Modeling designs. Requirements for the modeler
In the last article, the concept of systems and designs. Their place in the design of information systems devoted to structures, I briefly touched on the hermeneutic circle - this is one of the ways of our thinking aimed at achieving understanding. The hermeneutic circle consists of two directions of thinking: analysis and synthesis.
Analysis is the process by which we represent the object under study as a set of its parts (we study various constructions into which the object under study can be expanded).
Synthesis is the reverse “assembly” of an object.
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It is argued that a sense of understanding is achieved when, after disassembling the object (analysis), and then assembling it (synthesis), the subject receives a consistent result. In the same article, I noted that standards, as a rule, are aimed at describing only one direction of thinking - analysis, but completely ignoring the second direction - synthesis.
Ignoring the synthesis process leads to the fact that we lose the ability to check the results of the analysis and begin to think patterns. For example, if you ask us what the bicycle consists of, then the “right” answer will be found rather quickly. But if you ask: " What is a bicycle part of? ", - we will find it very difficult to answer.
The set of patterns that we memorize relate to only one direction of movement - in the direction of analysis and almost never - in the direction of synthesis. As soon as we hear the questions: “ How does something work? ”, “ How does something work? ”, An image of the structure appears immediately in the mind. However, as often as we hear the question: “ How does an object work? ”, Just as rarely do we hear the question: “ Within what context does an object exist? "," Part of what it is? "Therefore, we are easily given answers to some questions, and with difficulty to others. If we were disciplined in our thinking, we would also easily answer the question: “ What is a bicycle part of? ”, As well as to the question: “ What does a bicycle consist of? ” And most importantly, would result in approximately the same number of answer options as one, so on the second questions.
Where can you face such questions in practice? For example, when it is necessary to solve the problem of describing an enterprise within a certain context. We ask ourselves: “ What is an enterprise part of? ” There are many answers to this question: an enterprise can be part of a city, part of an industry, part of a holding. In the construction of each such facility, the company plays its unique role and is connected by its unique connections with various counterparties. Have you seen the standards that describe the approach to modeling various structures, part of which is the object under study? I'm afraid to say one hundred percent, but, to my shame, I don’t know such standards. They are either not there, or they are little known. Therefore, there are no frameworks for working with such models. And there is a need for this kind of tools, for example, when we want to analyze the connections of our counterparties within various collaborations.
We formulate the requirement for a framework modeling the structure:
The ability to present one object in the form of various constructions, as well as the opportunity to present one object as part of various constructions
The next limitation that holds us back when modeling structures is the lack of understanding of what sets of objects are and how a set is modeled.
Set is one of those axiomatic concepts that cannot be defined through other concepts. Cantor said that the multitude is much that is conceivable as a whole.
For example, suppose there are many objects on the space station, or many living organisms on Earth, or many seashells on the beach. The set is also an object of accounting, but specific, distinct from the object. The set has a composition. What is included in the set? The answer is funny: a lot of objects. Some vicious circle turns out - the set of objects has a structure, and the structure consists of a set of objects. The reason for this is that two different concepts are denoted by one term:
It turns out that the set (mat.) Has a composition, and there are MANY objects in it.
Colloquially, we never use the term set in a mathematical sense. For example, when we say that on the street a lot of people danced and sang , then, of course, we mean a lot as a synonym for a word a lot. Many can not dance: on the street a lot of people danced and sang .
It’s another thing to say: A lot of people dancing in the street have a non-zero intersection with a lot of people singing in the street . It is clear that here we are talking about the set in the second sense of the word. In colloquial speech you will not hear it. At the same time a lot of dancing people has a composition. This composition includes many dancing people.
If colloquially mention the word set, they mean MANY objects. But MANY objects are not many. A set in the mathematical sense is that which is thought as a whole. When I asked to present a lot of objects on the space station, most of you presented various objects that can be seen there. But this representation is not a representation of a set in a mathematical sense. This is a representation of a multitude of objects in the sense of MANY objects. A set in a mathematical sense is something else. This is what we represent as one. The fact that you presented a lot of objects does not give you an idea of the set. You submitted the composition of the set. Now it is necessary to present this composition as one unit (for a start, give it a name, for example). Here lies the mystery of the set - not everyone is capable of thinking of many objects as a single whole, and the image created in this case will not necessarily coincide with the image represented by another subject. That is why it is so difficult to explain what a multitude is. That is why it is easier to introduce this concept axiomatically, without any reliance on common sense.
