Why does space have three dimensions? Proved with Three Oranges
The palace of the Chinese emperor, the front hall, a meeting of the Sofa. Before the arrogant princess Turandot, Prince Calaf in love with her.
Turandot : And you, a stranger, are ready to risk your life in vain hope to get my hand?
Calaf : Ready, my beloved princess.
Turandot : Well, fine, you signed yourself a death sentence. To get rid of formalities as soon as possible, I will limit myself to one question instead of three. The question is: WHY DOES THE SPACE THREE MEASUREMENTS, NOT TWO OR FOUR?
Calaf : Nothing is easier. But to answer, I need a blackboard with writing accessories and three oranges.
Turandot : Bring him what he asks. Let the executioner get ready.
A board and three oranges are brought into the hall.
Calaf: I will begin the proof that the universe consists of objects.
Turandot : Sure, a stranger?
Calaf : Absolutely. Any system consists of elements. But if you, my beloved princess, can call me a system, that is, something that consists of nothing, then I turn off the evidence and go to an audience with the executioner.
Turandot : Something that consists of nothing? For example, emptiness.
Calaf : Sorry, princess, but what do you mean by emptiness? If something, then it is nothing and your argument is not accepted. And if emptiness is really nothing, then your system is empty. And empty systems cannot mean anything, so we don’t touch them. Do you agree?
Turandot : Well ... let's say I agree.
Calaf : Then I will call the elements of our universe objects. My next statement: any system must be defined externally and internally.
Turandot ( triumphing ): Consider yourself dead, stranger! The system is closed in itself, but why define it externally? Take the orange you brought. He is definitely enclosed in his peel, where is the external definition here ?! There is no external definition. Hey executioner ...
Calaf : Take your time, my love. The internal definition of a system is the relationship in the system between its various elements. At the same time, the system must be defined externally, since without an external definition it becomes meaningless, and we agreed not to consider empty systems.
Turandot: Speak more clearly, stranger.
Calaf : I apologize, the light of my life, now I will try to explain.
He takes in his hand one of the brought oranges.
Suppose you want to register an orange in the system. The registration method is obvious: one field for the identifier denoting the object, the remaining fields for signs characterizing the object.
Chalks on the table blackboard.
Our object is characterized by one sign, but there could have been more.
Wise Men of the Sofa : Yes, yes, It is.
They nod gray beards.
Calaf : Everyone agrees that the first field here defines the internal structure of the system, and the rest - its external content, that is, data about the object?
Supplements the table with explanations.
Turandot: I do not agree.
Calaf : Well, try differently. Imagine, my beloved, that the text styles are unfamiliar to you.
Make corrections to the drawing.
Turandot : What kind of gibberish?
Calaf : Really gibberish. In the case of gibberish, the system loses its content. And we agreed not to consider systems that mean nothing, because of their meaninglessness. Please note, Princess, that the identifier may mean something - for me it means the first serial number - or it may not mean, while still maintaining the identification function. And the symbols denoting a sign, when replacing them with meaningless ones, lose their function, since they cease to express external substantial characteristics.
Turandot: But the inscription itself remains. The inscription is far from an empty place.
Calaf : If we consider the outlines of unfamiliar characters as content, then of course, but if the outlines also become indefinable, what will remain?
The sages nod their beards.
Turandot : And if this incomprehensible inscription is a link to something else, understandable and present in the table?
Calaf : This is possible. But in this case, the original meaning should be meaningful - that which the previous ones refer to. Anyway, without an initial value defined outside the framework of the system - in other words, without a transcendental one - the system ceases to denote anything other than its internal structure.
Turandot : I'm tired of hearing about the beyond.
Calaf: I'm talking about something else, actually.
Turandot : What about?
Calaf : That to designate the internal structure of the system requires at least one identifier. This identifier must indicate an object. Because if we decide to register other objects in the system, the identifier will help distinguish them.
He nods at the two remaining oranges and draws the table.
Turandot : This is obvious. An identifier is required to indicate objects. So what? I think you're fooling me, trying to delay the moment of execution.
Calaf : What are you, darling ?! Would I dare to distance the unearthly pleasure that you will give me on my wedding night?
Turandot: Continue your evidence, stranger, my executioner eagerly listens to you.
Calaf : I proceed to my next statement. To understand why space is three-dimensional, you need to understand that the very concept of an object assumes its opposite - another object from which it was formed.
Turandot : I don’t understand.
Calaf : Patience, my beloved bride, I will try to explain myself. So I cut a slice from one of the oranges. If I want to display this fact in the system, I will have to enter a new field into the system, which is a link to the object identifier. Since I cut a slice from the third orange, then ...
Draws on the board.
Compare with registration just slices and admit that in another way information about a slice of an orange cut precisely from the third orange, and not some other one, cannot be registered.
Erases the arrows and the last column of the table.
In the first case, it appears from the system — that is, by reference you can establish — that the slice is cut off from a whole orange, and in the second case, the slice is registered along with whole oranges. Moreover, the link changes not only one object - a slice of an orange, which is actually registered - but also the second object - once a whole orange, which, due to the removal of a slice from it, decreases in size. Saying "orange slice", we thus assume not only the slice itself, but also the orange from which this slice was pulled. Is not it?
