Alexander Dewdney "Planiversum. Virtual contact with the two-dimensional world

When I saw this book, Martin Gardner's Mathematical Leisures and Math Puzzles and Fun, which I read when I was still in school, came to mind. I remembered that one of these books described a book about an imaginary two-dimensional country of Flatland. This book was published under the pseudonym A. Square, which can be translated into Russian as "A Certain Square". The main character of the book "Flatland" was a square that lived in this two-dimensional country. I remember exactly that this book was written in the 19th century. But I have never heard of the book "Planiversum". The author's surname reminded me of the surname of the author of a book of puzzles, which was often mentioned in Martin Gardner's books - Dudeney. As I found out later, in the books of Martin Gardner, Henry Ernest Dudeney was mentioned - an Englishman, and the author of this book is Alexander Kivatin Dewdeny - a Canadian. Alexander Kivatin Dewdney is also known as the author of a computer game for programmers - CoreWars, which in Russian is called "Memory Fight".

I didn't expect much from this book. Well, what can you think of a flat world? Since there is one dimension less in this world, there is clearly nowhere to turn around and write something interesting. But I was wrong.

Firstly, the author made a very competent eyeliner to the story. One would have expected the book to start off somewhat ordinary: "Let's imagine a world in which there is no third spatial dimension, what would it be?" Or: “Once upon a time in a flat country there lived flat man". The end of the book is already imagining: “And then I suddenly woke up.” Not interested.

In fact, it all starts with the fact that a teacher at a university gives his students a task - to create a program for modeling a two-dimensional world. It all starts with a model of the planetary system, in which round flat planets revolve around a round flat sun. Then the students began to fill this program with various additional elements - someone modeled the continents and seas, someone modeled the weather, and someone populated this country with two-dimensional living beings. One of the students added a lexical module to this program - it became possible to ask the program to describe the environment.

Further, this program sometimes starts to behave strangely - it writes words that are not in the dictionary, but does not recognize them when these words are used by the operator sitting at the computer. The fact is that the world modeled in the program turns out to be so similar to the real-life two-dimensional world that it enters into resonance with it, so that through the program it becomes possible to look at the real two-dimensional world. However, the connection with this world is through a local resident named Yndrd, whom the teacher and students call Yendred for convenience.

It was first. And now - secondly. Secondly, the details of the structure of this world are not thoughtlessly copied from our three-dimensional world. The two-dimensional world has its own specifics, and what is familiar to us in the two-dimensional world turns out to be unviable. For example, in this two-dimensional world, the weather is always predictable: the low pressure area forms from the direction of the sun, and the surface wind always blows towards the sun. In the morning the wind blows to the east, where the sun rises, and in the evening it starts to blow to the west, where the sun sets.

It rains in this world, but the rivers do not have a channel: water flows over the surface of the planet, not being able to go around obstacles to the right or left. That is why the inhabitants of the planet do not build houses. If you build a house, then the water flowing from the side of the mountains will reach the house and fill the entire lowland formed by the mountain and the house. Therefore, local residents live in houses that resemble our dugouts, and animals live in burrows. So that the dugout is not flooded, it is clogged as soon as they hear the sound of approaching water.

In this world, the door hinges we are accustomed to cannot exist, and ropes cannot be tied into knots. Door hinges resemble ball joints - the circle is inserted into a semicircular hole, and the door attached to the circle moves up and down. Ropes are usually glued or attached to each other with hooks. However, this also has positive side: since it is impossible to tie a knot on a rope, the ropes never get tangled.

As a boat in this world, you can use a simple stick, the ends of which are bent in one direction. Such a boat cannot turn around - only change direction. A pole is used as a sail, which is installed vertically in the center of the boat. Since the wind always has a predictable direction, in the east every morning you can go by boat to the ocean, and by the evening the wind will blow in reverse side- toward the mainland. In the west, the opposite is true - you can go to the ocean in the evening, and return to the mainland in the morning.

Local creatures do not have an internal rigid skeleton, because the skeleton in this case would divide the body into independent parts. All creatures in this world have an external skeleton, like beetles. There is no through digestive tract, because if it were, then the creature would split into two parts. Therefore, through the mouth, both the consumption of food and the removal of digestive waste occur - they are spit out. The circulation, however, still exists. The tissues separate, capture the fluid bubble, and then join. The fluid bubble moves between the tissues in such a way that, in the course of its movement, the tissues are separated, and behind they are connected. It turns out a kind of blood peristalsis.

