Palace of the Chinese Emperor, front hall, Divan meeting. In front of the arrogant princess Turandot Prince Calaf in love with her.
Turandot : And you, a stranger, are willing to risk life in the vain hope of winning my hand?
Kalaf : Ready, my beloved princess.
Turandot : Well, fine, you signed a death sentence for yourself. To get it over with the formalities, I will limit myself to one question instead of three. The question is: WHY DO THE SPACE THREE DIMENSIONS, AND NOT TWO OR FOUR?
Kalaf : There is nothing easier. But to answer, I need a writing board and three oranges.
Turandot : Bring him what he asks. And let the executioner get ready.
A board and three oranges are brought into the hall.
Kalaf : I will begin the proof with the fact that the universe consists of objects.
Turandot : Sure stranger?
Kalaf : 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 fold the evidence and set off for an audience with the executioner.
Turandot : Something that consists of nothing? For example, emptiness.
Kalaf : 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 can not mean anything, so we do not touch them. Do you agree?
Turandot : Well ... let's say I agree.
Kalaf : Then I will call the elements of our universe objects. The following is my statement: any system must be defined externally and internally.
Turandot (
triumphant ): Consider yourself dead, stranger! The system is closed in itself, but why determine it externally? Take an orange brought to you. Is it determined to be closed in its skin, where is the external definition here ?! There is no external definition. Hey, executioner ...
Kalaf : 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 also be defined externally, since without an external definition it becomes meaningless, and we have agreed not to consider empty systems.
Turandot : Be clear, stranger.
Kalaf : Forgive forgiveness, the light of my life, now I will try to explain.
Takes one of the brought oranges in hand.
')
Suppose you need to register an orange in the system. The method of registration is obvious: one field for the identifier denoting an object, the remaining fields for signs characterizing the object.
Draws with chalk on the blackboard table.
Our object is characterized by one sign, but they could be more.
Wise Men of the Sofa : Yes, yes, it is.
Nod with gray beards.
Kalaf : Everyone agrees that the first field here defines the internal structure of the system, and the rest - its external content, that is, the data about the object?
Supplements the table with explanations.
Turandot : I disagree.
Kalaf : Well, let's try otherwise. Imagine, my beloved, that text styles are unfamiliar to you.
Makes corrections to the drawing.
Turandot : What kind of gibberish?
Calaf : Truly 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, the princess, that the identifier may mean something - in my case it means the first sequence number - or it may not mean, while still retaining the identification function. And the symbols denoting a sign, when they are replaced by meaningless ones, lose their function, since they cease to express external informative characteristics.
Turandot : But the inscription itself remains. The inscription is far from empty.
Kalaf : If we consider the outlines of unfamiliar signs as content, then of course, and if the outlines also become indefinable, what remains?
The sages nod their beards.
Turandot : And if this incomprehensible inscription is a link to something else, understandable and present in the table?
Kalaf : This is possible. But in this case, the original value should be meaningful - the one to which the previous ones refer. Anyway, without an initial value defined outside the framework of the system - in other words, without the beyond, the system ceases to designate anything other than its internal structure.
Turandot : I'm tired of hearing about the beyond.
Kalaf : I'm about a friend, actually.
Turandot : About what?
Kalaf : The fact that to identify the internal structure of the system requires at least one identifier. This identifier must denote an object. Because if we decide to register other objects in the system, the identifier will help them to be distinguished.
He nods at the two remaining oranges and draws a table.
Turandot : It's obvious. An identifier is required to identify objects. What from that? It seems to me that you are fooling me, trying to postpone the moment of execution.
Kalaf : What are you, darling ?! Would I dare to put off the unearthly delight with which you will give me the first marriage night?
Turandot : Keep up your evidence, stranger, my executioner eagerly listens to you.
Kalaf : I proceed to the following statement. To understand why space is three-dimensional, it is necessary to understand that the very concept of an object implies its opposite — another object from which it was formed.
