In the last article What is hidden behind the term modeling, I examined what modeling is. From this story a feeling should have arisen that the exchange of descriptions is rather impossible than possible. Each subject has his own world in his mind. Someone sees the model in the form of an image, someone hears it in the form of speech, someone perceives it. How we at the same time manage to agree on something is completely incomprehensible. And yet we do it. How we manage to do this is a question for psychologists. We should be surprised and take this opportunity to move on.
Ideally, it should be like this: two different entities, having received the same information as an input, should give its description in the same form. Remember descriptive geometry. You are given the task of drawing 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 at which everyone will draw similar drawings, write similar texts, etc ...
To do this, you need to come up with a single modeling language. For machine builders, builders, and technologists, the language of descriptive geometry, or projection geometry, was invented. Initially, it was 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.
I pretend to create a similar language, but to describe objects of a wider class: operations, functions, objects. This story is my story today.
Projection Modeling Language
Basic entities and constructs
The object of our modeling will be a 4-dimensional object in space-time. The following assumptions are made:
- We consider the Euclidean space in which time is absolute (Newtonian "khamenika"). If we need to generalize this language to the case of relativistic “khameniki”, then we will think.
- We believe that everyone around us sees (perceives) the same thing, but they can interpret it differently. This thesis suggests that in some mystical way, the way I perceive the blue color coincides with the way you perceive it (of course, this is impossible to verify!).
- We are not bound by anthropomorphism. This means that we can easily change our perception. Example: when perceiving 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 temporary events. It is difficult for us to imagine ourselves very slow.
Modeling 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:
- 3-D Object
3-D Object and operation are axiomatic concepts that do not require a definition.
- 3-D object, the width of which can be neglected, is the surface.
- 3-D object, the width and thickness of which can be neglected, is a line.
- 3-D object, the thickness, width and length of which can be neglected, is a point.
- An operation whose duration can be neglected is an event.
Neglect, of course, is possible only within the framework of the problem being solved.
Constructs of two types are assembled from basic objects:
- Construct from a finite number of 3-D objects. This is a construction.
- Construct from an infinite number of 3-D objects. This is a bunch. Galaxy example
- Construct from a finite number of operations - a script.
- A construct of an infinite number of operations is a function. Example rotation function.
There are constructs from constructs:
- Construct from a finite number of heaps. Example: a group of galaxies.
- Construct from an infinite number of heaps. An example has not yet been invented. I would be grateful if you tell me.
- A construct from a finite number of functions is a functional structure. Example: a diagram in IDEF0 notation models this kind of construct.
- Construct from an infinite number of functions. An example has not yet been invented.
A construct from a finite or infinite number of constructs and scenarios does not make sense.
Relations between elements
In the construct, there may be connections between the elements of the construct. Communication is the common parts of construct elements. And this thesis is very important. It differs from the generally accepted thesis that objects are divided among themselves and connected by threads that do not belong to them. This modeling method leads to collisions. Therefore, it is replaced by the thesis that communication is a common part of the elements. Example: the connection between the nut and the bolt is the common plane of contact. The relationship between the diesel fuel production function and the pumping function will be the common function of fueling the pipeline. This means that the gulf function belongs to both the production function and the pumping 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 bodies. Etc. Learning to think in this way is a separate and rather difficult task that requires training. But without this, consistent models cannot be built.
The same 4-D object can be considered from different points of view. And its projections on the plane may differ depending on the chosen 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 design. The first and second projections are in no way connected with each other. However, in the mind of the subject, such a relationship may arise. It is called: an object and its construction. Why "him"? Because the subject does the analysis and in his mind divides the object into parts, while receiving the design. Then he makes a synthesis and receives 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 model this representation, two projections can be used,
You can project an object for a while and get the operation. You can project the same object onto space and get volume. Then, in the imagination of the fashion designer, 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 3D object and for a time that gives us a function, in the imagination of the subject can give rise to the following statement: the motor is spinning.
The simultaneous projection of an object on time from different points of view: on the one hand, as an operation, on the other - as a scenario, generates in the imagination of the subject the thesis that this operation consists of suboperations.
The simultaneous projection of an object onto time as a function and as a set of operations generates a thesis in the consciousness of the subject that this function consists of operations.
The simultaneous projection of an object as a function and as a construction gives rise to the idea in the mind of the subject that such and such objects participate. In particular, if there is only one object, we again obtain the thesis that the motor is spinning.
Analysis of modeling standards
This 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. However, it is not clear what systems engineering means by an object and its parts. These can be projections in the form of an object, in the form of a construction, in the form of a function and in the form of a functional structure. I am afraid to assume that all four projections in systems engineering are called the same - system. From this, duality, triality, and other ali arise. The thing is that in system engineering these projections are not shared.
We, having divided the projections, will be able to conduct analysis and synthesis consciously. Exactly the same applies to 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, knowing how to build projections, we can greatly simplify modeling by simply explaining the intersection of objects. And this gives us another advantage. Now we do not need to imagine the impossible - the life cycle of the system supposedly begins from the moment it was conceived. No, of course, the life cycle begins with its construction and ends with destruction. And the idea of the system does not apply 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!
I didn't even start talking about projection. This topic is huge. I just showed the way where we went all these four years. Hope that was interesting. Thanks!