, entirely full-fledged world of numbers results.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/03/bc61treeration.jpg)</center>
+
+Most importantly, this world provides a convenient approach to well-known complex problems in mathematics. In particular, the *p*-adic framework has proven very useful for clarifying general questions about the solvability of algebraic equations.
+
+Since every system of *p*-adic numbers is being built — or grows like a tree — separately for each prime number *p*, it can be said that Kurt Hensel discovered, in mathematics, an infinite number of parallel universes. Moreover, each of these worlds is no worse than the real numbers in terms of filling all the gaps between rational numbers — representing irrational numbers (roots of equations, values of logarithms, sines-cosines, and so on) as infinite decompositions in powers of* p*.
+
+And what is particularly noteworthy, each of these *p*-adic universes has a granular structure, formed based on its own "indivisible atom"* p*.
+
+Against the backdrop of these explanations, the important successes of physics achieved simultaneously with the emergence of *p-*adics begin to look significantly different. On one hand, there are the rich outcomes of classical physics, gathered concerning the granular structure of space (Kelvin's model for ether as a "vortex sponge") [i62]. On the other hand, Planck's ideas about quantized, hence also "granular," nature of energy…
+
+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…
+
+<center>(48)</center>
+
+Why such an abstract, it would seem, mathematical result as Ostrowski's theorem in number theory turns out to be extremely important for the fundamental foundations of physics will become clearer a bit later. For now, it's the perfect time to recall the more ancient "French connection".
+
+With the "Descartes' tree" and the role of this image in describing *p-*adic numbers, the situation is probably already quite clear. But what about the "Pascal's sphere"?
+
+To clarify this question, it's useful to consider the construction and properties of *p-*adics from another perspective — in terms of so-called ultrametric spaces, introduced into number theory by Krasner in 1944.
+
+(Marc Krasner was another mathematician of Russian origin, who, like Ostrowski, had to move to the West from Russia at a young age due to anti-Semitism and revolutionary turmoil. In the mid-1930s, he defended his dissertation in Paris under Jacques Hadamard and remained a Frenchman for the next fifty years, until his death in 1985. As for Alexander Ostrowski, he settled in Switzerland by 1927 after moving between cities and countries, where he secured a mathematical professorship at the University of Basel. For the remaining 60 years of his long life, this city became Ostrowski's home…)
+
+Already from the name "ultrametric space," it's clear that this involves a set where the metric — i.e., the measure of distance — between elements is defined differently from usual.
+
+What is a regular metric is best illustrated by Euclidean geometry, where the properties of distances between points are intuitively clear and self-evident. The metric is always positive and equals zero only when points coincide. The distance from point *A* to point *B* equals the distance from point *B* to point *A*. Furthermore, for the vertices of a triangle, the distance between any two points does not exceed the sum of distances from these points to the third point.
+
+The last of these properties is typically known as the triangle inequality. However, if you strengthen it slightly by requiring that the distance between any vertices in any triangle always not exceed the length of the largest side of the other two (strong triangle inequality), something remarkable happens. It turns out that the geometry of a space with such an "ultrametric" not only looks substantially different from Euclidean but also our ordinary intuition about the properties of the space completely stops working here.
+
+For example, in any ultrametric space, every triangle is either equilateral or isosceles. Moreover, the base of an isosceles triangle cannot be greater than the lengths of the other sides.
+
+One of the curious consequences of this property is that any two spheres in an ultrametric space either do not intersect at all or one is entirely contained within the other. Similar behavior is observed in mercury droplets.
+
+Due to these properties, ultrametric spaces form what is sometimes called a system with a natural hierarchy. In such a system, smaller radius spheres fill larger radius spheres completely without intersections and voids. Moreover, within any such sphere, the distance between any two points is always the same and equals the radius of that sphere.
+
+A completely logical but nonetheless surprising and unusual consequence of this "natural hierarchical" structure is this: **every point of an ultrametric sphere is its center.**
+
+No one may have forgotten how Blaise Pascal described the construction of nature?
+
+Well, the direct relevance of this entire construction to the mathematics of *p-*adic numbers comes from the fact that Marc Krasner introduced the very concept of ultrametric spaces based directly on them.
+
+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>![](https://kniganews.org/wp-content/uploads/2013/03/bc61p-adic.jpg)</center>
+
+<center>Conventional depiction of 3-, 5-, 7-adic numbers (in reality, there are no gaps between circles)</center>
+
+<center>(49)</center>
+
+To make the natural transition from abstract *p-*adic numbers to quite concrete explorations of mysteries in the structure of matter, consciousness, and reality as a whole, just one step remains. In the language of mathematicians, this step is called **non-Archimedean analysis**.
+
+Among the important characteristics of ultrametric spaces, it is always noted that their geometry is non-Archimedean. Specifically, in this context, non-Archimedean property means that from any point in an ultrametric space, it is impossible to escape a distance greater than some magnitude *R* if taking steps no larger than *R*. That is, to step outside a circle, one must take a step exceeding the radius of that circle…
+
+It is clear that this strange feature does not align at all with our experience and perceptions of the world described by Euclidean geometry and its axioms. In particular, because among the axioms of classical geometry, there is one rather special — the so-called Archimedean axiom — which mathematicians overlooked for thousands of years.
+
+This axiom was first isolated and analyzed by Giuseppe Veronese and David Hilbert. Its significance for the foundations of mathematics can be compared to the discovery of non-Euclidean (Riemannian) geometry of curved spaces. Because it showed how renouncing Archimedes' axiom leads to entirely different, non-Archimedean geometry, which also demonstrates its completeness and consistency.
+
+And this was discovered — worth noting — at the very end of the 19th century, just a few years before the first discoveries in quantum physics. But at that time, of course, to see the relationships here was incredibly challenging…
+
+So what is the essence of Archimedes' axiom, which had invisibly been present in mathematics as a self-evident truth for tens of centuries?
+
+Consider a straight line and choose two segments on it, having different lengths and starting from the same point. Archimedes' axiom states that if we repeatedly place the shorter segment along the line, eventually we will exceed the length of the second, longer segment.
+
+In fact, this axiom describes the standard procedure of measurement — we essentially compare an arbitrary magnitude with a smaller standard. For this reason, Archimedes' axiom is sometimes called the axiom of measurability. One natural consequence is that it should always be possible to measure any small distance by selecting an even smaller standard.
+
+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."
+
+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.
+
+In other words, for traditional mathematical physics, an insurmountable barrier has been revealed. Yet all science is structured in such a way that any barrier is treated merely as a signal to search for new, non-traditional tools to solve the problem.
+
+The crux of the problem, in this context, appeared as follows. The generally accepted system of analytical task description in science operates with real numbers. This seems completely natural, as this has always been the case in mathematical physics, starting with Newton and Leibniz, who created the apparatus of differential and integral calculus.
+
+This apparatus, in its foundations, is built on the key feature of real numbers: any interval of length or time can be decreased to infinity. Or alternatively, if needed, measurement precision — in the decimal notation of magnitude — can be increased to any required digit following the decimal point.
+
+But upon reflecting a bit deeper on this point, one concludes that from a physical standpoint, this involves an excessively strong, indeed incorrect, assumption. Both in experimental and theoretical senses.
+
+Because **in any physical experience, any needed magnitude can truly be measured only by a rational number **— as a ratio of one whole number to another. To the extent afforded by the instrument's calibration… Rephrasing slightly, rational numbers and only they are genuinely "physical" numbers.
+
+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.
+
+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.
+
+<center>(50)</center>
+
+The founding figures of this entirely new research approach are rightfully considered Vasily S. Vladimirov and Igor V. Volovich, whose works first demonstrated the importance of non-Archimedean analysis and *p-*adic numbers for theoretical physics. [o45] (Strictly speaking, there were a few other attempts in this vein before them, but they failed to attract the attention of their colleagues.)
+
+Already in Vladimirov and Volovich's first publication on this topic, in 1984, it was hypothesized and justified that *p-*adic numbers could be used to describe space at Planck scales. Moreover, the mathematicians' calculations indicated that **nature turns out to be unexpectedly and substantially simpler when viewed from the number-theoretical perspective**.
+
+A seminal step for integrating *p-*adics in physics was Volovich's 1987 work, suggesting intriguing approaches to employing the *p-*adic apparatus in string theory. This article [o46] in the journal "Classical and Quantum Gravity" managed to attract the attention of prominent string theorists, including Edward Witten, and sparked a wave of publications on *p-*adic strings in the international community.
+
+The active interest of other researchers combined with new exciting findings stimulated the development of many other *p-*adic physical models. Moreover, year by year, the areas of application for this apparatus and ultrametric analysis, in general, continue to grow steadily.
+
+Over time, *p-*adic models of quantum mechanics and field theory emerged alongside *p-*adic descriptions of complex systems like spin glasses — an unusual solid state that structurally resembles Kelvin's "vortex sponge." Because of their structural peculiarities, *p-*adic numbers turn out to be an exceedingly convenient tool for describing various systems with fractal or granular structures.
+
+Furthermore, *p-*adics have found appealing applications in biology. To make it clearer why this aspect of introducing new approaches into science is especially important, one can quote the well-known words of Israel M. Gelfand, one of the world's leading authorities on the mathematical description of biological systems.
+
+Playing on Eugene Wigner's famous phrase [i63], he said: "*There is only one thing even more incomprehensible than the incomprehensible effectiveness of mathematics in physics. And that thing is the incomprehensible INeffectiveness of mathematics in biology*."
+
+Perhaps the key to solving this mystery has already been found. As Sergei V. Kozyrev, a well-known researcher in biophysics using methods of *p-*adic analysis, writes, "*the ineffectiveness of mathematical methods in biology may be connected precisely with the fact that biology, like physics, tried to apply methods of real analysis, while the basic models of biology may need to be expressed in an ultrametric language*". [o47]