Turandot : I do not understand.
Kalaf : Patience, my adorable 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 into the system a new field, which is a link to the object identifier. Since I cut a slice from the third orange, then ...
Draws on the board.
Compare with the registration just slices and acknowledge that there is no other way for information about the orange slice, cut from the third orange, and not just any other, can be registered.
Erases the arrows and the last column of the table.
In the first case, it is clear from the system - that is, by reference you can establish that the slice is cut off from the whole orange, and in the second case the slice is registered along with the whole oranges. Moreover, the link changes not one object - an orange slice, which is actually registered, - but also the second object - the once whole orange, which, due to the removal of its lobules, is reduced in size. Having said “orange slice”, thus we 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 mean here?
Kalaf : But do you agree that the use of the second identifier in the system is necessary?
Turandot : Here it is! 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 am patient.
Kalaf : Charming!
Turandot : I am not at all ... Cgm ... Well, a stranger, go on, if you have already begun.
Kalaf : The fact is that I registered the first three oranges from their zero object.
Turandot : From what?
Kalaf : As I explained earlier, each object is opposed to its predecessor, from which it was formed. An orange slice confronts an orange, from which it was cut. And what do other objects in the system oppose, in particular the very first object that cannot be formed from the previous one, because no previous object is registered in the system? What opposes the first orange in the system, I ask everyone?
A questioning look around the sofa. The wise men are silent and scratching their gray beards. Calaf has to answer himself.
The first object in the system is formed from a zero object, which is everything else that is not the first object. But since nothing is registered before the first object, the zero object, unlike the registered objects, has indefinable - in other words, unknowable - content. However, an indefinable zero object has to be in the system no less than the first object and all subsequent ones. Here, look ...
Strikes a closed area on the board.
This is what we called the empty system. This is the same thing as nothing: such a system simply does not exist. But here we register the first object ...
Strokes the blackened area and brings an orange to it.
... and the system is filled, and with two objects at once. By registering the first object, we determined not only the first object itself, but also its predecessor, the zero 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 from a non-zero object, forming parts of each other. So our universe acquires nesting - one of the most important characteristics of space.
Turandot : Somehow very cunning.
Kalaf : Okay, I ask easier. From what, in your opinion, my beloved princess, the universe was formed?
Turandot : Well, they know it even in China. From the big bang, of course.
Kalaf : What then exploded?
The princess is not responding.
Wise Men of the Sofa : According to the latest scientific data, our universe is infinite.
Kalaf : You mention infinity, because you cannot 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, how the system becomes meaningful, begins to exist. Here, look, I register the first object, but the explosion does not occur.
Draws a table.
The explosion does not occur, because the first object is formed from zero, in this system is indefinable and beyond its limits. 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.
Finishes the table.
However, this system is not complete.
Wise Men of the Sofa : In what sense?
Kalaf : In the sense that a null object is unique by definition, and a system can have several subsystems. How do tables differentiate from each other? To do this, enter the third identifier in the system.
Draws 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 ... we think ... So, so! It seems, we begin to understand.
Turandot : And I do not.
Kalaf : This is extremely simple. The third identifier is required to designate the subject. Because the interconnected picture, which appears before the gaze of each of us, is precisely a subjective picture, on the whole, a component of the overall objective. Each person is like a separate table, a subsystem of a common system. Well, look, I am covering oranges ...
Covers oranges with his hands.
At the moment you see oranges completely, but they are blocked from me, our information subsystems are different. A third identifier is required to identify subsystems. If the table shows my version of the objective world, then ...
Finishing off
The reality is somewhat more complicated than I am describing here: each object formed from zero represents, as it were, a primordium of the soul and must be denoted by a separate identifier of the subject, but, if to take briefly, the subject can be identified with a separate table.
Turandot : Nonsense some ... Executioner, executioner!
The Wise Men of the Sofa : Yes, we understand.