The set (as well as the object) is necessary as a tool for describing reality. The concept of an object seems to us understandable only because we get acquainted with this concept in childhood, and the set is incomprehensible, because we get to know it at the institute when we study the fundamentals of mathematics.
And nevertheless, the concept of a set sits in us deeply enough and is known to everyone just as the concept of an object is known, but is not realized by us as clearly. The term set was not introduced accidentally, but as a result of the realization of this fact.
Recently, I made an attempt to introduce the concept of an object as we would introduce it if it were completely unknown to us — by classifying those models that we create in our imagination when we hear the mention of an object. This attempt is described in the article: Strict definition of concepts: object, state, event, business operation and business function. An attempt to introduce the concept of set through the models that we create in our imagination was made by me in the context of structural modeling in the article: Classification of structures: examples and errors . This article provoked a heated discussion, but it seemed to me that they did not discuss classification, but questions that could be called religious rather: for example, should the structure have emergence, or can the structure consist of one element? It is clear that the formal theory of systems should not limit itself to any narrow circle of structures, otherwise it will be impossible to perform operations on systems. From this I concluded that the reasoning about the sets is rather difficult and decided once again to elaborate on this topic.
When we talked about the design, we talked about it as:
Question: under the set of objects in this definition is understood what? Set in the sense of "mathematical set", or set in the sense of "many"? In the last article I did not focus on this, now we can make out this definition in more detail.
We see that the definition of a construction practically repeats the definition of a set: a construction is a lot of objects that can be thought of as a whole. A set in a mathematical sense and a construction are objects of the same kind. The composition of a set is many objects, and the composition of a structure is many objects and many connections. At the same time, the set — there are not many objects, and the construction — there are not many objects and connections. If we say that a structure consists of a set of objects that can be thought of as a whole, we mean that the structure of the structure includes many objects, but the structure is one. That is why I said that the concept of set sits deeply in our consciousness, but we are not aware of it in the same way as the concept of an object is realized.
It can be said this way: a construction is a set (in the mathematical sense) of objects and connections between them. Then we should not say that it is necessary to think of it as a whole, because this requirement is included in the definition of the term of a set (in the mathematical sense) and a tautology is obtained.
Therefore, the design definition can be given both in the first method and in the second.
In order to more clearly imagine the analogy that exists between the concept of a set and the concept of a structure, draw a picture.
The set corresponds to the set. The set has a composition, and the design has a composition. The set includes many objects and the structure includes many objects (communications are also objects).
Since such an analogy suggests itself, it is possible to construct the same algebra on constructions as on sets: constructions can be added, they can be intersected, subtracted. In order for such an algebra to take place, it is necessary to add a zero element, an analogue of an empty set, an empty construction consisting of an empty set of elements. In addition, it will be necessary to admit the existence of a structure from one element or from one connection, which seems counterintuitive, but without this it will not be possible to carry out operations on structures. That is, in order to conduct operations on structures (and systems), we must adopt the same axiomatics with respect to the term as with respect to the set. This will allow us to connect structures, separate them, look for intersections, and so on. What is funny, in mathematics sets appeared in response to the question: how to simulate reality, including constructions, but after a century we never learned how to use this tool!
You can often hear such expressions as: "The design produces electricity . " Since the set does not “do” anything, has no size, does not weigh anything, all these properties can have either an object in the set or an object synthesized on the basis of this set, but not the set itself. It turns out that when we say that a construction produces electricity, we mean either some of its elements or an object synthesized on its basis, but in no case do we mean a set of objects and connections conceived as a whole! This is important to remember, and we will need it in the following articles.
In the information systems I deal with, there is no built-in mechanism for modeling sets. Modeling of a set (assignment of a name, attributes, the ability to work with it as with a regular object, calling it by name, access its attributes, perform addition, subtraction, and intersection operations) while being implemented manually. From this it follows that the design must be modeled manually. The following requirement for a framework that has the goal to model constructs:
The ability to model sets and perform operations on them.