+
+The validity of this viewpoint is convincingly supported by the successes of mathematicians applying new methods of ultrametric analysis to describe the genetic code of DNA and to models of the dynamics of biological macromolecules like proteins.
+
+However, when listing numerous unequivocal successes and achievements of the new *p-*adic approach, it's important to emphasize one very crucial nuance. Each *p-*adic model is constructed on the basis of its own prime number *p*. For describing DNA or, say, for cryptography, the 2-adic model is very convenient. For other tasks, these could be 3-, 5-, 7-, 11-, or even (should anyone need it) 1999-adic systems.
+
+There are infinitely many such systems, they are all different, and each is essentially self-sufficient. However, which number in this infinite series is best suited for describing the world — no one can tell you.
+
+Fortunately, the direction to get out of this difficult situation was found almost immediately. In technical terminology, it is called **adeles**, and in essence, it leads all *p-*adic systems to democratic equality.
+
+Initially highly abstract, the construction of adelic numbers was introduced into mathematics slightly earlier than ultrametric, at the turn of the 1930-1940s. The progenitor of adeles was the French mathematician Claude Chevalley, best known as the youngest co-founder of the famous "Bourbaki" group. He was also known as a person who, according to his friend and colleague André Weil, was engaged in maximally dehumanized, that is, formal and very far from life mathematics.
+
+It was only by the late 1980s that it became clear — thanks to the now-famous Freund-Witten adelic formula [o48] — that in fact, Chevalley's abstract construction has the most direct relation to quantum physics. As they say in similar cases, the right idea was ahead of its time by about half a century (although, of course, this depends on how you look at it — but more on that later).
+
+The essence of the arrangement of the unusual number with the somehow feminine name adele boils down to the fact that it is a vector or an infinite sequence of numbers, where the first place is taken by an arbitrary real number, and all others are *p-*adic expressions for the very same number in all possible growing values of the prime *p*.
+
+Relations that record an arbitrary number as an infinite product in terms of prime numbers are widely used in mathematics and are known under the name of Euler's representation. Transforming a magnitude to this form usually greatly simplifies the analysis.
+
+As for the properties of adelic objects, an adelic coordinate contains both a real and all *р-*adic coordinates. Thanks to this composite structure, they simultaneously exhibit properties of Archimedean and fractal (non-Archimedean) topology. However, adelic objects as a whole tend to be simpler than their Archimedean (real) components.
+
+Moreover, thanks to Eulerian product formulas, embodying the idea of the equality of all topologies, information about the real component of an adelic object can be gleaned either from this real component itself or from the product of *p-*adic components for all *p*.
+
+Relying on this mathematical apparatus, Peter Freund and Ed Witten, interested in Volovich's work on *p-*adic strings, in 1987 derived an important formula combining ordinary quantum mechanics with *р-*adic and adelic mathematics.
+
+They showed that the wave function describing the evolution of a free particle in standard quantum mechanics can be represented as a product of wave functions of *р-*adic strings. This relation is sometimes interpreted to mean that the energy of an ordinary quantum particle actually consists of the energies of its *р-*adic components…
+
+This result is very important for at least three reasons. First, it became clear that finding adelic formulas for describing physical systems can significantly simplify their analysis.
+
+Second, the merger of adelic mathematics with quantum physics by the late 1990s allowed the previously mentioned Alain Connes [i64] to find an "almost proof" (more precisely, a beautiful approach to a solution) of one of the greatest mathematical problems — the Riemann Hypothesis about the zeros of the zeta function.
+
+And third, **adeles indicated a real path to a holistic description of consciousness and matter as a single system**.
+
+<center>(51)</center>
+
+In 1987, feeling a powerful trend in the processes of "immersing" (or conversely, ascending) physics into number theory, the prominent Russian mathematician Yuri I. Manin [i65] outlined his vision of the opening picture of reality:
+
+> On the fundamental level our world is neither real, nor *p*-adic, it is adelic. For some reasons reflecting the physical nature of our kind of living matter (e.g., the fact that we are built of massive particles), we tend to project the adelic picture onto its real side. We can equally well spiritually project it upon its non-Archimedean side and calculate most important things arithmetically [according to Manin, "spiritual projection" occurs in the Platonic realm of mathematical ideas].
+>
+> The relation between "real" and "arithmetic" pictures of the world is that of complementarity, like the relation between conjugate observables in quantum mechanics.
+
+These ideas of Manin look particularly remarkable when compared with Wolfgang Pauli's statements, one of the key figures in the "TBC guide." At the turn of the 1940-50s, summarizing his metaphysical reflections on the nature of the world and the future of science, Pauli wrote about these things as follows [i61][i66]:
+
+> In my personal opinion, in future science, reality will be neither mental nor physical but somehow both at once, and at the same time one or the other separately…
+>
+> The most important and extremely complex task of our time is to lay a new idea of reality … And the most optimal would be if physics and the soul were represented as complementary aspects of the same reality.
+
+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.
+
+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]
+
+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.
+
+In 1989, after attending one of Vladimirov and Volovich's lectures, mathematician Andrey Yu. Khrennikov became deeply interested in the practical applications of *p-*adics. Another five years later, by 1994, already a prominent specialist in this field and the author of a well-known monograph [o49] on the applications of *p-*adic analysis in mathematical physics, Khrennikov concluded that he was not quite dealing with what he should be.
+
+All his accumulated experience suggested that *p-*adic approaches were needed not so much for microphysics but for describing something else, some other part of nature… It was hardly a coincidence, but at just the same time, he became interested in the works of Sigmund Freud. While reading Freud's books, Khrennikov was struck by an idea: to create a mathematical theory describing psychological behavior and, in particular, formalizing psychoanalysis.
+
+In Freud's works, flows of ideas, representations, and desires were vividly depicted, and these flows or "spiritual objects" appeared no less real than material objects. Spiritual objects are also capable of evolving, interacting with varying intensity. Thus, as a mathematical physicist, Khrennikov intuitively sensed that he had come across such dynamics in mental space that closely resembled the dynamics of material objects in physical space.
+
+Then, as a research analyst, he only needed to introduce an appropriate system of spiritual coordinates and mathematically describe the mental flows. The standard models based on real coordinates, long and actively used for mapping neural networks of the brain, were decisively discarded by Khrennikov as unsuitable for a number of fundamental reasons. But at the same time, having considerable experience working in *p-*adic physics, he immediately noticed that *p-*adic trees were almost ideally suited for describing spiritual spaces.
+
+Ten years later, this initial idea resulted in an impressive series of about a dozen monographs and papers by Khrennikov dedicated to the mathematical modeling of thought processes in the system of *p-*adic coordinates. [o50]
+
+It cannot be said that these innovative and profound works went entirely unnoticed in the scientific community. Specialists do know them, of course (Professor Khrennikov is also known as the head of the "International Center for Mathematical Modeling in Physics and Cognitive Sciences" at the University of Växjö, Sweden). However, these works have not yet sparked a revolution in the science of mind and brain. Primarily because numerical *p-*adic models cannot provide answers to the main questions about the mysteries of consciousness.
+
+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?
+
+No one today is capable of providing clear and convincing answers to these questions.
+
+However, it can be noted that geometry might offer some very substantial insights on this front. In particular, the geometric ideas developed by a colleague, neighbor, and close acquaintance of Wolfgang Pauli in Zurich…
+
+More correctly, in this context, it is talk not so much about geometry in general but about its section called topology. [i68]
+
+<center>([Read more](/tbc/62/))</center>
+
+### Inside links
+
+[i59] Descartes' Dreams, [https://kniganews.org/map/e/01-01/hex50/](https://kniganews.org/map/e/01-01/hex50/)
+
+[i60] Pascal-Pascheles-Pauli, [https://kniganews.org/map/n/00-01/hex12/](https://kniganews.org/map/n/00-01/hex12/)
+
+[i61] Two Worlds, [https://kniganews.org/map/n/00-01/hex10/](https://kniganews.org/map/n/00-01/hex10/)
+
+[i62] Odyssey of the Vortex Sponge, [https://kniganews.org/map/e/01-01/hex51/](https://kniganews.org/map/e/01-01/hex51/)
+
+[i63] The Missing Idea, [https://kniganews.org/2012/11/17/langlands-plus/](https://kniganews.org/2012/11/17/langlands-plus/)
+
+[i64] TBC_5.2_soul, [https://kniganews.org/2013/01/07/beyond-clouds-52/](https://kniganews.org/2013/01/07/beyond-clouds-52/)
+
+[i65] The Garden of Converging Paths: Manin and Pauli, [https://kniganews.org/2012/03/25/manin-and-pauli/](https://kniganews.org/2012/03/25/manin-and-pauli/)
+
+[i66] Something Else, [https://kniganews.org/map/n/00-01/hex13/](https://kniganews.org/map/n/00-01/hex13/)
+
+[i67] Something Happened, [https://kniganews.org/map/n/00-01/hex1c/](https://kniganews.org/map/n/00-01/hex1c/)
+
+[i68] Rubber Geometry, [https://kniganews.org/map/e/01-10/hex6c/](https://kniganews.org/map/e/01-10/hex6c/)
+
+### Outside links
+
+[o44] Kurt Hensel, *Über eine neue Begründung der Theorie der algebraischen Zahlen.* Jahresbericht der Deutschen Mathematiker-Vereinigung, Band 6, 1899, 6 (3): 83–88.
+
+[o45] Владимиров B.C., Волович И.В. *Суперанализ, 1. Дифференциальное исчисление*. ТМФ. 1984. Т. 59, № 1. С. 3-27 ; —, —. *Суперанализ, 2. Интегральное исчисление*. ТМФ. 1984. Т. 60, № 2, С. 169-198 ; Vladimirov V.S., Volovich I.V. *P-adic quantum mechanics*. Commun. Math. Phys. 1989. V. 123, C. 659-676; V.S. Vladimirov, I.V. Volovich, Ye.I. Zelenov, *P-adic Analysis and Mathematical Physics*, World Scientific, Singapore, 1993
+
+[o46] Volovich I. V., "*p-adic string*". Class. Quant. Grav. 1987. V. 4. P. 83-87.
+
+[o47] Kozyrev S. V., "*Methods and applications of ultrametric and p-adic analysis: from wavelet theory to biophysics*" (in Russian), Sovr. probl. matem., Issue 12, MIAN, M., 2008
+
+[o48] P. G. O. Freund, E. Witten, "*Adelic string amplitudes*", Phys.Lett. B, 199 (1987), 191–194
+
+[o49] Khrennikov A. Yu. "*p-adic valued distributions and their applications to the mathematical physics*". Dordrecht: Kluwer Acad. Publ., 1994.
+
+[o50] Khrennikov A. Yu. "*Non-Archimedean analysis: quantum paradoxes, dynamical systems and biological models*". Dordrecht: Kluwer Acad. Publ., 1997. ; Khrennikov A. Yu. "*Human subconscious as the p-adic dynamical system*". J. of Theor. Biology. 1998. V. 193. P. 179-196. ; Khrennikov A. Yu. "*Description of the operation of the human subconscious by means of p-adic dynamical systems*". Dokl. Akad. Nauk. 1999. V.365. P. 458-460. ; Khrennikov A. Yu. "*Modeling of thinking processes in p-adic coordinate systems*" (in Russian). M.: FIZMATLIT, 2004.

