Planiversum is a virtual contact with the two-dimensional world. The Two-Dimensional World of Christian Imaginations

Design by artist A. Balashova.

When the book The Planiversum first appeared 16 years ago, it took quite a few readers by surprise. The line between voluntary refusal from distrust and ingenuous acceptance, if it exists, it is very thin. Despite the sly, ironic overtones, there were those who wanted to believe that we had come into contact with the two-dimensional world of Arde, a disk-shaped planet inscribed in the outer shell of a vast, shaped hot air balloon space called the Planiversum.

It is tempting to imagine that both gullible and incredulous readers did so because of the convincing logic and consistency of the cosmology and physics of this infinitely thin universe with its bizarre, but strangely efficient organisms inhabiting it. After all, not just an ordinary universe, generated by a game of imagination, opened before them. Planiversum is more than a bizarre, fantastic place, since most of it was "made" by a virtual team of scientists and technologists. Reality - even the pseudo-reality of such a place is much more strange than it seems at first glance.

To begin with, we will try to understand what a flat universe Planiversum is. Understand that two dimensions means two dimensions. If the page of this book is a small piece of the Planiversum, then the curved line drawn on it may turn out to be a piece of a planiversal cord or string, the two free ends of which cannot be connected, because this requires an additional, third dimension, which, so to speak, goes beyond this page. But give us some planiversal glue and we'll stick one end to the other, trapping whatever is inside the loop of lace once the glue dries.

The appendix to the book contains a fairly complete history of the origin of the flat universe Planiversum. As soon as an article about Planiversum appeared in Scientific American in Martin Gardner's column on math games, thousands (not even hundreds) of readers sent letters containing enthusiastic responses and new ideas. Both professional scientists and engineers wrote, and even a few well-informed readers who sent reasonable suggestions.

We wove something homogeneously seamless from these ideas, but we needed a plot - a story, to make it interesting book. A story that would take us on a journey through Arda, a disc-shaped planet floating in the 2D Planiversum universe.

From the preface to the final, the narration is conducted with a serious, even impassive face. It's written in pen scientific worker, whose literary possibilities are constantly under the pressure of events. The story features a modern deus ex machina - a computer. It was through him that a group of students made first contact with the 2D universe of Planiversum and its four-armed hero Yendred, whose craving for the "higher" turned into fear when he finally came face to face with it.

The author was surprised and disturbed that so many people took the fiction at face value. The subtext of this fantastic, though very rich in detail, story has gone unnoticed by so many. Neoteny trends rooted in Western culture even before 1984. And of course, the fantastical allegory introduced into the narrative - that is, what makes the book, in the words of the Oxford humanist Graham Stuart, "a Sufi parable" - went completely unnoticed by these readers. The temptation to bring to life the higher (third) dimension as a symbol of the forces lurking on the other side of the apparent reality of our world turned out to be too great to be overcome. The story opens with an old preface waiting for you on the next page.

A. K. Dyudni.

January 2000

I want to note that I am not so much the author of the book as its compiler, but main merit that this book has seen the light belongs to the creature depicted on the first page. His name is Yendred, and he lives in a two-dimensional universe that I have named the Planiversum. The history of the discovery of Planiversum - a world in the reality of which few people could believe, will surely seem interesting to you. I want to tell her.

The first acquaintance with this world took place at our university about a year ago. My students have worked with computer program 2DWORLD, which they themselves wrote over several semesters. Initially, the purpose of the program was to give students the opportunity to practice scientific modeling and programming, but soon 2DWORLD took on a life of its own.

It all started with an attempt to model a two-dimensional model physical body. For example, a simple two-dimensional object might be disk-shaped and made up of many two-dimensional atoms.

It has some mass (depending on the type and number of atoms it contains) and can move around in two-dimensional space, such as this page. But, unlike a page, two-dimensional space has no thickness, and the disk cannot go beyond it. Suppose that all objects in this space obey laws similar to those that operate in our three-dimensional world. That is, if we push the disk to the right, it will start moving at a constant speed in the plane that is the continuation of the page. Sooner or later, while continuing to move in this imaginary plane, the object will leave the surface of the Earth, unless, of course, it collides with another similar object.

When such two objects meet, they will experience what physicists call an "elastic collision." In the figure, we see two objects at the moment of greatest deformation, when they collided and are about to roll away from each other. In accordance with the well-known law of physics operating in our three-dimensional universe, the sum of the kinetic and potential energies of two disks before and after the collision remains unchanged. Moving in this way, the discs cannot help but collide. They cannot "dodge" and avoid a collision. In a two-dimensional world, they simply have nowhere to "dodge".

This physical process can be easily displayed on a computer by writing a program that will simulate the behavior of two disks at the moment of collision. Of course, if we take into account that disks are composed of individual atoms, this will complicate the work of the programmer and increase the load on the processor during the execution of the program. But almost any programmer is able to write such a program and display the results on the screen.