In the next article we will also consider in detail the concepts of “type” and “attribute”.
Analysis is the process by which we represent the object under study as a set of its parts (we study various constructions into which the object under study can be expanded).
Synthesis is the reverse “assembly” of an object.
')
It is argued that a sense of understanding is achieved when, after disassembling the object (analysis), and then assembling it (synthesis), the subject receives a consistent result. In the same article, I noted that standards, as a rule, are aimed at describing only one direction of thinking - analysis, but completely ignoring the second direction - synthesis.
Ignoring the synthesis process leads to the fact that we lose the ability to check the results of the analysis and begin to think patterns. For example, if you ask us what the bicycle consists of, then the “right” answer will be found rather quickly. But if you ask: " What is a bicycle part of? ", - we will find it very difficult to answer.
The set of patterns that we memorize relate to only one direction of movement - in the direction of analysis and almost never - in the direction of synthesis. As soon as we hear the questions: “ How does something work? ”, “ How does something work? ”, An image of the structure appears immediately in the mind. However, as often as we hear the question: “ How does an object work? ”, Just as rarely do we hear the question: “ Within what context does an object exist? "," Part of what it is? "Therefore, we are easily given answers to some questions, and with difficulty to others. If we were disciplined in our thinking, we would also easily answer the question: “ What is a bicycle part of? ”, As well as to the question: “ What does a bicycle consist of? ” And most importantly, would result in approximately the same number of answer options as one, so on the second questions.
Where can you face such questions in practice? For example, when it is necessary to solve the problem of describing an enterprise within a certain context. We ask ourselves: “ What is an enterprise part of? ” There are many answers to this question: an enterprise can be part of a city, part of an industry, part of a holding. In the construction of each such facility, the company plays its unique role and is connected by its unique connections with various counterparties. Have you seen the standards that describe the approach to modeling various structures, part of which is the object under study? I'm afraid to say one hundred percent, but, to my shame, I don’t know such standards. They are either not there, or they are little known. Therefore, there are no frameworks for working with such models. And there is a need for this kind of tools, for example, when we want to analyze the connections of our counterparties within various collaborations.
We formulate the requirement for a framework modeling the structure:
The ability to present one object in the form of various constructions, as well as the opportunity to present one object as part of various constructions
The next limitation that holds us back when modeling structures is the lack of understanding of what sets of objects are and how a set is modeled.
Set is one of those axiomatic concepts that cannot be defined through other concepts. Cantor said that the multitude is much that is conceivable as a whole.
For example, suppose there are many objects on the space station, or many living organisms on Earth, or many seashells on the beach. The set is also an object of accounting, but specific, distinct from the object. The set has a composition. What is included in the set? The answer is funny: a lot of objects. Some vicious circle turns out - the set of objects has a structure, and the structure consists of a set of objects. The reason for this is that two different concepts are denoted by one term:
- The set is a lot of things, conceived by us as a whole (mat).
- The set is synonymous with the word "many."
It turns out that the set (mat.) Has a composition, and there are MANY objects in it.
Colloquially, we never use the term set in a mathematical sense. For example, when we say that on the street a lot of people danced and sang , then, of course, we mean a lot as a synonym for a word a lot. Many can not dance: on the street a lot of people danced and sang .
It’s another thing to say: A lot of people dancing in the street have a non-zero intersection with a lot of people singing in the street . It is clear that here we are talking about the set in the second sense of the word. In colloquial speech you will not hear it. At the same time a lot of dancing people has a composition. This composition includes many dancing people.
If colloquially mention the word set, they mean MANY objects. But MANY objects are not many. A set in the mathematical sense is that which is thought as a whole. When I asked to present a lot of objects on the space station, most of you presented various objects that can be seen there. But this representation is not a representation of a set in a mathematical sense. This is a representation of a multitude of objects in the sense of MANY objects. A set in a mathematical sense is something else. This is what we represent as one. The fact that you presented a lot of objects does not give you an idea of the set. You submitted the composition of the set. Now it is necessary to present this composition as one unit (for a start, give it a name, for example). Here lies the mystery of the set - not everyone is capable of thinking of many objects as a single whole, and the image created in this case will not necessarily coincide with the image represented by another subject. That is why it is so difficult to explain what a multitude is. That is why it is easier to introduce this concept axiomatically, without any reliance on common sense.