I will not say anything more about the structure of this world, I will only mention that it has metallurgy, steam engines, clockwork, musical instruments, rockets, space stations, astronomy, chemistry, cell biology, electricity, books, art and computers. Every scientific field, every mechanism is explained In a similar way- not just copying the things of our world, but with an explanation of the principles of operation and inherent limitations. For example, it explains how cells manage to exchange nutrients without splashing their contents out. Explains how nerve cells transmit signals along intersecting paths without mixing signals. The same problem is explained in relation to the design of computers - how logic gates transmit signals along intersecting paths without mixing signals. Explains how electrical power is supplied to the computer's valves.

From what I said, one might get the impression that the book has no plot and it only says about what and how it works. This is not true.

Spoiler (plot reveal) (click on it to see)

The protagonist Yendred heard about a monk who lives in another country - Vanicle. Vanitsla is located in the east of the mainland, behind the mountains. There and keeps the way main character. Before leaving, Yendred went fishing with his father. In the city of Is-Felblt, he visits his uncle, who runs a printing house and prints books. With their uncle's children, they go to the market, where they buy a balloon for travel. Then the younger children go home, and Yendred eldest daughter uncle goes to musical concert. Then Yendred visited the only scientific institute his countries are Punicla. Along the way, he walks, moves on hot-air balloon, holding it in his hands, makes a flight on a transport balloon and on a rocket. Finally, he reaches a mountain plateau, where he nearly dies in a quarry from a flying kite. Then he finally meets the very monk named Drabk, whom he wanted to meet. Then the monk initiates Yendred into secret knowledge, after which Yendred stops communicating, losing interest in the inhabitants of the three-dimensional world.

In some way, this book reminded me of Andrey Rodionov's article "Game is a Serious Matter", which I once read in the science fiction magazine "If". This article began as a regular article describing the classification of computer games. Then the author talks about how he made his computer game. This story flows smoothly into the genre science fiction. Then I still went to school, my skeptical thinking was practically absent and I believed almost everything. It is not surprising that this article made a tremendous impression on me then - I simply did not notice the transition from the journalistic genre to the science fiction genre and took the story about a computer game at face value. Both in this book and in Andrei Rodionov's article, reality smoothly turns into fiction, which gives credibility to the sci-fi component. Both in the book and in the article we are talking about the creation of a virtual world, which, unexpectedly for the creators themselves, shows unforeseen properties, starting to live its own life.

By the way, much later, when I became interested in the musical genre Synth Pop, I found albums by Andrey Rodionov and Boris Tikhomirov. I really like some of the songs from these albums, and at one time I even used the song "Electronic Alarm" as an alarm signal on my phone. I did not immediately connect the musician and the author of that article in my head. And then he did find out that he really developed computer games. For example, one of his games is called Major of Pistols at the Factory. It's funny that the world of this game is also flat. True, in it the main character knows how to mirror himself :)

However, I digress. Let's go back to the Planiversum. The book was not written as a result of individual reflections. At the end of the book, the author explains that for a long time he has been collecting articles about the arrangement of various things in a flat world, which were written for fun by other people. Prior to writing this fiction book, the author wrote the monograph "Science and Technology in a Two-Dimensional World". Later, an article was written about this monograph ... Martin Gardner. The idea of ​​a rocket plane was thrown to the author by Jeff Raskin, the initiator of the Apple Macintosh project. He also created the lesser-known but very peculiar Canon Cat computer. Before reading this book, I was just thinking about buying Jeff Raskin's book "Interface: New Directions in Computer System Design".

This is quite possibly the best science fiction book I have ever read. This book is based on just one fantastic assumption - there is a two-dimensional world inhabited by intelligent living beings, and you can communicate with this world. Here, of course, there is no intensity of emotions, no moral messages, but the book is addictive. I would say that I read it avidly, but in fact, I deliberately diverted from it from time to time, because it takes you to another world that operates according to other laws, but has its own logic. While reading, the thinking is reorganized so much that, being distracted from reading, you feel disorientation - thoughts continue to swarm in your head, which suddenly turn out to be inapplicable to the familiar three-dimensional world. It takes a few seconds to push those thoughts aside and get back to reality.

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: an income line, infinite, and represented by an infinite straight line; rainbow line, terminal, with bounding walls, represented by a line segment; eolian line of wind directions, finite-periodic, represented by a segment whose left end coincides with the right, or, what is the same, a circle. In passing, I mentioned another example - about the world, infinite in one direction, and finite in the other. In another article, I emphasized that there are many types of dimensions, but the physical dimensions of space have unique and special (and also very obvious) properties that distinguish them from dimensions of another type.

