The two-dimensional world of Christian imagination. Quantum physics - measurements

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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 as a point and a line.

2. Two dimensions have 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. Beyond the fourth dimension, in higher dimensions feelings, thoughts, and ideas appear that influence events and actions.

There are many invisible things that affect our lives and the functioning of the worlds. Every action comes from intention! Imagination is already a creation of form, which has all the intentions of movement and germ necessary for fulfillment.

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

Many people have settled on a two-dimensional view of the world. They do not have the courage to think and think about new things that would lead them forward along the path of prosperity. Seems to be the target of someone or some dark forces it was so that a person could not guess what fantastic creature he is. Eventually, man would be able to imagine himself as having creative power. But in what dimension does this creative ability operate?

Let's imagine a two-dimensional world, for example a flat world. Flat people live in this flat world. They have no idea that there are many dimensions, because everything there is two-dimensional. In this flat world, two-dimensional people see only two dimensions.

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

The case of a three-dimensional rocket speeding through a two-dimensional world:

A three-dimensional rocket flies through a two-dimensional world. What will living two-dimensional creatures see?

A rocket rushing 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 leaves this two-dimensional world. What will the inhabitants of this two-dimensional world say when watching this? Oh my God! Here, in our world, there were dots, circles and other symbols.

There are, however, people in this world who think differently and have the courage to make themselves heard. A differently thinking two-dimensional creature arriving there will look at the sky, again at the circles and the dot, then dare to look up again, close its eyes and say: there was a three-dimensional rocket here, leaving prints behind it.

Who is right? - we ask.

At their own level of consciousness - everyone. Residents of a one-dimensional world will probably say: a completely crazy creature is talking about something that doesn’t exist. To this, two-dimensional people will say: so abstract, thinks differently, different from us.

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

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

Measurements

Our joys and misfortunes experienced in higher dimensions are also visible in 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 the form of a healthy body in visible dimensions.Two-dimensional impressions of bodily symptoms, just like a three-dimensional rocket, are just symbols. The world is more high level, reflected on worlds of a lower level, has the attribute of symbols.

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

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

Task beyond nine points:

There are nine points in the task. Please connect them with straight lines. This can be done in any order without lifting the pencil, touching each point.

If you can go beyond the nine points in the two-dimensional boundaries, then you not only go 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 nine points, but are able to go beyond them.

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

In order to look at the solution to our problem from higher dimensions, we must mentally rise above our knowledge and way of seeing. People make any sacrifices to achieve titles and ranks. 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 one wants to go beyond a certain way of seeing, supported by two-dimensional and three-dimensional X-ray, ultrasound, CT and MRI images, he must have great courage, have strong faith, fundamental knowledge and will. The idea already in many cases carries the key to the solution - it 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 requires free thinking. We not only move into three-dimensional space, but also go beyond it, into the higher realms of thought.

Limited human consciousness acts and thinks on the same plane. Anyone who unexpectedly accomplishes things unimaginable for others deserves to be called a dimensional traveler with his versatility.

Sum of interior angles of a triangle:

(Equator)

The answer to this question modern man with an inferior 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: the Earth is round.

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

A significant portion of students today grew up with Euclidean geometry. They think in a plane - that's how they were taught. (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 and thought only in planes, life would be contained in two dimensions. Of course, those who set out to think in many dimensions sometimes encounter 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, specific, flat thinking imposed on us?

When people meet 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 as attached to ingrained dogma and faith, just as an alcoholic or smoker is to the subject of his passion.

We should think carefully about whether we intend to change our views. Those who embrace the challenge of adventure and travel will become healthier, happier, more hopeful, successful, out-of-the-mundane people.

What is the Laboratory of Nanoptics and Plasmonics known for? If we try to describe its activities in one sentence, then behind nanooptics and plasmonics there 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. Among Russian partners we can highlight groups from Moscow State University, Skoltech and ITMO University. The laboratory plans 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 professors of the Department of General Physics of MIPT Anatoly Gladun and Vladimir Leiman, while big influence Phystech graduates Sergei Bozhevolny and Alexander Tishchenko contributed to its formation. She is now part of the Center for Photonics and Two-Dimensional Materials at the Physics and Technology 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 was done 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 near-field research - 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 nano-sized samples at distances much smaller than the wavelength of light, with a spatial resolution of up to 10 nm. A range of instruments ranging from spectral ellipsometry to Raman spectroscopy is used to analyze materials and samples. Experimental studies are accompanied by theoretical studies and numerical simulations. Objects for research are also manufactured directly in the laboratory and the Collective Use Center of MIPT.