data/tzo/62.md

@@ -0,0 +1,301 @@
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62spacewarp.jpg)</center>
+
+<center>(52)</center>
+
+It happened that in the cemetery of Zollikon, an upscale suburb of Zurich, the urns with the ashes of Wolfgang Pauli and Heinz Hopf are located close to each other. This serves as a kind of symbol of the ongoing dialogue between two great scientist-friends who headed the faculties of physics and mathematics at the same ETH institute, lived nearby, occasionally battled in chess, and loved to stroll and converse in the surrounding forests.
+
+What they liked to talk about there is now probably lost to time. Although some things are known on this point. Always distinguished by his sense of humor, after one such walk, Hopf commented on their conversations as follows: "Today, we had a heated discussion about what mankind was created for – to engage in Pure Mathematics or Applied Mathematics. Alas, we couldn't solve this problem"…
+
+The amusing and somewhat sad irony is that the ready answer for such a "difficult problem" was actually found by Hopf himself long ago. It just took many, many years for mathematicians and physicists to grasp the meaning of this answer. Almost half a century. By that time, neither Hopf (1894-1971) nor especially Pauli (1900-1958) were still in this world.
+
+The actual Answer itself is an astonishingly rich mathematical construction discovered by Heinz Hopf back in 1931 [o51], and now widely known as the Hopf fibration or Hopf fiber bundle. Initially discovered and described as an entirely abstract object in the field of pure mathematics, the Hopf fibration, as it turned out many decades later, has a wide range of applications in applied mathematics and especially in various fields of physics.
+
+In other words, the distinction between pure and applied mathematics seems to be a characteristic of researchers just beginning to explore nature. However, the more a person learns about the world and themselves, the more often they discover that any branch of mathematics can have applied significance. Moreover, finding a purely practical application for previously entirely abstract ideas is now particularly exciting and captivating in mathematics.
+
+Now, however, is the time to delve deeper into what the Hopf fibration is in general terms and its various physical applications.
+
+The essence of this remarkable object is such that the internal composition of three-dimensional space, as Hopf discovered, has from a topological perspective not a simple structure, but rather, on the contrary, a very nontrivial and rich construction.
+
+In principle, there are various ways to discuss this " structure of our space" depending on the aspects to underline. One can describe it like this, for example.
+
+Basically, Heinz Hopf found a way to fill all of space with circles. Generally speaking, for this task, there are simple solutions like this – take a straight line and string onto it concentric circles ad infinitum.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62filspace.jpg)</center>
+
+However, Hopf tackled a more general task – the construction of a mapping of a three-dimensional spherical surface or 3-sphere, located in 4-dimensional space, onto the more familiar 3-dimensional Euclidean space, which is commonly referred to as flat and denoted **R<sup>3</sup>**.
+
+In a sense, this task is analogous to the problem of how to display the surface of a globe – or 2-sphere – onto the surface of a flat map. It is clear that any form of projection inevitably introduces various distortions to the picture. For this purpose, Hopf applied the known stereographic projection in geography and geometry that preserves angles between lines (this is called conformal transformation), and circles are also translates into circles or straight lines (alternatively, circles of infinite radius).
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62stereograf.jpg)</center>
+
+If one develops the same analogy with the globe, i.e., the more familiar 2-sphere, one of the important features of the mapping studied by Hopf is this. When the points of the 3-sphere forming the surface in 4-dimensional space are arranged on such a globe strictly along the line of "latitude," then in Euclidean space **R<sup>3</sup>**, this configuration corresponds to a shape known as a torus of revolution (and in form corresponds to a vortex ring).
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62torus.jpg)</center>
+
+The thickness of the tube of such a torus changes depending on the location of the latitude between the plane and the projection point. As the latitude shifts from the projection point, the torus passes through all intermediate states between two extreme ones. In one extreme, becoming ever thinner, it degenerates into a circle. In the opposite case, the torus swells to such an extent that its "hole" degenerates into a straight line perpendicular to the equatorial plane.
+
+In other words, Hopf filled all of space **R<sup>3</sup>** with nested tori. But the most important thing here is this. For each point on the globe, located on the latitude line, there is a corresponding circle line on the torus surface. This line captures the "donut hole" and obliquely encircles the tube. Just as a multitude of points fill the entire circumference of latitude, so a collection of such rings, linked with each other, completely covers the surface of the respective torus.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62hopf-frames.jpg)</center>
+
+For historical reasons, such circles on the torus are called Clifford parallels – after an English mathematician who introduced these objects in the 19th century to study the properties of curved spaces. Therefore, this whole construction is sometimes called the Clifford-Hopf fibration. Fibers here are those linked circles that form the surfaces of the tori, and hence – fill the entire volume of space.
+
+This initial construction gave rise to an extremely fruitful direction in topological research, studying fibrations of spaces of various configurations and dimensions. But characteristically, for quite a while, all such investigations were in the realm of exclusively abstract pure mathematics.
+
+By the end of the 1970s, however, it became clear to physicists that the Hopf fibration plays a fundamentally important role in gauge approaches to quantum field theory. It also effectively served as the core of the entire model in Roger Penrose's twistor theory, and later in several other approaches to quantum gravity theory.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62twistor.jpg)</center>
+
+Today, the list of possible physical applications for this construction is very long – from magnetic monopoles to the polarization of transverse waves and solid-state mechanics, from the geometric properties of quantum entanglement and the organization of qubits in a quantum computer to the relativistic deformation of the celestial sphere. [o52]
+
+Stating the same thing differently, one can constate that in the structure of the geometric object called the Hopf fibration, there currently lies a unified fundamental basis for several of the physicists' most significant modern ideas about the structure of reality. In particular, for the fractal-holographic model – where every smallest fragment reproduces the whole. For the multiverse model – as a multitude of simultaneously existing parallel worlds. For the universe as a quantum computer. And for such a physical system, finally, that organically and inseparably combines matter and consciousness.
+
+In short, there are solid reasons to consider the Hopf fibration as a general structure uniting all those directions in mathematical physics which had begun to develop but clearly did not achieve their full potential – Hugh Everett, Claude Shannon, and, of course, Wolfgang Pauli, who dreamt of the return of the "soul of matter" to science.
+
+<center>(53)</center>
+
+To smoothly and naturally approach the picture of how the memory or soul of matter in general and the collective consciousness of humanity, in particular, can be embedded into the Clifford-Hopf fibration, it is initially useful to pay attention to the "mystical" component of this entire story.
+
+As already mentioned, according to documentary evidence, Heinz Hopf's discovery dates back to 1931. It was precisely in that year that Hopf moved to the city of Zurich, where he accepted the mathematics department at the institute ETH, previously headed by Hermann Weyl (one of the great mathematicians of the 20th century, among other things, the first to propose the idea of gauge interactions as a basic principle for the unified description of all forces in nature).
+
+The physics department of Zurich's ETH at that time was already headed by Wolfgang Pauli. And in that same 1931 year, a noteworthy acquaintance occurred between Pauli and the famous psychiatrist, father of analytical psychology Carl Gustav Jung, beginning their friendship and partnership for the rest of their lives.
+
+The third noteworthy event of 1931 was the publication by Paul Dirac, one of the founding figures of quantum theory, of another article titled "Quantised singularities in the electromagnetic field." This article holds a special place in Dirac's oeuvre because in it he managed, with very elegant mathematics, to propose a possible explanation for one of the fundamental enigmas of physics – the quantization of electric charge.
+
+The exquisite solution to this problem was Dirac's hypothesized particle called "magnetic monopole," later better known as the Dirac monopole. The essence of the hypothesis was that if it were possible to find a particle with only one magnetic pole rather than two, then the existence of particles with a minimal electric charge, of which none is smaller and which all other charges are multiples of, would receive a simple and natural explanation.
+