Kalaf : So, the first identifier is necessary for designating an object, the second identifier is for designating the object from which the registered object is formed, that is, the place of its registration, and the third identifier - for designating 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 tired already. Since there is no evidence of the need for exactly three-dimensional, and not some other, space, I order you to execute you.
Kalaf : Did you not understand my future spouse?
Turandot : What should I understand?
Kalaf : With three spatial dimensions, these are system identifiers. There are three of them, because the concept of an object leads to the need to display the three-dimensional internal structure of the system. The identifiers of the universe are its spatial dimensions.
Draws a three-dimensional coordinate system.
Spatial coordinates are so imperceptible and at the same time explicit, because they are identifiers: they do not mean anything on the external side of the system, but at the same time they define its internal structure.
Turandot : No this is proof. I can push as many identifiers into your table.
Kalaf : In my table you can, if you like, and in the universe - it is unlikely.
Turandot : And time, time! .. Here is the fourth dimension that you need to add to the table! .. Go to the scaffold, stranger.
Kalaf : Excuse me, dear princess, but time is not a system identifier. There is no space-time. Well what time is it? Sequence of cyclically replacing each other objects. Day is replaced by night, and night is daytime, the seasons alternate, and sand in an hourglass, if you turn them over, begins to crumble again. And if the room is as dark as in our boudoir on the night after the wedding, time will stop, we will completely stop distinguishing it.
Turandot : Some sexual maniac!
Kalaf : No, princess, time is not the fourth spatial dimension, but the objects themselves, at least those that are cyclically repeated ... There are many other proofs of my being right.
Wise men of the couch : It would be interesting to listen.
Kalaf : For example, here it is. Creation three-dimensional? Yes, but how to explain that spatial three-dimensionality is not homogeneous in its three dimensions. What does each of us see in front of us, is it a uniform three-dimensional spatiality? In no case! We see a two-dimensional image, going 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 behind 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 to us small because of the device of our eyes.
Kalaf : Excuse me, princess, but which is more primary: 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 not spatially homogeneous at all, as we are mentally imagined. The two dimensions are uniform, and the third dimension is to the bodily shell. Three-dimensional spatiality concentrates around the human body, and disappears from it.
Corrects drawing on the board.
This is how much space is available to us in sensations, not a uniform three-dimensional ...
Draws more.
But it is not at all what it is thought to be between the ignorant. Not like that.
Corrects the drawing.
Turandot : And how is the heterogeneity of space, a stranger, associated with your identifiers?
Wise Men of the Sofa : Yes, please clarify the distinguished prince.
Kalaf : Connected very simply. Two system identifiers, the first and the second, are object identifiers, in this sense they are homogeneous. And the third identifier required in the system is no longer an object, but something else, the designation of a table as a collection of objects, in fact, a special view of the world inherent in each individual living being, that is, the subject. But each subject, by definition, feels only what is marked with his identifier, therefore the third dimension perceived by him is limited to 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 inquiries we make up a concept about these countries: so the spatial boundaries of our universe, as our knowledge of it increases, expand more and more. The third spatial dimension is a coordinate that is more intelligent than that given in sensations.
Wise Men of the Sofa : Exactly! Right!
Kalaf : Well, great. I invite you to my wedding today with Princess Turandot.
Turandot : And I invite to execution. Because I have not heard any evidence.
Kalaf : I explain once again, especially for my dear princess. The space is forced three-dimensional, because it does not exist by itself, but constitutes a characteristic of the system. And the system consists of objects in which the concept of three-dimensionality is immanently inherent. Saying the "object", we are forced, willy-nilly, to imply a three-dimensional object, and not any other. Of course, this applies only to well-developed systems. If, for example, objects do not provide for nesting - that one object may form part of another - the second identifier is not required. And if the subject is present in the system in the singular, then there is no need for a third identifier. , , . . Now it is clear?
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A curtain