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. Just this year, scientists launched a facility for CVD synthesis of two-dimensional materials. The laboratory categorically disagrees with the common statement in Russia that two-dimensional materials are just a fashion, and considers them as a key construction material for nanophotonics, and also agree with the words of Andrei 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 laboratory, 30% of the publications in his journal are work related to one degree or another with two-dimensional materials. The competition here is very high, but this is what is needed at Phystech.

Biosensors and graphene

One of the important areas of the laboratory is highly sensitive biosensors for pharmacology and medical diagnostics. It is directly related to plasmonics - we're talking about about plasmonic biosensors - but this is where biology comes into play. This type of work requires other qualifications.

« My colleagues specifically studied biology and chemistry in order to begin this difficult task with a new background. Biology and chemistry integrate well with our interest in practical use 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 significantly higher sensitivity compared to those presented on this moment sensor chips on the market. Increased sensitivity is achieved by replacing standard connecting layers with graphene (or graphene oxide), 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 has significantly reduced their cost, primarily due to the compatibility of copper with standard technological processes.

Single-photon sources and nanolasers

The laboratory is also conducting research into creating electrically pumped true single-photon light sources - devices that emit single photons when an electric current is passed through. The transition to such single-photon technologies will not only make it possible to increase the energy efficiency of existing information processing and transmission devices by more than a thousand times, but will also open the way to the creation of various quantum devices. Another related task in this area 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 two-dimensional materials at the Third International Conference “Metamaterials and Nanophotonics” (METANANO-2018). The conference will be attended by scientists - leaders in their fields, and will be opened by a graduate of the Faculty of Philosophy of Philosophy (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, laboratory students will go on an internship at the Danish company Newtec, with which the laboratory has been collaborating for several years. The company is not directly related to science - it develops and produces high-tech robotic complexes for sorting vegetables and fruits - however, it has a very powerful research department, including 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 vegetables and fruits. Joint research with the Danes not only helps the laboratory master new technologies and approaches to working with two-dimensional materials, but also allows us to look at the world of research and development from a completely different angle. This cannot be learned at university.

You know that what makes the world one-dimensional is that the position in it is determined by one unit of information.

It must also be continuous (or close to continuous from a practical point of view). I have described several examples of dimensions: a revenue line, infinite, and represented by an infinite straight line; rainbow line, finite, with bounding walls, represented by a segment; an aeolian line of wind directions, finitely periodic, represented by a segment whose left end coincides with the right, or, what is the same, a circle. I briefly mentioned another example - about a world that is infinite in one direction and finite in the other. In another article, I emphasized that there are many types of dimensions, but physical dimensions of space have unique and special (and also very obvious) properties that distinguish them from other types of dimensions.

Rice. 1: two-dimensional worlds

What about two-dimensional worlds? It is not surprising that there are many more types of two-dimensional worlds than types of one-dimensional worlds. Several examples of such spaces are shown in Fig. 1. You can imagine a world that is infinite in both directions: a plane (top left). One can imagine a world that is infinite in one direction and forms either a segment or a circle in the other. Such worlds are naturally called strip and tube (bottom left). One can imagine a finite world in both directions ( right part rice. 1). And how many opportunities there are! Only in this picture you can see from top to bottom a square, a cylinder (the round part of the jar without lids and insides), a disk, a torus (something like a car tire), a sphere (only the surface), a double tire. And these are not all the options. If we extrapolate into the future, it becomes clear that by the time we get to three dimensions and go further, we will no longer be able to make such lists.

As with one-dimensional spaces, position in two-dimensional space is determined by two pieces of information.

An example of a sphere (to a good approximation) would be the surface of the Earth: any location can be indicated by latitude and longitude. An ant walking along a garden hose moves along a two-dimensional pipe, and at any given time is located at a certain distance from the tap and under certain angle to the vertical. A multi-lane highway is essentially a two-dimensional strip with a very long side and a short side: the two pieces of information needed to determine your position are the distance from the beginning of the road and the distance from its right edge.

Let's remember the income line. "Your income for last year is a specific number in your local currency. It can be positive or negative, large or small; it can be represented as a point on a line, as in Fig. 1, which we will call the “income point”. Each point on the line represents possible income." If you are married and both you and your spouse have income, two are included in your household cash flow can be represented as a two-income plane. The two numbers that describe a point on this plane will be your income and your spouse's income.