Around this time, work began on the 2DWORLD program. In the first semester, students under my guidance not only described in the program a certain set of objects and the law of conservation of energy, but also created a whole system of planets revolving around a star. One of the planets, which they named Astria, won particular popularity among the students. By the end of the first semester, talk began about how to draw a map on this planet and populate it with living beings - the Astrians. I nipped these aspirations in the bud: the semester was coming to an end, and there was nothing left before the exams. And it was unrealistic to implement the idea - my students were not so strong programmers.

In any case, 2DWORLD turned out to be very useful program and it was incredibly interesting to work with her. I especially remember the process of the formation of a galaxy from a chaotic cluster of stars. In short, I came to the conclusion that the project was a success and that I was right when I decided to limit the physical space of the model to two dimensions. Thanks to this, students understood what real modeling is.

Professor Yen entered the office and looked around the class.

Greetings to all gathered at the lesson on the study of magical items. Today we have a new, somewhat unusual topic: Two-dimensional world.

So, how many dimensional spaces do you know?
Of course, everyone is familiar with the three-dimensional space in which we live. It has three dimensions: length, height and width. The fourth dimension is considered to be time, but we will not take it into account.
A two-dimensional space is a plane. *the professor took a sheet of parchment and drew a little man on it* Without leaving the plane, objects can only be measured in two perpendicular directions: for example, in width and height.
And one-dimensional space will be a straight line. Objects in it will have a single dimension: in length.
Here you, of course, ask: what objects? Can objects exist on a straight line?
But why not? But the question "is there life in a one-dimensional world" I will include in your homework. I think it will be of interest to you no less than the Muggle question "Is there life on Mars." -))

The next question you should ask yourself is: are there worlds with a large number measurements? And what do they look like?
Of course you, as young wizards, should know that nothing is impossible, especially in this case. And traveling through the worlds is a matter of technique and imagination.
But imagining a world with a dimension greater than 3 is not so easy. For this, we will first need to go on a journey into a two-dimensional world.
After all, putting yourself in the place of the "two-dimensional", looking at them from the side of our dimension and understanding how they think and perceive the nature around them, you can understand how beings from 4 dimensions would perceive us, and what needs to be done to go beyond boundaries of the familiar world. Above last question many magicians racked their brains, and if it interests you, then I advise you to turn to their works, tk. I won't talk about it in the lecture. In this lecture, we will only touch on the two-dimensional world and objects in it, because. I think it will be interesting, informative and may serve as an impetus for further reflection.

So, does a two-dimensional world really exist? And can we get into it?
Of course, it is very difficult to imagine, and even more so to recreate a two-dimensional world in our three-dimensional space. After all, even the thinnest sheet of parchment still has a finite thickness. But, as I said, nothing is impossible. And from the Parallel Worlds course, you should at least imagine that the worlds are different, and not even necessarily parallel)
The English magician, wizard and mathematician Charles Howard Hinton was the first to discover and describe life in a two-dimensional world in the book The Episode in Flatland, published in London in 1907. I won’t be surprised if this is the only magician who managed to look into the two-dimensional dimension and told us about it, because. no other similar sources are known. Therefore, we will not go to the two-dimensional world - it is too unusual and unsafe for an unprepared person - but first we will try to imagine it well in order to know what awaits us there.

You can easily imagine a two-dimensional world by putting a few coins on the table. Let one coin, a galleon, be the Sun. And small coins - knuts and sickles - planets revolving around him. Consider one such planet-coin. Let's call her Astria. The inhabitants of Astria can only move around the rim of the planet, remaining in the plane of this world. Trees grow and houses stand in the same plane. Therefore, when a tree hits, an Astroitan must either climb over it or cut it down. To get around one another, one inhabitant must jump over the other, as acrobats would do on a taut rope (I think the inhabitants of such a world should be able to jump and fly very well). In such a world, it is impossible for an inhabitant to turn around in the other direction: in order to look behind his back, an Astroitian must either stand on his head or use a mirror. Since the second method is more convenient, not a single resident leaves the house without a mirror.
The structure of the houses of the Astroites is interesting: all the houses are also equipped with mirrors, and the houses have windows and doors so that they can be entered and exited. But to keep the house from collapsing, only one door or window can be opened at a time. If the west door is open, the east doors and windows must be closed or the top of the house will collapse.
The bodies of the Astroitans have a complex structure. But for now, for simplicity, we can represent them as triangles with arms, legs and one eye. All men of Astria are born with faces facing east, and women - west. Thus, it is easy for an Astroite to kiss her husband or son, but to kiss her daughter, she needs to turn her upside down.))
In a two-dimensional world, wheels with axles are completely excluded. Objects can be transported using the method of rolling through circles (similar to how we can move heavy things on cylindrical rollers placed under them).

In Hinton's world there is love, and war, and an impending catastrophe (the approach of another planet, which can change the orbit of Astria so much that life there will become impossible), and even a happy ending.
Of course, I cannot teach you to travel between worlds, especially worlds with different dimensions, but the main thing is to know where you can go and what you will encounter - everything else is up to you.