Turandot: What does the three-dimensionality of space have to do with it?
Calaf : But do you agree that the use of a second identifier in the system is necessary?
Turandot : There you go! You registered the first three oranges without any second identifier, which means that you do not need a second identifier! .. Pa-a-alach!
Kalaf : Oh Buddha, how impatient!
Turandot : I'm patient.
Calaf : Charming!
Turandot : I'm not at all ... Ahem ... Okay, stranger, go ahead if you already started.
Calaf : The fact is that I registered the first three oranges from their zero object.
Turandot : From what?
Calaf: As I explained earlier, each object is opposed to its predecessor from which it was formed. A slice of orange resists the orange from which it was cut. And what are the other objects in the system opposing, in particular the very first object that cannot be formed from the previous one, because no previous object is registered in the system? What does the first orange in the system withstand, I ask everyone?
Looks around inquiringly Sofa. The sages are silent and scratch their gray beards. Calaf has to answer himself.
The first object in the system is formed from the zero object, which is everything else that is not the first object. But since nothing is registered before the first object, the null object, unlike registered objects, has indefinable - in other words, unknowable - content. However, an indefinable null object has in the system no less than the first object and all subsequent ones. Here, look ...
Crosses out a closed area on the board.
This is what we called the empty system. This is the same as nothing: such a system simply does not exist. But here we register the first object ...
Strokes the crossed out area and brings an orange to it.
... and the system fills up, moreover, with two objects at once. By registering the first object, we determined not only the first object itself, but also its predecessor, the null object. A zero object appeared in the system at this moment, although it was not registered in it. It is from the same region of the beyond as the significant feature of the object. Subsequent objects can be registered not from the zero object, forming parts of each other. So our universe acquires nesting - one of the most important characteristics of space.
Turandot : It’s somehow very cunning.
Calaf : Okay, I’ll ask easier. From what, in your opinion, my beloved princess, the universe was formed?
Turandot : Well, even in China they know. From the big bang, of course.
Calaf: What then exploded?
The princess is not responding.
The Wise Men of the Sofa : According to the latest scientific evidence, our universe is infinite.
Calaf : You mention infinity because you are not able to answer a very simple question. Meanwhile, the systems are not infinite at all, and for their formation there is no need for a big bang, it is enough to enter information about the first object, as the system becomes meaningful, begins to exist. Here, look, I'm registering the first object, but the explosion does not occur.
Draws a table.
Explosion does not occur, because the first object is formed from the zero, in this system, indefinable and beyond it. And the whole system, consisting of three oranges and a slice cut from the third orange, should look like this.
Slices a slice from one of the oranges.
Draws the table.
However, this system is not complete.
Wise Men of the Sofa : In what sense?
Calaf : In the sense that the zero object is unique by definition, and the system may have several subsystems. How to distinguish tables from each other? To do this, enter the third identifier in the system.
Attaches a column to the table.
Do you know what the third identifier will express?
Turandot : Stop fooling me, stranger!
Wise Men of the Sofa : We think ... think ... So-so! It seems we are beginning to understand.
Turandot : But I do not.
Calaf: It is extremely simple. A third identifier is required to indicate the subject. Because the interconnected picture that appears before the gaze of each of us is just a subjective picture, as a whole, making up the general objective. Each person is like a separate table, a subsystem of the general system. Well, look, I cover oranges ...
She covers oranges with her hands.
You currently see oranges completely, but they are blocked off from me, our information subsystems are different. A third identifier is required to indicate subsystems. If my variant of the objective world is displayed in the table, then ... It
The reality is somewhat more complicated than I describe here: each object formed from zero represents, as it were, the rudiment of the soul and should be indicated by a separate identifier of the subject - but, in short, the subject can be identified with a separate table.
Turandot : Some kind of nonsense ... Executioner, executioner!
Wise Men of the Sofa : Yes, yes, we understand.
Calaf : So, the first identifier is needed to indicate the object, the second identifier is to designate the object from which the registered object is formed, that is, the place of its registration, and the third identifier is used to designate the subject. The three named identifiers make up the internal structure of any system ... Everything, princess, my proof of the three-dimensionality of space is complete.
Turandot: Well, glory to the Buddha, otherwise I’m already tired. Since there is no evidence of the need for just three-dimensional, and not some other, space, I order you to be executed.
Calaf : Do not you understand, my future wife?
Turandot : What should I understand?
Calaf : That the three spatial dimensions are system identifiers. There are three of them, because the concept of an object leads to the need to display exactly the three-dimensional internal structure of the system. Identifiers of the universe - this is its spatial dimensions.
Draws a three-dimensional coordinate system.
The spatial coordinates are so imperceptible and at the same time explicit, because they are identifiers: they mean nothing from the side external to the system, but at the same time they determine its internal structure.
Turandot : None of this is evidence. I can push as many identifiers into your table as possible.
Calaf : You can go to my table if you wish, but hardly to the universe.
Turandot : And time, time! .. Here is the fourth dimension that needs to be added to the table! .. Go to the chopping block, stranger.
