December 18, 2017 at 09:17The concept of communication in projection modeling
I continue to talk about projection modeling .
The next topic that I want to touch on is the explanation of why we defined the connection in the design as a 4-D object. Let me remind you that in projection modeling, communication is a common part of construct elements. Since the elements of the construct are 4-D objects, the connections are also 4-D objects. That is, for a relationship to exist between two 4-D objects, there must be a common 4-D volume belonging to both of these objects.
We are used to considering a connection as something that exists between two objects, but no one in analytics has yet given an exact definition of this concept. We did it for the first time. I will tell you why in this discipline, communication is defined in this way and not otherwise.
Let's start with a simple: let the objects are connected by a general position in space or in time. These are connections like “right”, “above”, “after”, “together”, etc. To model this kind of relationships, we need to consider the 4-D space in which the 4-D objects we are considering are placed. 4-D space plays the same role as other 4-D objects. Typically, the simulation begins precisely with the fact that we form the boundaries of the model, that is, a 4-D space in which we then place 4-D objects. For some reason, about this very first 4-D object is forgotten immediately after its determination. But it is precisely his properties that allow us to describe the relationships I have indicated.
In the construction of this kind of connection can arise when we say that the roof will be above the building, and not under, or next to. When designing processes of this kind of connection can arise when we say that this operation follows the previous one. All these connections are properties of 4-D space, which we created first and into which then we place 4-D objects.
The second type of ties - “supports”, “rests”, “transfers effort”, that is, everything that is connected with force. A force arises at the boundary of two bodies in Newtonian physics, as a result of the interaction of fields in field theory and as a result of particle exchange in quantum mechanics.
Let one body press on another. This means that there is a common part between them - the border. This boundary belongs to both the first and second bodies. If you think that this is not so, then it means that between the boundaries of two bodies there is a third body - the medium through which the interaction (field) is transmitted. And which has a common part with both the first body and the second. Be that as it may - in the interaction model there are always common parts, whether it be objects or the environment. If you think that the field is the result of an exchange of particles, then you yourself can understand that the problem has been reduced to the previous one.
The statement that there is always something in common between interacting bodies is not the result of an analysis of natural phenomena, but the result of an analysis of our ideas about nature. Do not confuse reality and its model. In our view, there is no way to transfer interaction directly without an intermediary. Therefore, any connection is a 4-D object transmitting this interaction. But, I repeat, not because nature is so arranged, but because we think so.
Another type of connection: when an object, being the result of the activity of one operation, is then used in another. Literally, it looks like this: there is a certain 4-D volume interpreted by us as a result that has common parts with the first and second operations. Since the operation is a projection of the 4-D volume, it turns out that the two operations have a common 4-D volume, which we interpret as the result of the first operation.
The next type of connection is flows between functions in a functional structure. They can be seen in the IDEF0 notation, modeled as arrows between function models. Why IDEF0 models functions and what a function can be read here: Function, script and approximation of events. Since a function is a set of operations (events), then for two functions some operations (events) can become common. For example, let there be a bearing production function and a bearing consumption function. Between them, we usually draw a flow of bearings. But let's look at this more closely. The production function has a part responsible for shipping bearings. And in the function of consumption - the part responsible for receiving bearings. Bearing transmissions are common to both functions. On the one hand, each such operation is interpreted as bearing transmission, and on the other, as bearing reception. But this is the same 4-D volume! By the way, if you “glue” all these operations together, you get the function “reception-transmission of bearings”, which is part of the function of production of bearings and consumption.
The whole power of defining a connection as a 4-D volume pops up in cases when we begin to build hierarchical models of composition and decomposition. When the models are planar, it makes no difference how to determine the relationship. But, when we change our point of view when moving to a more detailed, or more global level, everything becomes not so obvious.
For example, you can consider the relationship between the electricity producer - hydroelectric power station and the consumer - the city. If the connection is a 4-D object, then at the stage of detailing, you can "reveal" it and show that it is a power line. Then the connection will turn into a power line. The power transmission line will be connected with one connection with the hydroelectric power station and the other with the city. Further detail may already “reveal” these connections. For example, substations will be allocated in the city, and an open distribution unit in the hydroelectric power station, power lines will be presented in the form of two circuits, and the connection will “open” and turn into the input of the circuits. The converse is also true. Suppose there are many links between the docking module and the space station. During generalization, these relations can be “generalized" to one connection.
In the modeling standards I know of, this kind of link transformation is not provided. There is a hint in the EPC standard where operations are interconnected by common events. But these events cannot be “revealed”. According to the author of the notation, these events precisely cut the time into “before” and “after” operations. However, at one time What is an event, or why is four-dimensional geometry a business intelligence? I showed that there is no exact division into "before" and "after". Operations often “pile on” each other, or vice versa, “disperse” in time. This becomes apparent when detailing the view. This kind of detailing is not possible in EPC notation, but possible in projection modeling.
So, the postulate that communication is a 4-D object allows us to model it in the same ways as any other object. This means that the relationship can also be represented in the form of an object, operation, function, heap, etc.