+The logic and mathematics of this outstanding theorist's argumentation looked beautiful and convincing, and therefore catching the Dirac magnetic monopole became, for many decades, one of the significant goals of experimental physics. But despite all the researchers' tense efforts, alas, this object has yet to be found in nature up to this day…
+
+To any person foreign to mystical worldview, there are absolutely no connections observable among the three described independent events of 1931. Scientists just keep writing articles (it's their job after all), people continually move from place to place searching for a better chance, and having arrived at a new place, they inevitably meet new people… In short, what here might be noteworthy and non-random?
+
+To learn to see hidden meanings and connections in seemingly disparate events, it is useful to recall Jung's concept, called "synchronicity" [i69]. According to Jung, such synchronicities act as peculiar knots connecting apparently independent events on other levels of consciousness and structuring the overall fabric of reality.
+
+Specifically, in the context of the example considered here, it is time to note that today, according to the results of theoretical physics, the still elusive yet even more desirable object known as the "magnetic monopole" — in the form of a topological defect (vortex) — has seemingly concentrated within itself the most important discoveries and yet unresolved enigmas at the border of physics and topology.
+
+In the mathematics of (Dirac) monopoles, effects of spontaneous symmetry breaking and the Higgs mechanism are found, nontrivial (Hopf) bundles, and special solutions of Yang-Mills gauge equations. Also present, upon closer inspection, are the ideas that once greatly excited Wolfgang Pauli about "duality and reduced symmetry," which opened to him a new perspective on nature and the inseparable link between matter and consciousness.
+
+Adding another layer to the picture illustrating how closely intertwined all these things are is the not-so-long-ago revealed story that Wolfgang Pauli was the first to derive what are now known as the Yang-Mills gauge equations [o53]. However, Pauli, famous for his scientific meticulousness, chose not to publish this work as he saw significant contradictions with already known facts in physics.
+
+As for Yang Chen-Ning and Robert Mills, they were at the time (1954) still "young theoreticians entitled to stupidity," according to the well-known expression by P. Ehrenfest [i70]. Despite Wolfgang Pauli's blunt disapproval, expressed personally to the authors during one of the preliminary discussions, Yang and Mills did publish their — clearly raw and underdeveloped — theory. This move marked the beginning of a highly productive and as yet inexhausted direction in modern physics.
+
+To understand how closely this theory is related to the geometry and topology of fibered spaces required over 20 more years. Historians of science have direct recollections regarding this from Chen-Ning Yang, mentioned by him at one of the commemorative conferences.
+
+In those years, when gauge field theory was just emerging, Yang and Mills were concerned exclusively with equations, and they did not even think about their geometric interpretation. Only two decades later did Yang become seriously interested in the topological interpretation of their theory and invited to the university where he worked at the time the prominent mathematician Jim Simons — to deliver a series of lectures on fibered spaces for theoretical physicists.
+
+Having learned and grasped a wealth of new information, physicists were "beside themselves with happiness," as Yang put it, when they realized that nontrivial bundles in topology are exactly the concept that helps them eliminate known difficulties in Dirac monopole theory. Physicists were particularly struck by the fact that "their" gauge fields were actually long known to mathematicians — under the name "connectedness in fiber bundle spaces." However, mathematicians studied these things purely abstractly, without any notions of the physical reality's structure.
+
+Discussing this astonishing discovery with Shiing- Shen Chern, a notable topologist of the 20th century, Yang told him: "This is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere." To which Chern immediately protested: "No, no, these concepts were not dreamed up. They were natural and real." [o54]
+
+<center>(54)</center>
+
+Relying on the authoritative testimony of mathematicians — regarding the "naturalness and reality" of fibered spaces — it is time to move on to ideas about how this universal construction relates to the form of the universe.
+
+Initially, it's helpful to consider how such seemingly different configurations as the torus and the sphere are simultaneously present within the structure of space. It's evidently much easier for a person to vividly see this through the example of 2-dimensional surfaces in 3-dimensional space.
+
+With the help of mathematical programs and computer graphics, among other things, specialists have shown how a 2-dimensional torus through smooth topological transformations (called homotopy) transforms through compressions, pinches, and stretches into a double-layered Riemann sphere. [o55]
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62tor2ball.jpg)![](https://kniganews.org/wp-content/uploads/2013/05/bc62threef2ball.jpg)</center>
+
+The grid of cells applied to the surface of the torus and twice reproducing the well-known configuration of a soccer ball is, of course, not accidental. Firstly, it allows for a more clear view of the deformation process, demonstrating the topological equivalence of the two distinct structures.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62fuller.jpg)</center>
+
+Secondly, as shown by fullerene molecules in nature, such a configuration is optimal in terms of minimizing energy on a spherical surface. Thirdly, most importantly, science today has substantial evidence that this very configuration underlies the structure of the universe — as a network of cells formed by superclusters of galaxies. [i71]
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62univball.jpg)</center>
+
+More precisely, when carefully articulated, the observational data available to science allows for the supposition of a cosmic form known as Poincaré's dodecahedral space. A simplified model of such a configuration is a ball sewn from 12 pieces in the shape of regular pentagons. Or, otherwise, a regular polyhedron-dodecahedron inflated to a sphere. [i72]
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62poincadod.jpg)</center>
+
+Distinct signs of this form of the cosmos were detected by J. Luminet's group in the cosmic microwave background radiation maps from the WMAP satellite [i73]. Polish researchers from Torun University identified on the same map 6 pairs of matching circles, even more definitively indicating the features of a closed-universe space in the shape of a dodecahedron. [i74]
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62sixpairs.jpg)</center>
+
+To clarify that this significant (but for some reason hushed-up) scientific discovery of the 21st century does not contradict the "classic" form of a soccer ball made out of 12 pentagons and 20 hexagons, one should note that even in the 32-cell variant, there are the same 6 pairs of "circles" as in the dodecahedron. Also, recall the dual topology of the cosmic sphere and the physics of forming convective cells in superfluid liquids. [i75]
+
+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.
+
+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.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62futbol.jpg)</center>
+
+If the key role of (topological) vortex effects in the picture of the formation of the cosmic cellular structure has become more or less clear, it is time to remind of the following. All the discussions here are certainly not proofs and, even more so, not the absolute truth.
+
+One might consider this an attempt to illustrate — using vivid pictures and simplified ideas — a truly significant thing. That Hopf fibration is very well-suited to serve as a universal geometric object or principle, allowing the integration of many disparate and poorly aligned facts established by science concerning our surrounding world.
+
+<center>(55)</center>
+
+Continuing in the same direction, it is time to more thoroughly examine why the Hopf fibration is called "nontrivial" and note why this feature helps naturally explain enigmatic facts such as the universe's left-handed chirality and the three generations of fermion particles.
+
+As an elementary example illustrating what comprises a trivial fibration, the form of a cylinder is typically referenced, formed from segments stemming from multiple points on a circle. The surface of such a cylinder is called a circle fibration, with its constituent segments dubbed fibers.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62triv-n-non.jpg)</center>
+
+Accordingly, a fibration is called nontrivial if the surface formed by the fibers demonstrates one-sidedness rather than being ordinary. The simplest example of such a surface — a nontrivial fibration — is the Möbius strip.
+
+To make it clearer how in the nontrivial Hopf fibration, where the fibers are circles, a crucial structure like the Möbius strip is present, it's helpful to introduce two seemingly different figures that are, in fact, topologically equivalent. One in the form of a ladder graph represents the traditional essence of the Möbius strip as a one-sided surface, while the other, employing the rubbery properties of topology, elongates the same graph into a circle, with opposite points connected by segment-fibers.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62twoeqmob.jpg)</center>
+
+The extent to which the nontrivial topology of a Möbius strip can be significant from the perspective of physics was recently beautifully demonstrated once more by a group of Chinese researchers from Beijing's Institute of Theoretical Physics [o56]. In 2009, they published a theoretical paper on the electronic properties of a sheet made of a new material, graphene, and taking the shape of a Möbius strip.