The set (as well as the object) is necessary as a tool for describing reality. The concept of an object seems to us understandable only because we get acquainted with this concept in childhood, and the set is incomprehensible, because we get to know it at the institute when we study the fundamentals of mathematics.
And nevertheless, the concept of a set sits in us deeply enough and is known to everyone just as the concept of an object is known, but is not realized by us as clearly. The term set was not introduced accidentally, but as a result of the realization of this fact.
Recently, I made an attempt to introduce the concept of an object as we would introduce it if it were completely unknown to us — by classifying those models that we create in our imagination when we hear the mention of an object. This attempt is described in the article: Strict definition of concepts: object, state, event, business operation and business function. An attempt to introduce the concept of set through the models that we create in our imagination was made by me in the context of structural modeling in the article: Classification of structures: examples and errors . This article provoked a heated discussion, but it seemed to me that they did not discuss classification, but questions that could be called religious rather: for example, should the structure have emergence, or can the structure consist of one element? It is clear that the formal theory of systems should not limit itself to any narrow circle of structures, otherwise it will be impossible to perform operations on systems. From this I concluded that the reasoning about the sets is rather difficult and decided once again to elaborate on this topic.
When we talked about the design, we talked about it as:
- the object
- a set of objects connected by connections and imaginable as a whole.
Question: under the set of objects in this definition is understood what? Set in the sense of "mathematical set", or set in the sense of "many"? In the last article I did not focus on this, now we can make out this definition in more detail.
We see that the definition of a construction practically repeats the definition of a set: a construction is a lot of objects that can be thought of as a whole. A set in a mathematical sense and a construction are objects of the same kind. The composition of a set is many objects, and the composition of a structure is many objects and many connections. At the same time, the set — there are not many objects, and the construction — there are not many objects and connections. If we say that a structure consists of a set of objects that can be thought of as a whole, we mean that the structure of the structure includes many objects, but the structure is one. That is why I said that the concept of set sits deeply in our consciousness, but we are not aware of it in the same way as the concept of an object is realized.
It can be said this way: a construction is a set (in the mathematical sense) of objects and connections between them. Then we should not say that it is necessary to think of it as a whole, because this requirement is included in the definition of the term of a set (in the mathematical sense) and a tautology is obtained.
Therefore, the design definition can be given both in the first method and in the second.
In order to more clearly imagine the analogy that exists between the concept of a set and the concept of a structure, draw a picture.
The set corresponds to the set. The set has a composition, and the design has a composition. The set includes many objects and the structure includes many objects (communications are also objects).
Since such an analogy suggests itself, it is possible to construct the same algebra on constructions as on sets: constructions can be added, they can be intersected, subtracted. In order for such an algebra to take place, it is necessary to add a zero element, an analogue of an empty set, an empty construction consisting of an empty set of elements. In addition, it will be necessary to admit the existence of a structure from one element or from one connection, which seems counterintuitive, but without this it will not be possible to carry out operations on structures. That is, in order to conduct operations on structures (and systems), we must adopt the same axiomatics with respect to the term as with respect to the set. This will allow us to connect structures, separate them, look for intersections, and so on. What is funny, in mathematics sets appeared in response to the question: how to simulate reality, including constructions, but after a century we never learned how to use this tool!
You can often hear such expressions as: "The design produces electricity . " Since the set does not “do” anything, has no size, does not weigh anything, all these properties can have either an object in the set or an object synthesized on the basis of this set, but not the set itself. It turns out that when we say that a construction produces electricity, we mean either some of its elements or an object synthesized on its basis, but in no case do we mean a set of objects and connections conceived as a whole! This is important to remember, and we will need it in the following articles.
In the information systems I deal with, there is no built-in mechanism for modeling sets. Modeling of a set (assignment of a name, attributes, the ability to work with it as with a regular object, calling it by name, access its attributes, perform addition, subtraction, and intersection operations) while being implemented manually. From this it follows that the design must be modeled manually. The following requirement for a framework that has the goal to model constructs:
The ability to model sets and perform operations on them.
In the next article we will also consider in detail the concepts of “type” and “attribute”.
Source: https://habr.com/ru/post/329576/
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