The concept of communication in projection modeling
I continue to talk about projection modeling .
The next topic I want to touch on is an explanation of why we defined the link in the design as a 4-D object. Let me remind you that in projection modeling the connection is a common part of the elements of the construct. Since the elements of the construct are 4-D objects, the links are also 4-D objects. That is, for a link to exist between two 4-D objects, there must be a total 4-D volume belonging to both of these objects.
We are accustomed to consider communication 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 why in this discipline communication is defined in such a way and not otherwise.
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Let's start with a simple one: let objects be related by a common position in space or in time. These are links like “right”, “above”, “after”, “together”, etc. To simulate such connections, we need to consider the 4-D space in which the 4-D objects we are considering are located. 4-D space plays the same role as other 4-D objects. Typically, the simulation begins with the fact that we form the boundaries of the model, that is, 4-D space, in which we then place 4-D objects. For some reason, this very first 4-D object is forgotten immediately after its definition. But it is his properties that allow us to describe the connections I have indicated.
In the construction of this kind of communication may occur when we say that the roof will be above the building, and not under, or next. When designing processes, this kind of connection may arise when we say that this operation follows the previous one. All these connections are properties of 4-D spaces, which we created first and into which we later place 4-D objects.
The second type of connections is “supports”, “rests”, “transmits effort”, that is, everything that is connected with force. 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 between them there is a common part - the border. This boundary belongs to both the first and second body. If you think that this is not the case, 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, be it objects or environments. If you think that the field is the result of the exchange of particles, then you yourself can understand that the task has been reduced to the previous one.
The assertion 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 transmit 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 this way.
Another type of communication: when the 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, which we interpret as a result, which has common parts with the first and second operations. Since an operation is a projection of a 4-D volume, it turns out that two operations have a common 4-D volume, interpreted by us as the result of the first operation.
The next type of communication is the flow between functions in the functional structure. They can be seen in the IDEF0 notation, modeled as arrows between function models. Why IDEF0 models functions and what a function is, you can read here: Function, script and event approximation . Since a function is a set of operations (events), some operations (events) can become common for two functions. For example, suppose there is a bearing production function and a bearing consumption function. Between them, we usually draw a stream of bearings. But let's look at it more closely. In the production function there is a part responsible for the shipment of bearings. And in the consumption function, the part responsible for receiving bearings. Bearing transfer operations are common to both functions. On the one hand, each such operation is interpreted as a bearing transfer, and on the other, as a bearing reception. But this is the same 4-D volume! By the way, if you “glue” all these operations together, you get the function “receiving and transmitting bearings”, which is part of the function of bearing production and consumption.
The whole power of defining a relationship as a 4-D volume pops up in cases when we begin to build hierarchical models of composition and decomposition. When models are planar, there is 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 less obvious.
For example, you can consider the relationship between the producer of electricity - hydroelectric power station and the consumer - the city. If the connection is a 4-D object, then at the stage of detailing it is possible to “open” it and show that it is a transmission line. Then the link will "turn" into power lines. A transmission line will be connected by one connection with the hydropower station and the other with the city. Further detailing can "reveal" these links already. For example, in a city substations will be allocated, and in hydroelectric power stations - an open distribution hub, power transmission lines will be presented in the form of two chains, and the connection will “unfold” and turn into circuit inputs. The reverse is also true. Suppose there are many connections between the docking module and the space station. During generalization, these connections can be “generalized” to one connection.
In the standards of modeling known to me, such transformations of links are not provided. There is a hint in the EPC standard, where operations are linked by common events. But you cannot “uncover” these events According to the author of the notation, these events precisely cut the time for “before” and “after” the operation. However, in due time What is an event, or why 4-D geometry for business analytics? I showed that there is no exact division into “before” and “after”. Operations often “pile on” each other, or vice versa, they “disperse” in time. This becomes apparent when detailing the view. This kind of detailing is not possible in EPC notation, but it is possible in projection modeling.
So, the postulate that a connection is a 4-D object allows us to model it in the same way as any other object. This means that the connection can also be represented as an object, operation, function, heap, and so on.