Calaf: Sorry, dear princess, but time is not a system identifier. There is no spacetime. Well, what is the time? A sequence of cyclically alternating objects. Day is replaced by night, and night by day, the seasons alternate, and sand in the hourglass, if you turn them over, begins to crumble again. And if the room is as dark as in our boudoir the night after the wedding, time will stop, we will completely cease to distinguish between it.
Turandot : Some kind of sexy maniac!
Calaf : No, princess, time is not the fourth spatial dimension, but the objects themselves, at least those that are cyclically repeated ... There are many other confirmations of my innocence.
The sages of the couch : It would be interesting to listen.
Calaf: For example, this. Is the universe three-dimensional? Yes, but how to explain that spatial three-dimensionality is not uniform across its three dimensions. What does each of us see in front of us, except for uniform three-dimensional spatiality? In no case! We see a two-dimensional image extending into the third dimension at a very shallow distance, after which the third dimension seems to stop. As a result, we can easily determine the height of the pagoda, which is close to us, and with difficulty the pagoda, which we see on the horizon or beyond the edge of the forest. Things on the horizon merge into a two-dimensional image.
Wise Men of the Sofa : But this is true.
Turandot : What else is true? Distant objects seem small to us because of the structure of our eyes.
Calaf: Sorry, princess, but what comes first: what we see, or what we think about it? We think that three-dimensional space is homogeneous in three dimensions, but we see something completely different. At the moment, I am explaining to you precisely the physical structure of our universe, and it is spatially not at all homogeneous, as it seems to us mentally. Two dimensions are homogeneous, and the third dimension gravitates toward the body shell. Three-dimensional spatiality is concentrated precisely around the human body, and away from it disappears.
Corrects the drawing on the board.
This is what space is available to us in sensations, not a homogeneous three-dimensional ...
But it’s not at all what is customary to think between ignoramuses. Not like that.
Corrects the picture.
Turandot: And how is the heterogeneity of space, a stranger, related to your identifiers?
Wise Men of the Sofa : Yes, yes, please clarify the respected prince.
Calaf: Connected very simply. Two system identifiers - the first and second - are identifiers of objects, in this sense they are homogeneous. And the third identifier needed in the system is no longer an object, but something else, the designation of a table as a set of objects, in fact, is a special view of the world inherent in each individual living being, that is, the subject. But each subject, by definition, only feels what is marked by his identifier, so the third dimension he perceives is limited by his own body. In order to expand the space in the third dimension, you need a mind that manifests itself in communication with other people. We ask travelers about distant countries and on the basis of questions we make up the concept of these countries: the spatial boundaries of our universe, as our knowledge of it increases, expand more and more. The third spatial dimension - the coordinate is more intelligent than this in sensations.
Wise Men of the Sofa : Exactly! Right!
Calaf : Well, great. I invite you to my wedding tonight with Princess Turandot.
Turandot : And I invite to execution. Because I have not heard any evidence.
Calaf: I explain again, especially for the dear princess. Space is forced three-dimensional, because it does not exist by itself, but is a characteristic of the system. And the system consists of objects to which the concept of three-dimensionality is immanently inherent. When pronouncing an “object”, we are compelled, perforce, to mean precisely a three-dimensional object, and not any other. Of course, this applies only to sufficiently developed systems. If, for example, objects do not provide for nesting — the fact that one object can be part of another — then a second identifier is not required. And if the subject is present in the singular, then there is no need for a third identifier. However, the presence in the system of nesting and several entities inevitably leads to the appearance of the second and third identifiers and, as a result, to the phenomenon of three-dimensional spatiality. Like in our universe. Now it is clear?
Turandot : Nothing is clear.
Calaf : You really do not understand or do not want to get married?
Turandot : Really did not understand.
Calaf ( in hearts ): Dumb woman!
Turandot : What did you say, stranger? .. But how are you ... Execute, execute him immediately!
Stomps in anger.
Calaf . Well, I didn’t understand and didn’t understand, but why set up a tantrum? (To the Sages of the Sofa ). But did you at least understand?
Wise Men of the Sofa : We understand.
Calaf: I suggest marking this event. Will there be a decent eatery in your Beijing? Three-dimensionality of space is what I can tell you more interesting. Do you want solipsism to refute just once?
Wise Men of the Sofa : But what about the wedding?
Calaf : What other wedding, I refuse the princess. They said she was an intelligent woman, but in fact the devil turned out to be ... She loves to pretend to be pretending. And the intelligence of a water rat.
Wise men of the Divan : Well, if so ... There is a caravanserai nearby, they feed well and the music is quiet, you can fully communicate. And inexpensive, by the way ... So what about solipsism, oh the smartest of all the princes we met?
Calaf: Guys, this is elementary. What is the main argument of solipsism? The fact that a person is not destined to get beyond the bounds of his own “I”: a person is organically incapable of feeling something without being in his own skin — therefore, solipsism concludes, there is no other “human skin”, only its own, darling. And you look at it from the point of view of ...
They are leaving.
Turandot ( after Calaf ): The water rat himself! Fool! I didn’t really want to!