Now, homework!

1. Is the existence of a one-dimensional world and life in it possible, do you think? Justify your answer. (3 points)
2. Think about the existence musical instruments perhaps in a two-dimensional world? (2 points)
3. Try to imagine a duel between two magicians in Astria.
   What items (perhaps magical)) would you need? What dueling rules would you recommend using? (3 points)
4. Draw a flower the way an Astrian artist would draw it. (If you find it difficult to draw and save the picture in jpg format can you describe the drawing in words)(2)

Those who have successfully completed their homework can consider that they are ready to go on a trip to the two-dimensional world.)))

What is the laboratory of nanooptics and plasmonics famous for? If you try to describe its activities in one sentence, then behind nanooptics and plasmonics are biosensors, nanolasers, single-photon sources, metasurfaces, and even two-dimensional materials. The laboratory cooperates with universities and research centers in many countries and continents. Russian partners include groups from Moscow State University, Skoltech and ITMO University. The plans of the laboratory not only Scientific research and development, but also their commercialization, as well as the organization of the first large-scale conference in Russia on two-dimensional materials.

The head of the laboratory is Valentin Volkov, visiting professor from the University of Southern Denmark in Aalborg. The laboratory was organized in 2008 on the initiative of the professors of the department general physics MIPT Anatoly Gladun and Vladimir Leiman, while graduates of the Moscow Institute of Physics and Technology Sergey Bozhevolny and Alexander Tishchenko had a great influence on its formation. Now it is part of the Center for Photonics and Two-Dimensional Materials at the Phystech School of Fundamental and Applied Physics.

« We take approaches that have worked well in practice in some areas of research and transfer them to new areas of research. For example, we took copper, which has proven itself well in electronics, combined it with two-dimensional materials and dielectrics, and it turned out that with its help in nanooptics you can do everything that you did before, but much better and cheaper.", - argues Valentin Volkov.

Head of the laboratory Valentin Volkov

The laboratory deals with both theory and experiment. It has the most modern equipment for research in the near field - aperture and non-aperture near-field optical microscopes. They make it possible to study the distribution of electromagnetic fields along the surfaces of micro- and nanosized samples at distances much shorter than the wavelength of light, with a spatial resolution of up to 10 nm. For the analysis of materials and samples, a set of tools is used from spectral ellipsometry to Raman spectroscopy. Experimental studies are accompanied theoretical research and numerical simulation. Objects for research are also made directly in the laboratory and the MIPT Shared Use Center.

Much attention in the laboratory is paid to the use of nanomaterials in optics. It all started with graphene and carbon nanotubes (together with colleagues from Japan and the USA), and now they are working with transition metal dichalcogenides, tellurene, and germanium-based compounds. Literally this year, scientists launched an installation for the CVD synthesis of two-dimensional materials. The laboratory categorically disagrees with the commonplace for Russia statement that two-dimensional materials are just a fashion, and consider them as a key building material for nanophotonics, and also agree with the words of Andrey Geim that the next 50 years will not be enough to study them. According to Fabio Pulizzi, editor-in-chief of Nature Nanotechnology, who recently visited the lab, 30% of the publications in his journal are papers related to two-dimensional materials to some extent. The competition here is very high, but this is what Phystech needs.

Biosensors and graphene

One of the important directions of the laboratory is highly sensitive biosensors for pharmacology and medical diagnostics. It is directly related to plasmonics - we are talking about plasmonic biosensors - but this is where biology comes into play. This job requires a different qualification.

« My colleagues specifically studied biology and chemistry in order to start this difficult task with a new background. Biology and chemistry are perfectly integrated with our interest in the practical use of two-dimensional materials.”, says Valentin Volkov.

A recent achievement of the laboratory is the creation of graphene biosensor chips for commercial biosensors based on surface plasmon resonance. The developed chips demonstrate a significantly higher sensitivity than those presented on this moment on the sensor chip market. An increase in sensitivity is provided by replacing standard bonding layers with graphene (or graphene oxide), which is characterized by a record surface area. An additional advantage of the development is the use of copper as a plasmonic metal instead of gold, which is standard for such chips, which made it possible to significantly reduce their cost, primarily due to the compatibility of copper with standard technological processes.

Single-photon sources and nanolasers

The laboratory also conducts research on the creation of truly single-photon light sources with electrical pumping - devices that emit single photons when an electric current is passed. The transition to such single-photon technologies will not only increase the energy efficiency of existing devices for processing and transmitting information by more than a thousand times, but will also open the way to the creation of various quantum devices. Another close problem in this field is the creation of coherent sources of optical radiation operating at room temperature from miniature power sources, the dimensions of which are only hundreds of nanometers. Such compact devices are in demand in optogenetics, medicine, and electronics.