+
+In this research, calculations demonstrated that a graphene Möbius strip behaves as a "topological insulator with a robust metallic surface" [i76]. That is, electron movements occur losslessly along the edge of the strip, while the rest (bulk) of the strip doesn't conduct electricity, showcasing insulating properties. In other words, the topology of the shape engenders the material's unusual properties.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62mobti.jpg)</center>
+
+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.
+
+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.
+
+To spectacularly enhance the same "layered" theme, one can revisit the smooth homotopic transformations demonstrating the richness of structures hidden in an ordinary soccer ball. American researcher Michael Trott, who thoroughly studied this configuration using the Mathematica scientific computer program, discovered the following fact. [o55]
+
+One of transformations shown by Trott through animated clips illustrates the morphing process between the already known two-layered soccer ball and the trefoil knot — another noteworthy form rich in its topological properties.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62tor2ball.jpg)![](https://kniganews.org/wp-content/uploads/2013/05/bc62threef2ball.jpg)</center>
+
+<center></center>
+
+For the sake of clarity, the smooth morphing is shown in the opposite direction - how the trefoil knot transforms into a soccer ball. To make this trick possible, the previous polygonal tiling grid – the 2x32 cells of a soccer ball – is applied to the toroidal surface of the knot, but now in three replica copies, closed into a periodic pattern.
+
+Then all three copies are simultaneously laid out on the two layers of the Riemann sphere representing the soccer ball. As a result, in the final diagram, all three pairs of soccer balls are superimposed in space with each other. [i77]
+
+A number of circumstances make this illustration very important in the context of Hopf fibration. First, there is a direct connection between the topology of the trefoil knot and the Möbius strip. If the Möbius strip is twisted not by one half-turn, as usual, but by three, and if this figure is cut along the axis line, you get a one-sided strip tied into a trefoil knot.
+
+Secondly, the trefoil knot is a classic example of a chiral figure, like the Möbius strip, meaning it does not coincide with its mirror image upon superposition. Accordingly, the presence of a smooth homotopic transformation between the trefoil torus and the two-layered sphere shows that even in this seemingly spherical figure, which has no right or left preferences, the property of chirality is embedded at some internal levels.
+
+And thirdly, the important point lies in the three copies of the two-layer covering, which are periodically arranged one after another on the surface of the trefoil knot, and on the Riemann sphere they are placed in three completely coinciding pairs. Such a picture indicates that if the universe's geometry contains the chiral topology of the trefoil knot, it is equivalent to the situation where each side of the membrane-surface has a three-layer structure. Or, in other words, naturally acquires an additional dimension and three generations of particles… [i78]
+
+<center>(56)</center>
+
+Attentive readers may have already noticed that important scientific discoveries pointing to hidden features in the structure of the universe are made based on unusual molecular constructions, the basis of which is the carbon atom: graphene and fullerenes. Bearing in mind that the atomic weight – that is, the number of nucleons in the nucleus – of carbon corresponds to number 12 (the number of faces of a dodecahedron), and that it is carbon that underlies all known forms of biological life, it is difficult to pretend that all these coincidences are mere chance.
+
+It is much more likely that in this case, we are dealing with yet another manifestation of the universal "holographic principle" – when even the smallest fragment of a construction reproduces key features of the whole… Consequently, focusing now on this idea, it is time to consider what connections are observed between holography and Hopf fibration.
+
+It is worth recalling that in theoretical physics, the term "holographic principle" is generally understood not as the relationship between a whole image and its parts but as something fundamentally different. The idea is that different sets of equations defining the behavior of distinct systems of various dimensions might actually describe the same physics. Approximately the same way as a flat (2D) holographic plate contains all the information for reproducing a volumetric three-dimensional image (3D).
+
+Among the key achievements of the holographic approach in modern theoretical physics is the so-called AdS/CFT correspondence, illustrating the same physics in two completely different systems. One is the five-dimensional anti-de Sitter (AdS) space-time, which has a hyperbolic geometry of negative curvature. The second system is the spherical 4-dimensional space acting as the boundary of AdS and described by a conformal field theory (CFT), overall resembling the physics of our world.
+
+To make the direct connection between AdS/CFT and Hopf fibration more clear and illustrative, it is useful to describe two different but equivalent approaches to filling the volume with curved surfaces. One of these methods, (a), is already familiar to us and represents Clifford parallels in the form of circles forming tori. The second method, (b), linearizes the first, so that Clifford parallels indeed become line segments, but at the same time form a curved "ruled surface" or hyperboloid of revolution with negative curvature. The boundary of such a surface is a circle or 1-sphere.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62eq-models-fib.jpg)</center>
+
+Based on these images, showing the connections with AdS/CFT becomes simpler. Because the outer part of a torus with positive curvature can be likened to the world of the spherical boundary system of CFT (here dimension 2D). And the inner space of the "hole," bounded by a hyperboloid of negative curvature, can be considered as the world of AdS (dimension 3D, respectively).
+
+In this modeling approach, AdS space-time looks like a stack of flat (2D) circles, each having a hyperbolic geometry of space, and all stacked on top of one another along the vertical time axis (forming 3D).
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62adssp.jpg)</center>
+
+<center>Left: Projection of hyperbolic space onto a plane. Each fish is actually the same size, and the boundary circle is infinitely far from the center of the disk. The compression of the fish sizes is done to fit an infinite space within a circle of finite size. This is a visual effect of strong spatial curvature. Center and right: Physics in such a space-time (“stack of disks”) is quite specific. Both a ball and a beam of light, launched from the center of the disk, return back in the same amount of time (with the distinction that the light manages to reach the edge of space). For details, see [o58]</center>
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62cft1d.jpg)</center>
+
+<center></center>
+
+If one makes a cross-section of the torus at any given moment in time, then every circle in the AdS world corresponds to a latitude circle on the outer shell — a snapshot of “our” CFT world. A 1D world that, along the same time axis, moves from the past (the bottom of the torus) to the future (the top of the torus).
+
+Since the "AdS world" geometrically resides in the "hole" of the torus, and every circle in the Hopf fibration forming the surface of the torus necessarily contains this "hole" inside, an intriguing possibility is visible for the point inhabitants of the "CFT world" living at the latitude. If considering the inclined circle of the Hopf fiber as their "memory," i.e., the basis of consciousness, the space inside that circle falling within the "hole" of the torus can be thought of as the 2-dimensional "hologram of consciousness." Moreover, due to the geometric features of the inclined section, this hologram allows the inhabitants of the "CFT world" to travel within their consciousness both in space and time.
+
+<center>![](https://kniganews.org/wp-content/uploads/2013/05/bc62krugivil.jpg)</center>
+
+As everyone knows, in a similar way — by the "power of thought" — people in our world can travel through space-time in their dreams, reveries, and in memories of near-death experience linked to staying in the other world of spirits and souls of the deceased. In other words, there are reasons to name this space — geometrically inseparably connected with ours — as the space of the other world.
+
+A significant point in AdS/CFT considerations is that the CFT physics on the boundary-shell, while generally similar to the physics of our world, lacks gravity. On the contrary, the physics of the 5-dimensional AdS, although this world is otherwise completely unlike ours, includes gravity naturally.
+
+To understand how this apparent, at first glance, discrepancy with the physics of the real world is overcome, it is useful to recall again the 2-brane Randall-Sundrum model, which requires 5 dimensions (see [4.4](https://kniganews.org/2013/01/01/beyond-clouds-44/)). And about the fact that the mysterious world of the "gravity brane" in their model can be much more naturally explained through the world of the membrane as a closed one-sided surface of the Möbius strip type. Where the second half of all the particles of our world is concentrated in stars. Or, in other words, in those regions of space whose geometry is strongly deformed by gravity effects.
+