Here's a clever example of a torus, showing how you can imagine interesting two-dimensional shapes whose dimensions are not the dimensions of physical space. In Fig. 3 articles on one-dimensional worlds, we saw that possible wind directions form a one-dimensional world in the form of a circle (or a line whose beginning and end coincide). The possible directions of movement of a sailing boat also form a similar circle. But anyone who has sailed knows that you don't have to go in the same direction as the wind; if you set the sail at an angle, you can sail west even if the wind is blowing from the north. So if I ask for two pieces of information - which direction the wind is blowing, and which direction my sailboat is moving - they will both be points on a circle. Two pieces of information, both located on a circle, represent a point on the torus.

Before I continue, let me mention a natural and common confusion. I already hinted at it in the description different worlds, given above. Don't confuse the dimensions of the shapes themselves with a particular way of representing those dimensions or shapes! The property of a circle is that if you move around it in any direction, you will return to where you started. A circle has nothing inside or outside. Simply representing a circle as a closed curve on a two-dimensional plane makes it appear as if it has an inside and an outside. But this is simply a property of the representation of a circle on a plane, and not a property of the circle itself.

Design by artist A. Balashova.

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

It is tempting to imagine that both gullible and distrustful readers did so because of the convincing logic and consistency of the cosmology and physics of this infinitely subtle universe with its bizarre, yet strangely efficient organisms. After all, what opened before them was not just an ordinary universe generated by a play of imagination. The planiverse is more than whimsical, fantastic place, since most of it was “made” by a virtual team of scientists and technologists. The reality - even the pseudo-reality of such a place is much stranger than it seems at first glance.

First, let's try to understand what the flat universe Planiverse is. Understand that two dimensions mean two dimensions. If the page of this book represents a small piece of the Planiverse, then the curved line drawn on it may turn out to be a piece of a planiverse 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 of this page. But give us some planiversal glue and we'll glue one tip to the other, trapping whatever ends up inside the lace loop once the glue dries.

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

We wove these ideas into something homogeneous and seamless, but we needed a plot - a story - to make it work interesting book. A story that would take us on a journey through Arda, a disc-shaped planet floating in the two-dimensional universe of the Planiverse.

From the preface to the end, the story is told with a serious, even impassive face. It's written with a pen researcher, whose literary possibilities are constantly under the pressure of events. The story features a modern deus ex machina - a computer. It was with his help that a group of students made first contact with the two-dimensional universe of the Planiverse 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 accepted the fiction at face value. The subtext of this fantastic, albeit very rich in details, story went unnoticed by many. Neoteny trends have taken root in Western culture even before 1984. And of course, the fantastic allegory introduced into the narrative - that is, what makes the book, in the words of the Oxford humanist Graham Stewart, a “Sufi parable”, went completely unnoticed by these readers. The temptation to bring to life a higher (third) dimension as a symbol of the forces lurking beyond the obvious reality of our world turned out to be too great to overcome. The story opens with an old preface waiting for you on the next page.

A. K. Dewdney.

January 2000

I would like to note that I am not so much the author of the book as its compiler, and the main credit for the fact that this book saw 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 call the Planiverse. The story of the discovery of the Planiverse, a world whose reality few could believe, will probably seem interesting to you. That's what I want to tell you.

The first acquaintance with this world took place at our university about a year ago. My students worked with the 2DWORLD computer program, which they themselves wrote over several semesters. The original 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 simulate a two-dimensional model of a physical body. For example, a simple two-dimensional object may be disk-shaped and composed of many two-dimensional atoms.

It has some mass (depending on the type and number of atoms it contains) and can move in a two-dimensional space such as this page. But, unlike a page, two-dimensional space has no thickness, and the disk cannot extend beyond its boundaries. Let's assume 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 begin to move at a constant speed in a plane that is an extension of the page. Sooner or later, 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 kinetic and potential energy two disks before and after the collision remains unchanged. Moving in this way, the disks 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 represented 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 consist of individual atoms, this will complicate the programmer's work and increase the load on the processor during program execution. But almost any programmer can write such a program and display the results on the screen.

This is roughly where work on the 2DWORLD program began. In the first semester, students under my guidance not only described a certain set of objects and the law of conservation of energy in the program, but also created an entire system of planets revolving around a star. One of the planets, which they named Astria, gained particular popularity among students. Towards the end of the first semester, conversations began about drawing a map on this planet and populating it with living creatures - 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 impossible to implement the idea - my students were not that strong programmers.

In any case, 2DWORLD turned out to be very useful program, and working with her was incredibly interesting. I especially remember the process of 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.