Conference in Sochi, robots in Denmark

This year, Valentin Volkov will organize a session on 2D materials at the Third International Conference "Metamaterials and Nanophotonics" (METANANO-2018). Scientists - leaders in their fields will take part in the conference, and it will be opened by FAPF graduate (1982) and Nobel laureate Andrey Geim. The laboratory staff also has a more ambitious goal - holding an annual large-scale conference on two-dimensional materials in Russia.

This summer, the laboratory students will go on an internship at the Danish company Newtec, with which the laboratory has been cooperating for several years. The company is not directly related to science - it develops and manufactures high-tech robotic systems for sorting fruits and vegetables - however, it has a very powerful research department, which includes a complex of laboratories for the study of two-dimensional materials. This company uses graphene to create hyperspectral cameras for high-speed diagnostics of sorted fruits and vegetables. Joint research with the Danes not only helps the laboratory master new technologies and approaches in working with two-dimensional materials, but also allows you to look at the world of research and development from a completely different angle. This cannot be learned in a university.

This is the fourth issue in a row. Volunteers are also requested not to forget which topics they have expressed a desire to cover, or maybe someone has just now chosen a topic from the list. From me repost and promotion on social networks. And now our topic: "string theory"

You have probably heard that the most popular scientific theory of our time - string theory - implies the existence of much more dimensions than common sense tells us.

The biggest problem for theoretical physicists is how to combine all fundamental interactions (gravitational, electromagnetic, weak and strong) into a single theory. Superstring theory just claims to be the Theory of Everything.

But it turned out that the most convenient number of dimensions needed for this theory to work is as many as ten (nine of which are spatial, and one is temporal)! If there are more or less dimensions, mathematical equations give irrational results that go to infinity - a singularity.

The next stage in the development of superstring theory - M-theory - has already counted eleven dimensions. And another version of it - F-theory - all twelve. And it's not a complication at all. F-theory describes 12-dimensional space with simpler equations than M-theory describes 11-dimensional space.

Of course, theoretical physics is called theoretical for a reason. All her achievements so far exist only on paper. So, to explain why we can only move in three-dimensional space, scientists started talking about how the unfortunate other dimensions had to shrink into compact spheres at the quantum level. To be precise, not into spheres, but into Calabi-Yau spaces. These are such three-dimensional figures, inside of which there is own world with its own dimensions. A two-dimensional projection of similar manifolds looks something like this:

Yes, it does seem a bit far-fetched. But perhaps this explains why the quantum world is so different from what we perceive.

Let's dive into history a bit

In 1968, the young theoretical physicist Gabriele Veneziano was poring over the many experimentally observed characteristics of the strong nuclear force. Veneziano, who at the time was working at CERN, the European Accelerator Laboratory in Geneva, Switzerland, had been working on this problem for several years until one day he had a brilliant idea. Much to his surprise, he realized that an exotic mathematical formula, invented some two hundred years earlier by the famous Swiss mathematician Leonhard Euler for purely mathematical purposes - the so-called Euler beta function - seemed to be able to describe in one fell swoop all the numerous properties of the particles involved in strong nuclear force. The property noticed by Veneziano gave a powerful mathematical description many features of the strong interaction; it has sparked a flurry of work in which the beta function and its various generalizations have been used to describe the vast amounts of data accumulated in the study of particle collisions around the world. However, in in a certain sense Veneziano's observation was incomplete. Like a memorized formula used by a student who doesn't understand its meaning or meaning, Euler's beta function worked, but no one understood why. It was a formula that needed an explanation.

Gabriele Veneziano

Things changed in 1970, when Yochiro Nambu of the University of Chicago, Holger Nielsen of the Niels Bohr Institute, and Leonard Susskind of Stanford University were able to discover the physical meaning behind Euler's formula. These physicists showed that when presented elementary particles small oscillating one-dimensional strings, the strong interaction of these particles is exactly described using the Euler function. If string segments are small enough, these researchers reasoned, they will still look like point particles, and therefore will not contradict the results of experimental observations. Although this theory was simple and intuitively appealing, string descriptions of the strong force were soon shown to be flawed. In the early 1970s High-energy physicists have been able to look deeper into the subatomic world and have shown that some of the predictions of the string-based model are in direct conflict with observations. At the same time, the development of quantum field theory - quantum chromodynamics - was going on in parallel, in which the point model of particles was used. The success of this theory in describing the strong interaction led to the abandonment of string theory.
Most particle physicists believed that string theory was forever sent to the dustbin, but a number of researchers remained faithful to it. Schwartz, for example, felt that " mathematical structure string theory is so beautiful and has so many amazing properties that it must surely point to something deeper” 2). One of the problems that physicists had with string theory was that it seemed to provide too many choices, which was confusing. Some configurations of vibrating strings in this theory had properties that resembled those of gluons, which gave grounds to really consider it a theory of the strong interaction. However, in addition to this, it contained additional interaction-carrier particles that had nothing to do with the experimental manifestations of the strong interaction. In 1974, Schwartz and Joel Sherk of the French ETH made a bold suggestion that turned this seeming flaw into a virtue. After studying the strange modes of vibration of strings, reminiscent of carrier particles, they realized that these properties coincide remarkably well with the proposed properties of the hypothetical gravitational carrier particle - the graviton. Although these "tiny particles" of the gravitational interaction have not yet been discovered, theorists can confidently predict some of the fundamental properties that these particles should have. Sherk and Schwartz found that these characteristics are exactly the same for some modes of vibration. Based on this, they suggested that the first advent of string theory ended in failure due to the fact that physicists overly narrowed the scope of its application. Sherk and Schwartz announced that string theory is not just a theory of the strong force, it is a quantum theory that, among other things, includes gravity).