+It is also appropriate here to remind and add such an essential nuance to this picture. Due to the constant flipping of particles from one side of the membrane to the other, we — as observers — find ourselves inside and then outside the surface of the sphere all the time. In such conditions, the natural averaging of all our observations concerning the curvature of space is that the geometry of the universe everywhere appears flat — like a sheet of paper on a table…
+
+Finally, another notable consequence of this construction, as previously demonstrated (see [4.3](https://kniganews.org/2012/12/30/beyond-clouds-43/)), is the effect of topological charge inversion with each flip of a particle from one side of the membrane to the other. If considering this process in terms of Dirac's magnetic monopole, it is not difficult to see that here precisely lies the geometric answer to the mysterious elusiveness in nature of the so desired object for theorists.
+
+In some sense, the search for Dirac's monopole is roughly the same as trying to see the whole particle, which on one side of the membrane is a proton, and on the other, an electron.
+
+<center>(57)</center>
+
+The geometric structure discovered by Heinz Hopf, as shown, allows us to fundamentally reconsider the abundance of mysteries and unresolved problems characteristic of modern physics. But it has also been demonstrated something that can be called the "Hopf paradox."
+
+On one hand, the importance of Hopf fibration for a vast number of applied physical tasks is an indisputable thing today that needs no proof. On the other hand, however, the situation seems like scientists are still hesitant to start applying this powerful toolkit to its full potential.
+
+This happens, most likely, because then (either at once or gradually but inevitably) too many generally accepted dogmas will collapse… Proving such an assertion with documents is unlikely within anyone's power, but it is quite possible to illustrate the idea with one more historical example.
+
+In 1949, the famous "pure" mathematician Kurt Gödel published one of his few articles devoted to physics — as a sort of gift for the 70th birthday of his senior friend, Albert Einstein. (Similar to the Pauli - Hopf duo, this pair of friends also loved joint hikes-discussions in the surrounding woods — not in Zollikon but Princeton.) In his "gift" article, Gödel found an exact and extraordinarily elegant solution for the GTR or Einstein's general theory of relativity equations.
+
+In other words, the theorist obtained a beautiful mathematical description of a universe which, according to the equations, has every right to be the world we all live in. Nature, as scientists have long known, is arranged so that the most beautiful equation solutions are usually the most correct ones. However, specifically for this solution, named the "Gödel metric," a categorical exception had to be made. Simply "because the real world cannot be arranged like that"… [i79]
+
+Gödel's universe is steady in size (stationary) — and science knows for sure that it is expanding. Gödel's universe rotates — and in science, not that it is established, but in all dominant theories, it is accepted to assume there is no rotation. Finally — the most unacceptable — Gödel's solution allows closed trajectories or loops along the time coordinate, and such "journeys" violate all scientific notions about the fundamental importance of cause-and-effect relationships for a universe of logical consistency.
+
+It may not be appropriate to discuss this story in detail here, but it is quite fitting to show— using one of the tori in Hopf fibration as an example — that Gödel's construction does indeed describe "our" world. But only in a broader context — with AdS taken into account. And all the objections to the Gödel metric, consequently, turn out to be built on contradictions that, in reality, do not exist.
+
+That is, a broader context is introduced using the same model that illustrated the essence of AdS/CFT. Then the torus considered there in 3D space is a model of a stationary 5D universe. The vertical axis, as before, is the time axis. And the outer horizontal circle in the torus section, respectively, is a one-dimensional model for the 3D space of our world at any specific moment of its evolution over time.
+
+From this illustration, it is quite clear that the three-dimensional space of the universe first expands to the maximum diameter and then begins to contract back. Following the same scheme, almost, as all quantum matter particles with their amplitude oscillations behave. Furthermore, similar to rotating particles, the universe rotates — this corresponds to "the current on the surface of a topological insulator." And it is also illustrated by the inclined circles of the fibration, which here denote the trajectories (world lines) of particles in space-time.
+
+Finally, the fact that all such line fibers are circles is the clear illustration of the "most outrageous" feature of the Gödel metric: the closed trajectory along the time coordinate. Or, put differently, a visual illustration of the endless repetition of cycles in the universe's evolutionary history.
+
+Of course, this illustration absolutely proves nothing. In fact, images are never required to do so. It is enough that they provide clear and simplified visuals for understanding the essence of the subject. As for more rigorous mathematical and experimental arguments, one can also find them in abundance if desired.
+
+There are many testimonies in the history of astrophysical observations that the universe is constantly rotating. Moreover, the content of observed data (asymmetry in the polarization of radiation from extragalactic sources, non-random distribution of low-frequency modes on the map of the cosmic microwave background of the universe, etc.) clearly indicates that the space of the universe has the shape of a torus or vortex ring. [i79]
+
+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.
+
+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]
+
+In Roger Penrose's model — another example — the idea of cyclic expansions and contractions of the cosmos is substantiated by significantly different considerations, relying on the second law of thermodynamics and addressing known inconsistencies in standard cosmology regarding the entropy of the universe. [o60]
+
+In the works of the mentioned renowned theorists, among other things, one can also find quite comprehensible mathematical explanations for why the universe, even when transitioning to cyclic contraction, will appear to observers as accelerating in its expansion. (One of the geometric explanations is called the "induced metric" and is directly related to well-known properties of conic sections in projective geometry — when a surface with a spherical metric appears as a parabola with branches diverging to infinity in projection.)
+
+However, these are not the most significant technical geometric nuances. Far more important are the general conclusions drawn from this entire picture regarding the inseparable unity of matter and consciousness.
+
+<center>([Read more](/tbc/7/))</center>
+
+### Inside links
+
+[i69] Language of Synthesis, [https://kniganews.org/map/n/00-01/hex17/](https://kniganews.org/map/n/00-01/hex17/)
+
+[i70] Spin on a Möbius Strip, [https://kniganews.org/map/e/01-10/hex67/](https://kniganews.org/map/e/01-10/hex67/)
+
+[i71] Convective Geometry, [https://kniganews.org/map/e/01-10/hex6d/](https://kniganews.org/map/e/01-10/hex6d/)
+
+[i72] Mysteries of the Dodecahedron, [https://kniganews.org/map/e/01-10/hex60/](https://kniganews.org/map/e/01-10/hex60/)
+
+[i73] Cosmos as a Hall of Mirrors, [https://kniganews.org/map/e/01-10/hex62/](https://kniganews.org/map/e/01-10/hex62/)
+
+[i74] Anomalous Facts and Structures, [https://kniganews.org/map/e/01-10/hex63/](https://kniganews.org/map/e/01-10/hex63/)
+
+[i75] Superfluid Crystal, [https://kniganews.org/map/e/01-10/hex65/](https://kniganews.org/map/e/01-10/hex65/)
+
+[i76] Universe as a Topological Insulator, [https://kniganews.org/2012/09/17/univer-topological-insulator/](https://kniganews.org/2012/09/17/univer-topological-insulator/)
+
+[i77] Granular Geometry, [https://kniganews.org/map/e/01-10/hex6e/](https://kniganews.org/map/e/01-10/hex6e/)
+
+[i78] Multidimensional Geometry, [https://kniganews.org/map/e/01-10/hex6f/](https://kniganews.org/map/e/01-10/hex6f/)
+
+[i79] And yet it rotates? [https://kniganews.org/map/e/01-10/hex64/](https://kniganews.org/map/e/01-10/hex64/)
+
+### Outside links
+
+[o51] Heinz Hopf, "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche", Mathematische Annalen (Berlin: Springer) 104 (1): 637–665 (1931)
+
+[o52] M. Nakahara, "Geometry, Topology and Physics," Institute of Physics Publishing, Philadelphia, 1990 ; J. Marsden and T. Ratiu, "Introduction to Mechanics and Symmetry", Springer-Verlag, New York, 1994 ; R. Mosseri and R. Dandolo, "Geometry of entangled states, Bloch spheres and Hopf fibrations," J. Phys. A 34 (2001), 10243-10252
+
+[o53] "A vision of gauge field theory", a chapter in "No time to be brief. A scientific biography of Wolfgang Pauli" by Charles P. Enz, . Oxford University Press (2002)
+
+[o54] C.N. Yang, "Magnetic Monopoles, Gauge Fields, and Fiber Bundles." Annals of the New York Academy of Sciences, Vol. 294, p. 86-97, November 8, 1977, 25568.
+
+[o55] Trott, M. "Bending a soccer ball – mathematically". Mathematica Guidebooks, June 2006, ([http://www.mathematicaguidebooks.org/soccer/](http://www.mathematicaguidebooks.org/soccer/))
+
+[o56] ZL Guo, ZR Gong, H Dong and CP Sun, "Mobius Graphene Strip as Topological Insulator". Physical Review B 80, 195310 (2009). Preprint arXiv:0906.1634
+
+[o57] David B. Kaplan and Sichun Sun, "Spacetime as a Topological Insulator: Mechanism for the Origin of the Fermion Generations". Phys. Rev. Lett. 108, 181807 (2012). Preprint arXiv:1112.0302 [hep-ph].
+
+[o58] Juan Maldacena, "The Illusion of Gravity". Scientific American, November 2005
+
+[o59] Paul J. Steinhardt, Neil Turok, "Endless Universe: Beyond the Big Bang". Broadway. 2008
+
+[o60] Roger Penrose. "Cycles of Time: An Extraordinary New View of the Universe". The Bodley Head. 2010