Rice. 1: 2D 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. One 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 in the other forming either a segment or a circle. Such worlds are naturally called strip and pipe (lower left). One can imagine a finite world in both directions (right side of Fig. 1). And how many possibilities are there! Only in this picture you can see from top to bottom a square, a cylinder (a round part of a can 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 options. If extrapolated 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, a position in a two-dimensional space is defined 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 represented 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 faucet and at a 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.

Consider 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 dot on the line represents a possible return." If you are married and both you and your spouse have income, the two cash flows in your household can be represented as a two-income plane. The two numbers describing a point on this plane will be your income and your spouse's income.

And here is a tricky example of a torus showing how interesting two-dimensional shapes can be imagined whose dimensions are not those of physical space. On fig. 3 articles on one-dimensional worlds, we saw that the possible directions of the wind form a one-dimensional world in the form of a circle (or a line that has the same beginning and end). The possible directions of movement of the sailboat also form a similar circle. But all who have sailed know that it is not necessary to sail in the same direction as the wind blows; if you put the sail at an angle, you can move to the west, even if the wind blows from the north. So if I ask for two pieces of information - which direction the wind is blowing, and which direction my sailboat is heading - they will both be points on a circle. Two units of information, both located on a circle, represent a point on the torus.

Before continuing, I will mention a natural and common confusion. I already hinted at it in the description different worlds, given above. Do not confuse the dimensions of the forms themselves with a particular way of representing those dimensions or forms! The property of a circle is that if you move along it in any direction, you will return to where you started. The circle has nothing inside or outside. Simply representing a circle as a closed curve on a two-dimensional plane looks like it has an inside and an outside. But this is simply a property of the representation of the circle on the plane, and not a property of the circle itself.

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 many 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 necessary for the operation of this theory 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 maybe that's the reason why quantum world 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 about 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 of 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. In a certain sense, however, Veneziano's observation was incomplete. Like a memorized formula used by a student who doesn't understand its meaning or significance, 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 "the mathematical structure of 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 much choice, 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 apparent flaw into a virtue. After studying the strange modes of vibration of strings, reminiscent of carrier particles, they realized that these properties coincide surprisingly exactly with the proposed properties of the hypothetical gravitational carrier particle - the graviton. Although these tiny particles Since no gravitational interaction has 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 realized 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 that summed up more than a decade of intense research that was largely ignored or dismissed by most physicists, Green and Schwartz found that the slight contradiction with quantum theory that string theory suffered could be allowed. Moreover, they showed that the resulting theory was broad enough to cover all four kinds of forces and all kinds of matter. Word of the 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 first-year graduate students, and the former gloom was replaced by an exhilarating sense of belonging to a 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 have definitively demonstrated that the 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 of the last century follow—and follow with such elegance—from such a simple starting point, clearly demonstrates to you the incredible power of this theory” 5 . 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 fulfill 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 correctly answer a number of important questions, thereby 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 frustration 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 unleash these dormant forces. The long period of "drought" was interrupted from time to time by 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, mankind 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 arrangement:

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, rather than 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 exact time 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 events that have existed, exist and will continue to exist are equally real, as real as a 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 at every single moment in 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 unique. 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 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 underlies many physical laws, and it is impossible to imagine how the physics of the Universe will change with the advent of another time dimension. 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 how important the curvature of the space-time continuum is. 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 ability 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 big bang, but in other conditions, and operating under 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 the 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 to Moscow at the invitation Polytechnic Museum Brian Green arrived. 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 -

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 Anatoly Gladun and Vladimir Leiman, professors of the Department of General Physics at the Moscow Institute of Physics and Technology, and Sergey Bozhevolny and Alexander Tishchenko, graduates of the Moscow Institute of Technology, had a great influence on its development. 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 common Russian assertion that two-dimensional materials are just a fashion, and consider them as a key construction material for nanophotonics, and also agree with the words of Andrey Geim that the next 50 years will not be enough for their study. 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 areas 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 biology comes into play here. 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 integrate perfectly with our interest in practical use 2D 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 currently available sensor chips on the 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 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 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 a graduate of the FOPF (1982) and Nobel laureate Andrew Game. 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.

736 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 the creation of form, which has all the intentions of movement and germ needed to carry it out.

looking from higher 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. Flat people live in this flat world. They have no idea that there are many dimensions, because there, they have everything 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 watching it? 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 point, 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 the other-minded person is indeed 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 the form of a 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 the higher realms.

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 will 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 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, have 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°. Add up internal corners formed triangle: 90°+90°+30°=210°. This, as can be seen, is greater than the sum of 180° indicated above.

A significant part of 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?

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 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, more hopeful, successful, out-of-the-ordinary person.