The physics community has reacted to this suggestion with great restraint. In fact, according to Schwartz, "our work was ignored by everyone" 4). The paths of progress have already been thoroughly littered with numerous failed attempts to unify gravity and quantum mechanics. String theory failed in its original attempt to describe the strong force, and it seemed pointless to many to try to use it to achieve even greater goals. Subsequent, more detailed studies of the late 1970s and early 1980s. showed that string theory and quantum mechanics have their own, albeit smaller, contradictions. It seemed that the gravitational force was again able to resist the attempt to build it into the description of the universe at the microscopic level.
This was the case until 1984. In a pivotal paper summarizing more than a decade of intense research that has been largely ignored or dismissed by most physicists, Green and Schwartz found that there is little contradiction with quantum theory, which string theory suffered from, can be resolved. Moreover, they showed that the resulting theory was broad enough to cover all four kinds of forces and all kinds of matter. Word of this result spread throughout the physics community, as hundreds of particle physicists stopped working on their projects to take part in an assault that seemed like the final theoretical battle in a centuries-old assault on the deepest foundations of the universe.
Word of Green and Schwartz's success eventually reached even the first-year graduate students, and the former gloom was replaced by an exciting sense of belonging to turning point in the history of physics. Many of us have stayed up late into the night, poring over heavy volumes of theoretical physics and abstract mathematics, the knowledge of which is necessary to understand string theory.

According to scientists, we ourselves and everything around us consists of an infinite number of such mysterious folded micro-objects.
Period from 1984 to 1986 now known as "the first revolution in superstring theory". During this period, more than a thousand papers on string theory were written by physicists around the world. These papers finally demonstrated that many properties of the Standard Model, discovered over decades of painstaking research, flow naturally from the magnificent system of string theory. As Michael Green remarked, “The moment you are introduced to string theory and realize that almost all of the major advances in physics last century follow - and follow with such elegance - from such a simple starting point, clearly demonstrates to you the incredible power of this theory. Moreover, for many of these properties, as we shall see below, string theory provides a much more complete and satisfactory description than the standard model. These advances convinced many physicists that string theory could deliver on its promise and become the ultimate unifying theory.

2D projection of a 3D Calabi-Yau manifold. This projection gives an idea of ​​how complex the extra dimensions are.

However, along the way, physicists involved in string theory again and again ran into serious obstacles. In theoretical physics, one often has to deal with equations that are either too complex to understand or difficult to solve. Usually, in such a situation, physicists do not give up and try to get an approximate solution to these equations. The situation in string theory is much more complicated. Even the derivation of the equations itself turned out to be so complicated that so far only their approximate form has been obtained. Thus, physicists working in string theory find themselves in a situation where they have to look for approximate solutions to approximate equations. After several years of amazing progress during the first revolution of superstring theory, physicists found that the approximate equations used were unable to give a correct answer to the series important issues, thus slowing down further development research. Lacking concrete ideas on how to go beyond these approximate methods, many physicists working in the field of string theory experienced a growing sense of disillusionment and returned to their previous studies. For those who stayed, the late 1980s and early 1990s were a testing period.

The beauty and potential power of string theory beckoned researchers like a golden treasure, securely locked in a safe, visible only through a tiny peephole, but no one had the key to release these dormant forces to freedom. The long period of "drought" was interrupted from time to time important discoveries, but it was clear to everyone that new methods were required that would allow going beyond the already known approximate solutions.

The stagnation was ended by a breathtaking talk given by Edward Witten in 1995 at a string theory conference at the University of Southern California - a talk that stunned an audience packed to capacity with the world's leading physicists. In it, he unveiled a plan for the next stage of research, thus initiating the "second revolution in superstring theory." String theorists are now hard at work on new methods that promise to overcome the hurdles encountered.

For the wide popularization of TS, humanity should erect a monument to Columbia University professor Brian Greene. His 1999 book The Elegant Universe. Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory" became a bestseller and won the Pulitzer Prize. The work of the scientist formed the basis of a popular science mini-series with the author himself as the host - a fragment of it can be seen at the end of the material (photo by Amy Sussman / Columbia University).

clickable 1700 px

Now let's try to understand the essence of this theory at least a little.

Start over. Zero dimension is a point. She has no size. There is nowhere to move, no coordinates are needed to indicate the location in such a dimension.