data/tzo/info.yaml

@@ -0,0 +1,139 @@
+part_1:
+  label: weather
+  toc:
+    - "About the \"two cloudlets\" that darkened the clear horizons of science at the start of the 20th century."
+part_21:
+  label: dark
+  toc:
+    - "Giant clouds of ignorance at the beginning of the 21st century: about 96% of the universe – unknown;"
+    - "Dark matter and dark energy."
+part_22:
+  label: unclear
+  toc:
+    - "Entanglement, the arrow of time, quantum gravity;"
+    - "The absence of consciousness in the scientific picture of the world."
+part_31:
+  label: hugh
+  toc:
+    - "Incompatibility of descriptions of the quantum world and our reality;"
+    - "Hugh Everett's branching worlds or particle systems as \"complex automata\";"
+    - "Birth of the multiverse concept or \"new theology,\" H.E.'s departure from science."
+part_32:
+  label: wolf
+  toc:
+    - "Wolfgang Pauli's great discovery: doubling and symmetry reduction;"
+    - "Pauli and Jung, a bridge between physics and consciousness, return of the \"soul of matter\";"
+    - "Sudden termination of research, broken ties, depression, cancer, and W.P.'s death."
+part_33:
+  label: claude
+  toc:
+    - "Claude Shannon – father of information theory and great recluse;"
+    - "Shannon's juggling theory and philosophy of cosmic jugglers;"
+    - "Deterministic randomness, roulette hacking, connections with H.E. and W.P."
+part_41:
+  label: basis
+  toc:
+    - "How mathematics relates to physics through the concept of motion;"
+    - "Music of quantum physics, harmonic oscillator, and generation of rotation;"
+    - "Perception of higher-dimensional objects, photon-mediated interactions;"
+    - "Superposition of states, Feynman integral, and \"It from bit.\""
+part_42:
+  label: twoworld
+  toc:
+    - 'Zig-Zag representation of spinor in the Dirac equation, Higgs field as an ether fluid;'
+    - "Carl Bjerknes' pulsating spheres theory and the relativistic effect in Maxwell’s theory"
+    - 'Ether as a "vortex sponge" and oscillons phenomenon in granular media;'
+    - "Zitterbewegung, antiferromagnetism, symmetry breaking, and double-division physics of \"brane-antibrane\"."
+part_43:
+  label: susy
+  toc:
+    - "Explanation of quantum entanglement, granular space structure as a basis for quantum gravity;"
+    - "Equal charges of proton and electron, Möbius strip spin geometry, mutual invisibility of particles with 
+       antiparallel spins;"
+    - "Horava-Witten two-brane model and reversal of particle rotation when jumping from brane to brane;"
+    - "Topological relationships between \"tube-bridge\" phase in particle jumps and SUSY concept, i.e., boson-fermion
+       SUperSYmmetry."
+part_44:
+  label: focus
+  toc:
+    - "Kaluza’s miracles due to transition to 5D, oscillating scalar field for uniting gravity with quantum physics via 
+       Bjerknes-Maxwell pulsating spheres concept;"
+    - "Graviton (spin 2) as a pair of photons linked in a \"Kelvin oval,\" same in another projection – as Higgs boson (spin 0);"
+    - "Randall-Sundrum model on a two-brane Möbius strip, asymmetric mapping nature;"
+    - "Separation of particles into three generations and natural configuration of 6D Calabi-Yau manifolds."
+part_51:
+  label: body
+  toc:
+    - "Quarks, gluons, heavy bosons, and other quasiparticles of nuclear interactions;"
+    - "Anyons and Hyde’s vacillation physics, quark-microvortices and gluon-waves;"
+    - "Nuclear physics phenomena as quantum computations, the universe as a quantum computer;"
+    - "Intermediate proton-neutron resonances and Shannon’s juggling theory;"
+    - "Kitaev's topological quantum computer, Landauer's computations without energy cost, and anyons in SUSY \"flat phase.\""
+part_52:
+  label: soul
+  toc:
+    - "Quantum physics as a history of fighting tachyons – \"particles not needed in science\";"
+    - "Tachyon condensation mechanisms and emergence of \"tachyonic crystal\" concept;"
+    - "Laminated or layered brane structure from tachyons – as matter’s memory mechanism, one-dimensional crystal fibers
+       forming networks penetrating time and resembling brain neurostructure;"
+    - "Wilczek’s time crystals, connections with DNA, harmonic structures in music, spiral structures in dusty plasma,
+       and Riemann hypothesis in number theory;"
+    - "Connections between Schrödinger’s wave equation and hidden life of Riemann’s zeta function, noncommutative geometry
+       as bridge between Riemann hypothesis and quantum gravity."
+part_53:
+  label: whole
+  toc:
+    - "Particle-wave duality as flawed foundation of quantum physics;"
+    - "Frozen dogmas and mobile solitons as wave-particles, holography as conceptual basis for more flexible physics;"
+    - "Black holes of cosmos and particle-holes of micro-world, information theory, and black hole thermodynamics;"
+    - "Birth of holographic principle and AdS/CFT correspondence;"
+    - "Importance of liquid-crystalline phase of matter in biology, the universe as a single living organism, human as
+       self-aware projection in nature of universal creative principle."
+part_61:
+  label: numbers
+  toc:
+    - "Sphere and tree in mathematics and philosophy, Pascal and Descartes as founders of scientific concept of unity of 
+       matter and consciousness;"
+    - "p-adic number apparatus as bridge for seamless transition from classical to quantum physics;"
+    - "Ultrametric spaces for \"Pascal’s sphere\" and \"Descartes' tree\";"
+    - "Non-Archimedean analysis and geometry at Planck scales;"
+    - "Approaches of p-adic physics, adelic mathematics apparatus for integral description of consciousness and matter as
+       unified system;"
+    - "Parallel ideas of unity through doubling: Yuri Manin and Wolfgang Pauli. p-adic numerical models of consciousness 
+       by Andrei Khrennikov."
+part_62:
+  label: shapes
+  toc:
+    - "Hopf fibration: numerous practical applications for abstract mathematical object;"
+    - "Yang-Mills gauge fields as connectedness in fiber bundle spaces;"
+    - "Torus topology as two-layer sphere, fullerene structure, and signs of Poincaré's dodecahedral space geometry in 
+       universe;"
+    - "Möbius ladder duality, universe as topological insulator, trefoil knot topology as six-layer soccer ball;"
+    - "Geometric links between AdS/CFT and Hopf fibration;"
+    - "Gödel metric with closed trajectories along time axis, stationary AdS universe, concepts of cyclic universe 
+       expansions-contractions."
+part_7:
+  label: unity
+  toc:
+    - "Cosmic spider-mother of ancient myths, doubled great cow of Sky and Water, Heh as infinity of figure eight;"
+    - "Pauli’s dream #59 about \"world clock\" and its connection to convective cellular structure of two-brane universe;"
+    - "Cyclical cosmology of Sphairos and Empedocles’ theory of evolution as a path of “soul purification”; Synchronicity
+       and harmony: teachings of Empedocles in the West and Buddha in the East; Multilayered world of consciousness in Buddhism
+       overlaid onto the Randall–Sundrum two-brane model of matter and the geometry of the universe in the form of nontrivial
+       Hopf fibration;"
+    - "The butterfly archetype as “psyche” in Nabokov and Pauli; unity code: Lorenz butterfly, graviton as a photon pair,
+       and Villarceau circles as the essence of AdS/CFT; physics of the “afterlife” in the descriptions by Frederic Myers;
+       physicist Oliver Lodge and his philosophy; neurosurgeon Alexander’s journey to “heaven” as immersion into an
+       optoacoustic hologram of the AdS world; biomimetics and butterfly wings as a path toward understanding the holographic
+       nature of consciousness and morphogenesis of the “solid” world;"
+    - "The bird archetype and multilayered structure of the soul in ancient Egyptian beliefs; the Sufi parable of the
+       search for the “king of birds” Simurgh; Mundaka Upanishad of Hinduism on two birds on the Tree of Life; Möbius
+       transformations and the Tree of Life in mathematician D. Mumford’s book “Indra's Pearls. The Vision of Felix
+       Klein”; holographic Tree of Life as the Net of Indra in the Avatamsaka Sutra of the Buddhist Hua-Yen school."
+    - "Shiva’s dance and Hindu views on matter in the context of modern physics; damaru — the two-membrane drum of Shiva 
+       played with one hand; Richard Feynman and the “world on the membrane of a drum”; secret US science and the four
+       twin gods in pre-Columbian American mythology; message from Shiva Nataraja to physicists at CERN: “Do not be
+       afraid”…"
+    - "Aliens and resolving the “Fermi paradox”; Cameron’s “Avatar” and Thoth-Djehuti of ancient Egyptians; Egyptian 
+       “Book of the Dead” and its Chapter 64 on comprehending all chapters of ascending to light in one chapter; Pauli,
+       Jung, and the arrival of aliens “from within our consciousness”; Peace as the universe in our hands and the simplest recipe for awakening."

deploy/deploy.sh

@@ -12,7 +12,6 @@ DIR=$(cd "$(dirname "$(readlink -f "$0")")" && pwd)
 DEV_DIR="$(realpath "$DIR/../")"
 STAGING_DIR="$HOME/staging"
 PROD_DIR="$HOME/www"
-PHP="$(which php)"
 REPO_URI=$(cat "$DEV_DIR/config.yaml" | grep ^git_repo | head -1 | awk '{print $2}')
 
 [ "$(hostname)" = "4in1" ] || die "unexpected hostname. are you sure you're running it on the right machine?"
@@ -40,12 +39,7 @@ if [ ! -d node_modules ]; then
 fi
 
 cp "$DEV_DIR/config.yaml" .
-
+"$DIR/static.sh" -o "$STAGING_DIR"
-"$DIR"/build_js.sh -i "$DEV_DIR/htdocs/js" -o "$STAGING_DIR/htdocs/dist-js" || die "build_js failed"
-"$DIR"/build_css.sh -i "$DEV_DIR/htdocs/scss" -o "$STAGING_DIR/htdocs/dist-css" || die "build_css failed"
-$PHP "$DIR"/gen_runtime_config.php \
-	--htdocs-dir "$STAGING_DIR/htdocs" \
-	--commit-hash "$(git rev-parse --short=8 HEAD)" > "$STAGING_DIR/config-runtime.php" || die "gen_runtime_config failed"
 
 cd "$DIR"
 
