Projection modeling

Introduction

In the last article What is hidden behind the term modeling, I looked at what modeling is. From this story, there should have been a feeling that the exchange of descriptions was more likely impossible than possible. Each subject has his own world in his mind. Someone sees a model as an image, someone hears it as a speech, someone perceives it. How we manage to come to an agreement on something is completely incomprehensible. And yet we do it. How we do this is a question for psychologists. We should be surprised and take this opportunity to go further.

Ideally, it should be like this: two different subjects, having received the same information at the input, should give its description in the same form. Recall the descriptive geometry. You are given the task to draw a cone. And all students draw similar drawings called drawings. So in the case of modeling more complex objects: enterprises, buildings, processes, we must achieve the same level of unification, in which everyone will draw similar pictures, write similar texts, etc ...

For this you need to come up with a single modeling language. For machine builders, builders, technologists, the language of descriptive geometry, or projection geometry, was invented. It was originally created as a language for describing fortifications, and was classified by the French. But then it became widely known and spread to other areas, becoming dominant over three centuries.
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I pretend to create such a language, but to describe objects of a wider class: operations, functions, objects. This language is my story today.

Projection modeling language

Base Entities and Constructs

The object of our simulation will be a 4-dimensional object in space-time. The following assumptions are made:

1. We consider the Euclidean space in which time is absolutely (Newtonian "Khamenika"). If it is necessary to generalize this language to the case of relativistic “Khameniki”, then we will think.
2. We believe that everyone around sees (feel) the same thing, but they can interpret it differently. This thesis says that in some mystical way, the way I perceive blue color coincides with the way you perceive it (of course, it is impossible to verify!).
3. We are not bound by anthropomorphism. This means that we can easily change our perception. Example: in the perception of very rare events, we can imagine ourselves living so long and perceiving time so slowly that the events in question merge before us in a single stream of indistinguishable events. When considering spatial objects, it is much easier to abandon anthropomorphism than when considering time events. It is difficult for us to imagine ourselves to be very slow.

The modeling of a 4-dimensional object consists in projecting it onto two conditionally perpendicular planes. The first plane is space, the second plane is time. When projecting projections are born. The basic entities from which the description of any projection is then built are as follows:

1. 3-D Object
2. Operation

3-D Object and operation are axiomatic concepts that do not require definition.

• 3-D object, whose width can be neglected - the surface.
• 3-D object, the width and thickness of which can be neglected - line.
• The 3-D object, whose thickness, width and length can be neglected, is a point.
• An operation whose duration can be neglected is an event.

Of course, it is possible to neglect only within the framework of the problem being solved.

Two types of base objects are collected:

1. Construct of a finite number of 3-D objects. This is a construction.
2. The construct of an infinite number of 3-D objects. This is a bunch. Galaxy example
3. The construct of a finite number of operations is a script.
4. The construct of an infinite number of operations is a function. An example of the rotation function.

There are constructs from constructs:

1. Construct of a finite number of heaps. Example: a group of galaxies.
2. An infinite number of heaps. The example has not yet been invented. I would be grateful if you tell me.
3. A construct of a finite number of functions is a functional structure. Example: a diagram in IDEF0 notation models this kind of construct.
4. Construct of an infinite number of functions. The example has not yet been invented.

A construct from a finite or infinite number of constructions and scenarios does not make sense.

Links between elements

In the construct there may be connections between the elements of the construct. Relationships are common parts of construct elements. And this thesis is very important. It differs from the generally accepted thesis that objects are separated from each other and are connected by threads that do not belong to them. This method of modeling leads to collisions. Therefore, it is replaced by the thesis that communication is common parts of elements. Example: the connection between the nut and the bolt is the common contact plane. The link between the diesel production function and the transfer function will be the general function of filling the fuel into the pipeline. This means that the Gulf function belongs to both the production function and the transfer function! The connection between one body in space and another will be a common gravitational field, which will be an integral part of the first and second body. And so on. Learning to think in this way is a separate and rather difficult task that requires training. But without this it is impossible to build consistent models.

Simulation examples

The same 4-D object can be viewed from different points of view. And its projections on the plane may differ depending on the selected point of view. For example, you can project a 4-D object into space and get a 3-D object. You can project and get a 3-D construction. The first and second projections are in no way connected with each other. However, in the mind of the subject such a connection may occur. It is called: the object and its construction. Why "him"? Because the subject makes the analysis and in his mind divides the object into parts, while receiving the construction. Then he does the synthesis and gets the object. If the analysis and synthesis were successful, the subject begins to think that he objectively understood the structure of the object. Although - this is only the result of his imagination - a representation. To simulate such a representation, you can use two projections, which are interconnected by a connection - “the object and its construction in the representation of such a subject”.

You can project an object on time and get the operation. You can project the same object on the space and get the volume. Then, in the designer's imagination, a connection may arise between these two projections of the type: the volume occupied by the operation. Then we say that the operation took place there.

The simultaneous projection of an object onto a space that gives us a 3-D object and for the time that gives us a function, in the imagination of the subject can generate the following statement: the motor is spinning.

Simultaneous projection of an object onto time from different points of view: on the one hand, as an operation, on the other - as a scenario, in the subject's imagination it generates the thesis that this operation consists of sub-operations.

The simultaneous projection of an object onto time as a function and as a multitude of operations gives rise to a thesis in the mind of the subject that this function consists of operations.

The simultaneous projection of an object as a function and as a construction gives rise in the mind of the subject to the idea that such-and-such objects are involved in this function. In particular, if the object is one, again we get the thesis that the motor is spinning.

Modeling Standards Analysis

Such an approach to modeling makes it easy to recognize all the errors of the process approach, and now also system engineering.

For example, take the term emergence. This term means that an object that is divided into parts has properties different from those of its parts. At the same time, it is not clear what system engineering understands by the object and its parts. These can be projections in the form of an object, in the form of a structure, in the form of a function and in the form of a functional structure. I am afraid to assume that all four projections in system engineering are called the same - the system. From this, duality, triality and other realities arise. The fact is that systems engineering does not share these projections.

We, having separated the projections, will be able to carry out the analysis and synthesis consciously. Exactly the same concerns the issue of accounting for functional and physical objects. This separation arose from the need to keep records in various sections, which gave rise to objects intersecting in space. But, being able to build projections, we can greatly simplify modeling, simply by explaining the intersection of objects. And it gives us another advantage. Now we don’t have to imagine the impossible - the supposedly life cycle of the system begins from the moment it is conceived. No, of course, the life cycle begins with its construction and ends with destruction. And the idea of ​​the system is not related to the system at all; it refers to the design of the system, which must be distinguished from the system itself. So welcome to the simple and clear world of simple and clear truths!

Conclusion

I didn't even start talking about projections. This topic is huge. I just showed the way where we went all these four years. Hope that was interesting. Thank!