Let's put a second point next to the first one and draw a line through them. Here is the first dimension. A one-dimensional object has a size - length, but no width or depth. Movement within the framework of one-dimensional space is very limited, because the obstacle that has arisen on the way cannot be bypassed. To determine the location on this segment, you need only one coordinate.

Let's put a point next to the segment. To fit both of these objects, we need already a two-dimensional space that has length and width, that is, area, but without depth, that is, volume. The location of any point on this field is determined by two coordinates.

The third dimension arises when we add a third coordinate axis to this system. It is very easy for us, the inhabitants of the three-dimensional universe, to imagine this.

Let's try to imagine how the inhabitants of two-dimensional space see the world. For example, here are these two people:

Each of them will see his friend like this:

And with this layout:

Our heroes will see each other like this:

It is the change of point of view that allows our heroes to judge each other as two-dimensional objects, and not one-dimensional segments.

And now let's imagine that a certain three-dimensional object moves in the third dimension, which crosses this two-dimensional world. For an outside observer, this movement will be expressed in a change in two-dimensional projections of the object on a plane, like broccoli in an MRI machine:

But for the inhabitant of our Flatland, such a picture is incomprehensible! He can't even imagine her. For him, each of the two-dimensional projections will be seen as a one-dimensional segment with a mysteriously variable length, appearing in an unpredictable place and also unpredictably disappearing. Attempts to calculate the length and place of occurrence of such objects using the laws of physics of two-dimensional space are doomed to failure.

We, the inhabitants of the three-dimensional world, see everything in two dimensions. Only the movement of an object in space allows us to feel its volume. We will also see any multidimensional object as two-dimensional, but it will change in an amazing way depending on our relative position or time with it.

From this point of view, it is interesting to think, for example, about gravity. Everyone has probably seen pictures like this:

It is customary to depict how gravity bends space-time. Curves... where? Exactly not in any of the dimensions familiar to us. And what about quantum tunneling, that is, the ability of a particle to disappear in one place and appear in a completely different one, moreover, behind an obstacle through which, in our realities, it could not penetrate without making a hole in it? What about black holes? What if all these and other mysteries modern science explained by the fact that the geometry of space is not at all the same as we are accustomed to perceive it?

The clock is ticking

Time adds one more coordinate to our Universe. In order for the party to take place, you need to know not only in which bar it will take place, but also the exact time of this event.

Based on our perception, time is not so much a straight line as a ray. That is, it has a starting point, and the movement is carried out only in one direction - from the past to the future. And only the present is real. Neither the past nor the future exist, just as breakfasts and dinners do not exist from the point of view of an office clerk at lunchtime.

But the theory of relativity does not agree with this. From her point of view, time is a valuable dimension. All the events that have existed, exist and will continue to exist are equally real, as real as the sea beach is, no matter where exactly the dreams of the sound of the surf took us by surprise. Our perception is just something like a searchlight that illuminates a certain segment on the time line. Humanity in its fourth dimension looks something like this:

But we see only a projection, a slice of this dimension into each separate moment time. Yes, yes, like broccoli in an MRI machine.

Until now, all theories have worked with a large number of spatial dimensions, and the temporary has always been the only one. But why does space allow multiple dimensions for space, but only one time? Until scientists can answer this question, the hypothesis of two or more time spaces will seem very attractive to all philosophers and science fiction writers. Yes, and physicists, what is already there. For example, the American astrophysicist Itzhak Bars sees the root of all troubles with the Theory of Everything as the second time dimension, which has been overlooked. As a mental exercise, let's try to imagine a world with two times.

Each dimension exists separately. This is expressed in the fact that if we change the coordinates of an object in one dimension, the coordinates in others can remain unchanged. So, if you move along one time axis that intersects another at a right angle, then at the point of intersection, time around will stop. In practice, it will look something like this:

All Neo had to do was place his one-dimensional time axis perpendicular to the bullets' time axis. A real trifle, agree. In fact, everything is much more complicated.

The exact time in a universe with two time dimensions will be determined by two values. Is it hard to imagine a two-dimensional event? That is, one that is extended simultaneously along two time axes? It is likely that such a world would require time-mapping specialists, just as cartographers map the two-dimensional surface of the globe.

What else distinguishes a two-dimensional space from a one-dimensional one? The ability to bypass an obstacle, for example. This is completely beyond the boundaries of our mind. An inhabitant of a one-dimensional world cannot imagine how it is to turn a corner. And what is this - an angle in time? In addition, in two-dimensional space, you can travel forward, backward, or even diagonally. I have no idea how it is to go diagonally through time. I'm not talking about the fact that time is the basis of many physical laws, and how the physics of the Universe will change with the advent of another time dimension is impossible to imagine. But it's so exciting to think about it!

Very large encyclopedia

Other dimensions have not yet been discovered, and exist only in mathematical models. But you can try to imagine them like this.

As we found out earlier, we see a three-dimensional projection of the fourth (temporal) dimension of the Universe. In other words, every moment of the existence of our world is a point (similar to the zero dimension) in the time interval from the Big Bang to the End of the World.