@@ -60,9 +54,9 @@ rsync -a --delete --delete-excluded --info=progress2 "$STAGING_DIR/" "$PROD_DIR/
     --exclude debug.log \
     --exclude='/log' \
     --exclude='/composer.*' \
-    --exclude='/htdocs/scss' \
+    --exclude='/public/*/scss' \
-    --exclude='/htdocs/js' \
+    --exclude='/public/*/js' \
-    --exclude='/htdocs/sass.php' \
+    --exclude='/public/sass.php' \
-    --exclude='/htdocs/js.php' \
+    --exclude='/public/js.php' \
     --exclude='*.sh' \
     --exclude='*.sql'

deploy/static.sh

@@ -0,0 +1,29 @@
+#!/bin/sh
+
+die() {
+    >&2 echo "error: $@"
+    exit 1
+}
+
+set -e
+
+PHP="$(which php)"
+SCRIPT_DIR=$(cd "$(dirname "$(readlink -f "$0")")" && pwd)
+APP_DIR="$(realpath "$SCRIPT_DIR/../")"
+OUTPUT_ROOT_DIR=
+
+while [ $# -gt 0 ]; do
+	case $1 in
+		-o) OUTPUT_ROOT_DIR="$2"; shift ;;
+		-h) usage ;;
+		*) die "unexpected argument: $1" ;;
+	esac
+	shift
+done
+[ -z "$OUTPUT_ROOT_DIR" ] && die "you must specify output directory"
+
+for project in ic foreignone; do
+	"$SCRIPT_DIR"/util/build_css.sh -i "$APP_DIR/public/$project/scss" -o "$OUTPUT_ROOT_DIR/public/$project/dist-css"                 || die "build_css failed"
+	"$SCRIPT_DIR"/util/build_js.sh -i "$APP_DIR/public/common/js" -o "$OUTPUT_ROOT_DIR/public/$project/dist-js"                       || die "build_js failed"
+	$PHP "$SCRIPT_DIR"/util/gen_runtime_config.php --commit-hash "$(git rev-parse --short=8 HEAD)" > "$OUTPUT_ROOT_DIR/config-runtime.php" || die "gen_runtime_config failed"
+done

deploy/util/build_common.sh

@@ -1,6 +1,7 @@
 #!/bin/sh
 
 set -e
+#set -x
 
 INDIR=
 OUTDIR=
@@ -57,7 +58,6 @@ check_args() {
     if [ ! -d "$OUTDIR" ]; then
         mkdir "$OUTDIR"
     else
-        # warning "$OUTDIR already exists, erasing it"
+        find "$OUTDIR" -mindepth 1 -delete
-        rm "$OUTDIR"/* || true
     fi
 }

deploy/util/build_css.sh

@@ -1,7 +1,7 @@
 #!/bin/sh
 
 DIR=$(cd "$(dirname "$(readlink -f "$0")")" && pwd)
-ROOT="$(realpath "$DIR/../")"
+ROOT="$(realpath "$DIR/../../")"
 CLEANCSS="$ROOT"/node_modules/clean-css-cli/bin/cleancss
 . "$DIR/build_common.sh"
 
@@ -9,7 +9,7 @@ build_scss() {
     entry_name="$1"
     theme="$2"
 
-    input="$INDIR/entries/$entry_name/$theme.scss"
+    input="$INDIR/$entry_name@$theme.scss"
     output="$OUTDIR/$entry_name"
     [ "$theme" = "dark" ] && output="${output}_dark"
     output="${output}.css"
@@ -41,7 +41,6 @@ create_dark_patch() {
 }
 
 THEMES="light dark"
-TARGETS="common admin"
 
 input_args "$@"
 check_args
@@ -49,12 +48,12 @@ check_args
 [ -x "$CLEANCSS" ] || die "cleancss is not found"
 
 for theme in $THEMES; do
-    for target in $TARGETS; do
+	while IFS= read -r target; do
-        build_scss "$target" "$theme"
+		build_scss "$target" "$theme"
-    done
+	done < "$INDIR/targets.txt"
 done
 
-for target in $TARGETS; do
+while IFS= read -r target; do
-    create_dark_patch "$target"
+	create_dark_patch "$target"
-    for theme in $THEMES; do cleancss "$target" "$theme"; done
+	for theme in $THEMES; do cleancss "$target" "$theme"; done
-done
+done < "$INDIR/targets.txt"

deploy/util/gen_runtime_config.php

@@ -1,16 +1,11 @@
 #!/usr/bin/env php
 <?php
 
-require __DIR__.'/../src/init.php';
+require __DIR__.'/../../src/init.php';
 
-$htdocs_dir = null;
 $commit_hash = null;
 for ($i = 1; $i < $argc; $i++) {
     switch ($argv[$i]) {
-        case '--htdocs-dir':
-            $htdocs_dir = $argv[++$i] ?? usage('missing value for --htdocs-dir');
-            break;
-
         case '--commit-hash':
             $commit_hash = $argv[++$i] ?? usage('missing value for --commit-hash');
             break;
@@ -20,26 +15,30 @@ for ($i = 1; $i < $argc; $i++) {
     }
 }
 
-if (is_null($htdocs_dir) || is_null($commit_hash))
+if (is_null($commit_hash))
     usage();
 
 $hashes = [
     'commit_hash' => $commit_hash,
     'assets' => []
 ];
-foreach (['css', 'js'] as $type) {
-    $entries = glob_recursive($htdocs_dir.'/dist-'.$type.'/*.'.$type);
-    if (empty($entries)) {
-        fwrite(STDERR, "warning: no files found in $htdocs_dir/dist-$type\n");
-        continue;
-    }
 
-    foreach ($entries as $file) {
+foreach (['ic', 'foreignone'] as $project) {
-        $hashes['assets'][$type.'/'.basename($file)] = [
+    foreach (['js', 'css'] as $type) {
-            'integrity' => []
+        $dist_dir = APP_ROOT.'/public/'.$project.'/dist-'.$type;
-        ];
+        $entries = glob_recursive($dist_dir.'/*.'.$type);
-        foreach (\engine\skin\FeaturedSkin::RESOURCE_INTEGRITY_HASHES as $hash_type)
+        if (empty($entries)) {
-            $hashes['assets'][$type.'/'.basename($file)]['integrity'][$hash_type] = base64_encode(hash_file($hash_type, $file, true));
+            fwrite(STDERR, "warning: no files found in $dist_dir\n");
+            continue;
+        }
+        foreach ($entries as $file) {
+            $hashes['assets'][$project][$type.'/'.basename($file)] = [
+                'integrity' => []
+            ];
+            foreach (\engine\skin\FeaturedSkin::RESOURCE_INTEGRITY_HASHES as $hash_type) {
+                $hashes['assets'][$project][$type.'/'.basename($file)]['integrity'][$hash_type] = base64_encode(hash_file($hash_type, $file, true));
+            }
+        }
     }
 }
 
@@ -50,7 +49,7 @@ function usage(string $msg = ''): never  {
     if ($msg !== '')
         fwrite(STDERR, "error: {$msg}\n");
     $script = $GLOBALS['argv'][0];
-    fwrite(STDERR, "usage: {$script} --htdocs-dir DIR --commit-hash HASH\n");
+    fwrite(STDERR, "usage: {$script} --commit-hash HASH\n");
     exit(1);
 }
 

htdocs/scss/bundle_common.scss

@@ -1,15 +0,0 @@
-@import "./app/common";
-@import "./app/head";
-@import "./app/foot";
-@import "./app/blog";
-@import "./app/form";
-@import "./app/pages";
-@import "./app/index";
-@import "./app/files";
-@import "./hljs/github.scss";
-@import "./app/widgets";
-@import "./app/pagenav";
-
-@media screen and (max-width: 880px) {
-  @import "./app/mobile";
-}

htdocs/scss/entries/admin/dark.scss

@@ -1,2 +0,0 @@
-@import '../../colors/dark';
-@import '../../bundle_admin';

htdocs/scss/entries/admin/light.scss

@@ -1,2 +0,0 @@
-@import '../../colors/light';
-@import '../../bundle_admin';

htdocs/scss/entries/common/dark.scss

@@ -1,2 +0,0 @@
-@import '../../colors/dark';
-@import '../../bundle_common';

htdocs/scss/entries/common/light.scss

@@ -1,2 +0,0 @@
-@import '../../colors/light';
-@import '../../bundle_common';

public/common/scss/app/blog.scss

@@ -161,7 +161,7 @@
 
     li {
       margin: 2px 0;
-      line-height: 150%;
+      line-height: 140%;
       > a {
         display: inline-block;
       }

public/common/scss/app/common.scss

@@ -137,7 +137,7 @@ a:hover {
 }
 
 p, p code, li {
-  line-height: 150%;
+  line-height: 140%;
 }
 
 .unicode { font-family: sans-serif; }
@@ -340,7 +340,7 @@ table.contacts div.note {
   &-updates {
     float: right;
     text-align: right;
-    line-height: 150%;
+    line-height: 140%;
     &-link-wrap {
       border-top: 1px $border-color solid;
       margin-top: 13px;

public/common/scss/colors/light.scss

@@ -1,5 +1,3 @@
-//@use 'sass:color';
-
 $head_green_color: #0bad19;
 $head_red_color: #ce1a1a;
 $link-color: #116fd4;

public/foreignone/scss/admin@dark.scss

@@ -0,0 +1,2 @@
+@import '../../common/scss/colors/dark';
+@import './admin';

public/foreignone/scss/admin@light.scss

@@ -0,0 +1,2 @@
+@import '../../common/scss/colors/light';
+@import './admin';

public/foreignone/scss/common.scss

@@ -0,0 +1,15 @@
+@import "../../common/scss/app/common";
+@import "../../common/scss/app/head";
+@import "../../common/scss/app/foot";
+@import "../../common/scss/app/blog";
+@import "../../common/scss/app/form";
+@import "../../common/scss/app/pages";
+@import "../../common/scss/app/index";
+@import "../../common/scss/app/files";
+@import "../../common/scss/hljs/github";
+@import "../../common/scss/app/widgets";
+@import "../../common/scss/app/pagenav";
+
+@media screen and (max-width: 880px) {
+  @import "../../common/scss/app/mobile";
+}

public/foreignone/scss/common@dark.scss

@@ -0,0 +1,2 @@
+@import '../../common/scss/colors/dark';
+@import './common';

public/foreignone/scss/common@light.scss

@@ -0,0 +1,2 @@
+@import '../../common/scss/colors/light';
+@import './common';

public/foreignone/scss/targets.txt

@@ -0,0 +1,2 @@
+common
+adminge