The next topic that I want to touch on is the explanation of why we defined the connection in the design as a 4-D object. Let me remind you that in projection modeling, communication is a common part of construct elements. Since the elements of the construct are 4-D objects, the connections are also 4-D objects. That is, for a relationship to exist between two 4-D objects, there must be a common 4-D volume belonging to both of these objects.
We are used to considering a connection as something that exists between two objects, but no one in analytics has yet given an exact definition of this concept. We did it for the first time. I will tell you why in this discipline, communication is defined in this way and not otherwise.
Spatial relationships
Let's start with a simple: let the objects are connected by a general position in space or in time. These are connections like “right”, “above”, “after”, “together”, etc. To model this kind of relationships, we need to consider the 4-D space in which the 4-D objects we are considering are placed. 4-D space plays the same role as other 4-D objects. Typically, the simulation begins precisely with the fact that we form the boundaries of the model, that is, a 4-D space in which we then place 4-D objects. For some reason, about this very first 4-D object is forgotten immediately after its determination. But it is precisely his properties that allow us to describe the relationships I have indicated.
In the construction of this kind of connection can arise when we say that the roof will be above the building, and not under, or next to. When designing processes of this kind of connection can arise when we say that this operation follows the previous one. All these connections are properties of 4-D space, which we created first and into which then we place 4-D objects.
Interactions
The second type of ties - “supports”, “rests”, “transfers effort”, that is, everything that is connected with force. A force arises at the boundary of two bodies in Newtonian physics, as a result of the interaction of fields in field theory and as a result of particle exchange in quantum mechanics.
Let one body press on another. This means that there is a common part between them - the border. This boundary belongs to both the first and second bodies. If you think that this is not so, then it means that between the boundaries of two bodies there is a third body - the medium through which the interaction (field) is transmitted. And which has a common part with both the first body and the second. Be that as it may - in the interaction model there are always common parts, whether it be objects or the environment. If you think that the field is the result of an exchange of particles, then you yourself can understand that the problem has been reduced to the previous one.
The statement that there is always something in common between interacting bodies is not the result of an analysis of natural phenomena, but the result of an analysis of our ideas about nature. Do not confuse reality and its model. In our view, there is no way to transfer interaction directly without an intermediary. Therefore, any connection is a 4-D object transmitting this interaction. But, I repeat, not because nature is so arranged, but because we think so.
Causality
Another type of connection: when an object, being the result of the activity of one operation, is then used in another. Literally, it looks like this: there is a certain 4-D volume interpreted by us as a result that has common parts with the first and second operations. Since the operation is a projection of the 4-D volume, it turns out that the two operations have a common 4-D volume, which we interpret as the result of the first operation.
Streams
The next type of connection is flows between functions in a functional structure. They can be seen in the IDEF0 notation, modeled as arrows between function models. Why IDEF0 models functions and what a function can be read here: Function, script and approximation of events. Since a function is a set of operations (events), then for two functions some operations (events) can become common. For example, let there be a bearing production function and a bearing consumption function. Between them, we usually draw a flow of bearings. But let's look at this more closely. The production function has a part responsible for shipping bearings. And in the function of consumption - the part responsible for receiving bearings. Bearing transmissions are common to both functions. On the one hand, each such operation is interpreted as bearing transmission, and on the other, as bearing reception. But this is the same 4-D volume! By the way, if you “glue” all these operations together, you get the function “reception-transmission of bearings”, which is part of the function of production of bearings and consumption.
Benefits of the proposed link definition
The whole power of defining a connection as a 4-D volume pops up in cases when we begin to build hierarchical models of composition and decomposition. When the models are planar, it makes no difference how to determine the relationship. But, when we change our point of view when moving to a more detailed, or more global level, everything becomes not so obvious.
For example, you can consider the relationship between the electricity producer - hydroelectric power station and the consumer - the city. If the connection is a 4-D object, then at the stage of detailing, you can "reveal" it and show that it is a power line. Then the connection will turn into a power line. The power transmission line will be connected with one connection with the hydroelectric power station and the other with the city. Further detail may already “reveal” these connections. For example, substations will be allocated in the city, and an open distribution unit in the hydroelectric power station, power lines will be presented in the form of two circuits, and the connection will “open” and turn into the input of the circuits. The converse is also true. Suppose there are many links between the docking module and the space station. During generalization, these relations can be “generalized" to one connection.
In the modeling standards I know of, this kind of link transformation is not provided. There is a hint in the EPC standard where operations are interconnected by common events. But these events cannot be “revealed”. According to the author of the notation, these events precisely cut the time into “before” and “after” operations. However, at one time What is an event, or why is four-dimensional geometry a business intelligence? I showed that there is no exact division into "before" and "after". Operations often “pile on” each other, or vice versa, “disperse” in time. This becomes apparent when detailing the view. This kind of detailing is not possible in EPC notation, but possible in projection modeling.
conclusions
So, the postulate that communication is a 4-D object allows us to model it in the same ways as any other object. This means that the relationship can also be represented in the form of an object, operation, function, heap, etc.