Introduction

Suppose that we have the task of creating an information system in which anyone can register to create models of their own ideas about the real world or imaginary worlds. Add the following conditions to this task:

1. Any object can become part of the design (the result of the synthesis process), or be divided into parts (the result of the analysis process). In this case, the synthesis and analysis can be done in different ways. This means that the same object can become part of different structures, or an object can be divided into parts in many ways.
2. The same object can be interpreted in different ways.
3. Any model can be expanded to reflect the change of point of view.
4. We do not consider the representations created by artificial intelligence and the languages ​​created by him to describe these representations. We do not consider mathematical refinements such as the Klein bottle, or fractals.
   

   To create such an information system, we will need a body of knowledge about which I am going to tell in my articles. I call this body of knowledge projection modeling, because the method outlined in it is very similar to descriptive geometry. Just as in descriptive geometry, projections are made on three orthogonal planes, so in projection modeling we make projections. But since our world is four-dimensional, the projections of 4-D objects are made on time and space. Just as in the descriptive geometry, the nature of the projected volume does not matter, so in projection modeling the interpretation of the projection is separated from the projection itself. That is, two subjects can interpret the same projection in different ways. For example, one subject may treat the projection as a machine, the second - as an amphibian.
   

   Brief description of terms

   
   

   Classification of projections of 4-D volumes on space

   
   

   In order to understand what projections we are doing, consider the following classification:

   
   A surface is a projection of a 4-D volume onto a space in the form of a surface bounding a volume.
   A structure is a projection of a 4-D volume onto space in the form of a “finite” set of objects or substances.
   A substance is a projection of a 4-D volume onto space in the form of an “infinite” set of objects, substances, or substances.
   
   

   Let me explain with examples.
   The surface can be interpreted as an object whose structure is unknown to us.
   The structure can be interpreted as a construction. For this we need to interpret each element of the projection. For example, the design of the aircraft consists of the wings of the tail and fuselage.
   Substance can be interpreted as a structure. A substance consisting of a "infinite" set of substances can be interpreted as a substance (a part of a substance is similar to the whole substance). To do this, treat each element of the projection as a substance. So we get a description of the type "milk".
   A substance consisting of an "infinite" set of objects can be interpreted as the composition of a substance (a crystal consists of atoms). For this we need to interpret each element of the projection. And, since their "infinite" number, it is necessary to split these elements into classes, and for each class to give a description of a typical element. So we come to the necessity of modeling second-order predicates.
   A substance consisting of a "infinite" set of structures can be interpreted as a complex structure of matter (water in a glass consists of molecules, each of which consists of two hydrogen atoms and one oxygen atom).

   
   

   An object whose size in the framework of the problem being solved can be neglected is called a material point.

   
   

   Classification of projections of 4-D volumes at a time

   
   

   Let's try to do the same with the projections of 4-D volumes at a time. To do this, consider the classification:

   
   
   1. The time interval is the projection of 4-D volume on time in the form of initial and final moments (analogue of the surface in space).
   2. The time structure is the projection of the 4-D volume on time in the form of a “finite” number of intervals and (or) time substances.
   3. The time substance is the projection of the 4-D volume on time in the form of an “infinite” number of intervals, time substances and (or) time structures.
   
   

   Let me explain with examples.
   The time interval can be interpreted as an operation.
   The temporal structure can be interpreted as a scenario. In the script can be both functions and operations. For example, the script "pushed off the ground, flew 6 meters, made a roll" consists of two operations and one function.
   The time substance can be interpreted as a function.
   A time substance consisting of a "infinite" number of time substances can be interpreted as a continuous movement, for example, the rotation of a motor shaft (part of the rotation is similar to the whole rotation).
   A time substance consisting of an "infinite" number of intervals can be interpreted as a function consisting of operations or events, for example, the function of concluding contracts consists of operations of concluding a contract.
   A temporary substance consisting of an "infinite" number of temporary structures can be interpreted as a function consisting of scenarios, for example, the function of building an aircraft consists of the sequence of operations "purchasing spare parts - assembling an aircraft - shipping an aircraft."

   
   

   The time interval, the duration of which can be neglected, can be interpreted as an event.

   
   

   Language difficulties

   
   

   When we read the definitions of terms, we do not distinguish between the definition of an object through the surface interpretation, the definition of an object through the interpretation of the structure, and the definition of the object through the interpretation of the substance. For example, it can be said that an airplane is a vehicle for the transport of goods and passengers by air. However, it can be said that the aircraft is a vehicle consisting of the fuselage, wings and tail. These two definitions define different projections of different 4-D volumes: projections in the form of an object and projections in the form of a structure. It is very important for an ontologist to separate these two definitions, because they require different models. But in practice we usually do not notice the difference in these definitions, because the context in which we are located inclines us to an unambiguous interpretation of the definitions. For example, we perceive a train as a structure, a cobblestone - as an object and milk - as a substance. But we do not realize how we make this choice. Therefore, quite often no distinction is made between an object called one term and a structure called the same term. Such a problem exists in the body of knowledge called system engineering. In this body of knowledge, both the object and the structure have one name — the system. Therefore, when I hear the term system, I have to make an effort to understand from the context what is at stake now: about the object or about the structure.

   
   

   There is not enough first-order predicates to model substances and time substances. You need to be able to build statements in second-order predicates, that is, you need to be able to model statements about sets. Perhaps this is the difficulty of modeling such objects.

   
   

   findings

   
   

   To meet the stated requirements, the following steps must be taken:

   
   
   1. Learn how to build projections of 4-D volumes correctly.
   2. Learn to correctly interpret the projection of 4-D volume. This can be seen in the example of determining the function through the interpretation of the projection of the 4-D volume for a while in the form of a time substance. This is one of the most difficult definitions I have ever given.
   3. Learn to separate the projection of 4-D volume from its interpretation. That is, two subjects, having made the same projection of a 4-D volume, should be able to interpret this projection in different ways (for one it will be a sale operation, for the other, a purchase operation).
   4. The standard mathematical model, which states that the set of points with a power of continuum spans a segment, should be replaced by another, in which there are no smallest indivisible particles from which extended objects can be constructed. In particular, this concerns the definition of an event. To do this, we need to build a segment on the time axis, and not a point, as previously thought. Just the length of this segment in the framework of a specific problem being solved, we neglect. This means that in another task this time interval can be interpreted as an operation. I understand that this sounds strange, but this is the only way to avoid collisions.
   5. With the help of the definitions introduced, one must learn to model all the necessary statements, for example: the object and its construction, the purpose of the object to perform a certain function, and so on. All this will be explained in the following articles.