Those of you who have read about time travel know what important role the curvature of the space-time continuum plays in them. This is the fifth dimension - it is in it that the four-dimensional space-time "bends" in order to bring two points on this straight line closer together. Without this, the journey between these points would be too long, or even impossible. Roughly speaking, the fifth dimension is similar to the second - it moves the "one-dimensional" line of space-time to the "two-dimensional" plane with all the consequences in the form of the possibility to turn the corner.

A little earlier, our especially philosophically minded readers probably thought about the possibility of free will in conditions where the future already exists, but is not yet known. Science answers this question like this: probabilities. The future is not a stick, but a whole broom of options development of events. Which of them will come true - we'll find out when we get there.

Each of the probabilities exists as a "one-dimensional" segment on the "plane" of the fifth dimension. What is the fastest way to jump from one segment to another? That's right - bend this plane like a sheet of paper. Where to bend? And again, correctly - in the sixth dimension, which gives the whole complex structure "volume". And, thus, makes it, like three-dimensional space, "finished", a new point.

The seventh dimension is a new straight line, which consists of six-dimensional "points". What is any other point on this line? The whole infinite set of options for the development of events in another universe, formed not as a result of the Big Bang, but in other conditions, and acting according to other laws. That is, the seventh dimension is beads from parallel worlds. The eighth dimension collects these "straight lines" into one "plane". And the ninth can be compared to a book that contains all the "sheets" of the eighth dimension. It is the totality of all histories of all universes with all laws of physics and all initial conditions. Point again.

Here we hit the limit. To imagine the tenth dimension, we need a straight line. And what could be another point on this straight line, if the ninth dimension already covers everything that can be imagined, and even what cannot be imagined? It turns out that the ninth dimension is not another starting point, but the final one - for our imagination, in any case.

String theory claims that it is in the tenth dimension that strings, the basic particles that make up everything, make their vibrations. If the tenth dimension contains all universes and all possibilities, then strings exist everywhere and all the time. I mean, every string exists in our universe, and every other. At any point in time. Straightaway. Cool, huh?

Physicist, specialist in string theory. Known for his work on mirror symmetry related to the topology of the corresponding Calabi-Yau manifolds. He is known to a wide audience as the author of popular science books. His Elegant Universe was nominated for a Pulitzer Prize.

In September 2013, Brian Green came to Moscow at the invitation of the Polytechnic Museum. A famous physicist, string theorist, professor at Columbia University, he is known to the general public primarily as a popularizer of science and the author of the book The Elegant Universe. Lenta.ru spoke with Brian Green about string theory and the recent difficulties that this theory has faced, as well as quantum gravity, the amplitude hedron, and social control.

Literature in Russian: Kaku M., Thompson J.T. "Beyond Einstein: Superstrings and the quest for the final theory" and what it was The original article is on the website InfoGlaz.rf Link to the article from which this copy is made -

735 Megtekintes

0 Kedveles

Let's remember what we were taught about measurements and turn to how quantum physics sees it. According to spiritual teachings, there are twenty-one dimensions in the universe.

Let's check how we feel the measurements on different levels consciousness.

1. One dimension has one extension, such are the point and the line.

2. Two dimensions have yes extensions - this is a plane. It has length and width.

3. Three dimensions have three extensions: length, width and height. Here objects appear in our world, for example, a cube.

4. Four dimensionshave four extensions, here three dimensions are complemented by time. At any moment, something is happening around us.

5. Outside fourth dimension, feelings, thoughts, ideas appear in higher dimensions, which influence events and actions.

There are many invisible things that affect our lives and the functioning of the worlds. Every action comes from an intention! Imagination is already a creation of form, which has all the intentions of movement and germ needed to carry it out.

Looking from the upper world, the order of measurements changes. The first dimension is intent. The dimensions of imagination, form, time, space, plane and point mean the most extreme dimensions.

Many of the people settled on a two-dimensional view of the world. They lack the courage to think and think about new things that would lead them forward along the path of prosperity. It seems to be the goal of someone or some dark forces it was so that a person could not guess what a fantastic creature he is. After all, man could imagine that he had creative power. But in what dimension does this creative ability operate?

Imagine a two-dimensional world, such as a flat world. In that flat world live flat people. They have no idea that there are many dimensions, because there, everything is two-dimensional. In this flat world, two-dimensional people see only two dimensions.

From the outside, as observers, we see both a two-dimensional and a three-dimensional world. Everything that happens there, we perceive and realize differently. We perceive the same phenomenon as two-dimensional and three-dimensional.

The case of a 3D rocket flying through a 2D world:

A three-dimensional rocket flies through the two-dimensional world. What will two-dimensional beings see living planes?

A rocket flying through the world leaves a trail behind it. When touching this world, the tip of the rocket describes a point, then circles, symbols corresponding to the size, and finally, the rocket will leave this two-dimensional world. What will the inhabitants of this two-dimensional world say, watching this? Oh my God! Here, in our world, there were dots, circles and other symbols.