The next topic I want to touch on is an explanation of why we defined the link in the design as a 4-D object. Let me remind you that in projection modeling the connection is a common part of the elements of the construct. Since the elements of the construct are 4-D objects, the links are also 4-D objects. That is, for a link to exist between two 4-D objects, there must be a total 4-D volume belonging to both of these objects.
We are accustomed to consider communication 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 why in this discipline communication is defined in such a way and not otherwise.
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Spatial connections
Let's start with a simple one: let objects be related by a common position in space or in time. These are links like “right”, “above”, “after”, “together”, etc. To simulate such connections, we need to consider the 4-D space in which the 4-D objects we are considering are located. 4-D space plays the same role as other 4-D objects. Typically, the simulation begins with the fact that we form the boundaries of the model, that is, 4-D space, in which we then place 4-D objects. For some reason, this very first 4-D object is forgotten immediately after its definition. But it is his properties that allow us to describe the connections I have indicated.
In the construction of this kind of communication may occur when we say that the roof will be above the building, and not under, or next. When designing processes, this kind of connection may arise when we say that this operation follows the previous one. All these connections are properties of 4-D spaces, which we created first and into which we later place 4-D objects.
Interactions
The second type of connections is “supports”, “rests”, “transmits effort”, that is, everything that is connected with force. 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 between them there is a common part - the border. This boundary belongs to both the first and second body. If you think that this is not the case, 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, be it objects or environments. If you think that the field is the result of the exchange of particles, then you yourself can understand that the task has been reduced to the previous one.
The assertion 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 transmit 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 this way.
Causal relationships
Another type of communication: when the 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, which we interpret as a result, which has common parts with the first and second operations. Since an operation is a projection of a 4-D volume, it turns out that two operations have a common 4-D volume, interpreted by us as the result of the first operation.
Streams
The next type of communication is the flow between functions in the functional structure. They can be seen in the IDEF0 notation, modeled as arrows between function models. Why IDEF0 models functions and what a function is, you can read here: Function, script and event approximation . Since a function is a set of operations (events), some operations (events) can become common for two functions. For example, suppose there is a bearing production function and a bearing consumption function. Between them, we usually draw a stream of bearings. But let's look at it more closely. In the production function there is a part responsible for the shipment of bearings. And in the consumption function, the part responsible for receiving bearings. Bearing transfer operations are common to both functions. On the one hand, each such operation is interpreted as a bearing transfer, and on the other, as a bearing reception. But this is the same 4-D volume! By the way, if you “glue” all these operations together, you get the function “receiving and transmitting bearings”, which is part of the function of bearing production and consumption.
The advantages of the proposed definition of communication
The whole power of defining a relationship as a 4-D volume pops up in cases when we begin to build hierarchical models of composition and decomposition. When models are planar, there is 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 less obvious.
For example, you can consider the relationship between the producer of electricity - hydroelectric power station and the consumer - the city. If the connection is a 4-D object, then at the stage of detailing it is possible to “open” it and show that it is a transmission line. Then the link will "turn" into power lines. A transmission line will be connected by one connection with the hydropower station and the other with the city. Further detailing can "reveal" these links already. For example, in a city substations will be allocated, and in hydroelectric power stations - an open distribution hub, power transmission lines will be presented in the form of two chains, and the connection will “unfold” and turn into circuit inputs. The reverse is also true. Suppose there are many connections between the docking module and the space station. During generalization, these connections can be “generalized” to one connection.
In the standards of modeling known to me, such transformations of links are not provided. There is a hint in the EPC standard, where operations are linked by common events. But you cannot “uncover” these events According to the author of the notation, these events precisely cut the time for “before” and “after” the operation. However, in due time What is an event, or why 4-D geometry for business analytics? I showed that there is no exact division into “before” and “after”. Operations often “pile on” each other, or vice versa, they “disperse” in time. This becomes apparent when detailing the view. This kind of detailing is not possible in EPC notation, but it is possible in projection modeling.
findings
So, the postulate that a connection is a 4-D object allows us to model it in the same way as any other object. This means that the connection can also be represented as an object, operation, function, heap, and so on.
Source: https://habr.com/ru/post/344936/
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