There are, however, other people in this world who think differently and have the courage to make themselves heard. Arriving there, otherwise thinking two-dimensional being will look at the sky, again at circles and a dot, then again dare to look up, close his eyes and say: there was a three-dimensional rocket, leaving prints behind him.

Who is right? we ask.

At their own level of consciousness - everyone. Residents of a one-dimensional world will surely say: a completely crazy creature speaks of something that does not exist. To this, two-dimensional people will say: so abstract, he thinks differently, different than we are.

If beings begin to think, they will understand that there are other dimensions beyond the horizon. They will be able to understand that he, otherwise thinking person, is actually right. Socrates was such a dissident person, who on the streets of Athens asked passers-by only questions that should be thought about. The inhabitants began to wake up consciousness, so the rulers of the city ordered to seize Socrates and forced him to drink poison. The city fathers were afraid of what would happen if people awakened self-consciousness.

The same thing happened with Jesus, who always makes people think with his spiritual messages. The Romans and the elders were horrified by the awakening of people's consciousness, so Jesus was killed. The fact of this terrible crime was distorted by the fact that they began to preach: God sacrificed his son.

measurements

Our joys, misfortunes, experienced in the higher dimensions, are visible in the lower ones. When bad thoughts, misfortunes or illnesses eat someone up, it can be seen physically. Shadows, projections of higher dimensions are symptoms of the body.

Happiness, spiritual freedom, flight takes shape healthy body in visible dimensions.The two-dimensional imprints of bodily symptoms, like the three-dimensional rocket, are just symbols. The world is over high level, reflected on the worlds of a lower level, has the sign of symbols.

Let someone try to convey, show their feelings, thoughts that form an invisible reality. Everyone knows that it exists, but we carry it invisible in ourselves.

How simple it would be if there were only that which is felt by the five kinds of senses. Simple, i.e. "one-dimensional". The “many-sided” person feels free in higher areas.

Setting beyond nine points:

There are nine points in the task. Please connect them with straight lines. You can do this in any order without lifting your pencil by touching each point.

If you can go beyond the nine points in the two-dimensional boundaries, then you can go not only from point to point, but you can also go beyond the area limited by the points. The secret of the task is that we do not think within the nine points, but are able to go beyond them.

In the process of solving the problem, it seems that we have not yet passed into another dimension.

In order to look at the solution of our problem from higher dimensions, we must mentally rise above our knowledge and way of seeing. People, in order to achieve titles, ranks, make any sacrifices. If only part of these efforts were spent on spiritual and spiritual growth, there would not be so many sick and unhappy people. The representatives and preachers of these noble ideas were the great mystics.

If anyone wants to go beyond a certain way of seeing, supported by 2D and 3D x-ray, ultrasound, ST and MRI, he must have great courage, strong faith, fundamental knowledge and will. The idea already in many cases carries the key to the solution - this is the highest dimension of form, which comes from intention.

Have the courage to go beyond the traditions, the familiar, the ingrained? What happens if you connect the dots with four lines? I solved the matrix, since this task already involves free thinking. We not only move into three-dimensional space, but also go beyond it, into higher areas of thought.

The limited human consciousness acts and thinks on the same plane. Anyone who unexpectedly accomplishes things that are unimaginable to others deserves to be called a traveler in dimensions with his versatility.

The sum of the interior angles of a triangle:

(Equator)

Answer to this question modern man with lower or even higher education: 180 degrees. This definition is one of the cornerstones of mathematics.

Let's analyze the triangle on the scale of the Earth. It is known that the Earth is not flat, many centuries ago it became known that the Earth is round.

Draw two perpendiculars to the Earth's equator. As you can see 90° + 90°, this is the sum of the angles of the triangle, equal to 180°. Now let's follow the two perpendiculars that will meet at the north pole and one more angle is closed there. This latter may have 1°, 30° or even 359°. Let's add the internal angles of the formed triangle: 90°+90°+30°=210°. This, as can be seen, is greater than the sum of 180° indicated above.

A significant part of the students today grew up on Euclidean geometry. They think in a plane - they were taught that way. (Another thing is that the theorems of Euclid and Thales are valid in plane geometry). However, thinking only in the plane will be fatal. If people saw everything, thought only in a plane, life would be enclosed in two dimensions. Of course, those who set out to think in many dimensions sometimes run into serious problems. Often, even very educated people live with a flat consciousness, i.e. in a limited world.

How will the human psyche react: if one day we go beyond the traditional, definite, flat thinking imposed on us?

People meeting a person who thinks differently, they will immediately condemn him. There is a danger that people will also have to change their views. Some are so attached to ingrained dogmas, faith, like an alcoholic or a smoker to the object of his passion.

It is well to consider whether we intend to change our views. Those who take on the challenge of adventure and travel will become a healthier, happier, hopeful, successful, out-of-the-ordinary person.