May 4, 2015 at 13:46Conceptual Modeling: How Many? How much
The question of what a class of objects is, whether it exists in nature, has been discussed by me for the past two articles: A class of objects or objects of a class? , Features of the conceptual modeling of the subject area . I ask myself: is it possible, describing the subject area, to connect an object and a class of objects with a semantic connection?
The question is actually not an idle one. I often come across models that do not accurately convey the meaning of what was said. For example, a car owner may say that his car contains a group of wheels. He could say that the car contains wheels, and that would be a completely different statement. What confuses me is that in the models I saw, the difference between these two statements is not made. However, in practice, there is a huge difference between them. Try to practice finding this difference yourself.
Modeling using UML adds fuel to the fire because, firstly, it does not allow modeling classes of objects ( Modeling functional and physical events in a logical paradigm), and secondly, it does not allow semantics to connect the class of objects and the object. Thus, in the field of modeling subject areas, an unexplored empty space is observed. I will allow myself to frolic a little on this field to show how really fun it is. Today I will talk about how my question is related to the concept of countability and uncountability of a noun.
Let me remind you that those nouns that designate individual objects that can be counted are considered countable. An example of a countable noun is the term spoon. This term refers to an object that is, firstly, indivisible, and secondly, we can create many such objects.
Countless nouns denote materials and other objects that are considered in the language as mass or multitude, and not as separate objects. An example would be such nouns: water, sugar, furniture. Note that in this definition there is mention of the set. This is what we are using now. I will try to prove that uncountable nouns describe sets, not objects. Thus, I will show that our consciousness operates with equal success both objects and sets of objects.
Suppose we store sugar in 1 kg slices. We chop a small piece from this piece and put it in tea. This method of use seems to us obvious, but it is not so obvious.
Suppose that in a certain country sugar is consumed in the form of a piece weighing 1 kg whole. In this world, there is no knowledge that sugar is divided into parts. Therefore, a piece of sugar, split in half, is sent to the factory for remaking, and they do not use it. A meter in such a world takes sugar into account only in pieces of 1 kg. Use the pieces as follows: put it in a tub with water and drink everyone with sweet water. Once a worker loading sugar stumbled, and only half of the sugar fell into the vat. The worker was very afraid that he would be punished and pretended that he was not at work. However, what a surprise it was when in the morning it turned out that people were still drinking sweet water and were happy with it! He told the master about this, and the two of them turned to the local scientist to help him deal with the problem. The scientist looked for an answer for a long time, until he realized what is the matter in accounting. Sugar - a substance that can be considered in another way - by weight! Since then, the technology for producing sweet water has been greatly simplified.
Now they could do it at home literally in a cup. This means that a piece of 1 kg could now be looked at as a collection of pieces. Pieces could be obtained arbitrarily, the main thing is that their mass be given. Sugar accounting has evolved from accounting for pieces in pieces to accounting for the mass of pieces. After some time, people realized that it was possible to grind sugar for sale, and sell it in the form of piles, like sand. Thus, accounting for sugar turned into accounting for many small pieces that no one already considered, but took into account the total mass. That is, now counted a lot, but not objects. In the final passage of grinding, we get powdered sugar. Powdered sugar is also a lot of small parts. And we take it into account as a set by weight. More interesting: fluid is also a multitude. And we take it into account like sugar. It turns out that water is a lot.
Now a little linguistics. We say: give me nails, and we can also say: give me water. Nails are in the plural, and water is in the singular. Water in this context is plenty. Therefore, it is in the singular. We can come up with a name for many nails: a bunch. And then we can say: give me a bunch. A heap is also a designation of a multitude.
Therefore, I conclude: if we are talking about uncountable nouns, then we are talking about sets. And if about countable, then about objects. But the one and the other accounting method is equally accessible to us.
You will say that a substance is a substance and that it can be divided. You are wrong. You can share everything, would be technology. For example, you can divide a spoon. But not the way you are used to. But in a different way. Imagine that the technology of splitting a spoon into parts was invented. Let these parts occupy a volume, they can be used as spoons, but these spoons have the property of being less durable, because they are more loose. However, for some purposes it is permissible to divide a spoon into two equal looser parts, but for some purposes not. If we can divide the spoon into parts in an arbitrary proportion, we get an analogue of dividing the substance into parts. But now we were able to divide not a substance, but a functional object into many functional objects. So it all depends on the technology available to us and the accounting method.
In how many ways can water be divided into parts, assuming that the smallest part of the water does not exist? In answering this question, we must commit violence against common sense: we must move on to the concept of a point and the concept of continuum. There will be a huge number of ways to divide water into parts. The power of so many divisions is M3, or the continuum continuum. It seems to me that the complexity of this design led the Greeks to a version about the molecular structure of matter.
So, if we hear the question: How many?, Then we are talking about objects. If: How Much ?, then we are talking about classes of objects! Will we discuss it?
The question is actually not an idle one. I often come across models that do not accurately convey the meaning of what was said. For example, a car owner may say that his car contains a group of wheels. He could say that the car contains wheels, and that would be a completely different statement. What confuses me is that in the models I saw, the difference between these two statements is not made. However, in practice, there is a huge difference between them. Try to practice finding this difference yourself.
Modeling using UML adds fuel to the fire because, firstly, it does not allow modeling classes of objects ( Modeling functional and physical events in a logical paradigm), and secondly, it does not allow semantics to connect the class of objects and the object. Thus, in the field of modeling subject areas, an unexplored empty space is observed. I will allow myself to frolic a little on this field to show how really fun it is. Today I will talk about how my question is related to the concept of countability and uncountability of a noun.
Let me remind you that those nouns that designate individual objects that can be counted are considered countable. An example of a countable noun is the term spoon. This term refers to an object that is, firstly, indivisible, and secondly, we can create many such objects.
Countless nouns denote materials and other objects that are considered in the language as mass or multitude, and not as separate objects. An example would be such nouns: water, sugar, furniture. Note that in this definition there is mention of the set. This is what we are using now. I will try to prove that uncountable nouns describe sets, not objects. Thus, I will show that our consciousness operates with equal success both objects and sets of objects.
Suppose we store sugar in 1 kg slices. We chop a small piece from this piece and put it in tea. This method of use seems to us obvious, but it is not so obvious.
Suppose that in a certain country sugar is consumed in the form of a piece weighing 1 kg whole. In this world, there is no knowledge that sugar is divided into parts. Therefore, a piece of sugar, split in half, is sent to the factory for remaking, and they do not use it. A meter in such a world takes sugar into account only in pieces of 1 kg. Use the pieces as follows: put it in a tub with water and drink everyone with sweet water. Once a worker loading sugar stumbled, and only half of the sugar fell into the vat. The worker was very afraid that he would be punished and pretended that he was not at work. However, what a surprise it was when in the morning it turned out that people were still drinking sweet water and were happy with it! He told the master about this, and the two of them turned to the local scientist to help him deal with the problem. The scientist looked for an answer for a long time, until he realized what is the matter in accounting. Sugar - a substance that can be considered in another way - by weight! Since then, the technology for producing sweet water has been greatly simplified.
Now they could do it at home literally in a cup. This means that a piece of 1 kg could now be looked at as a collection of pieces. Pieces could be obtained arbitrarily, the main thing is that their mass be given. Sugar accounting has evolved from accounting for pieces in pieces to accounting for the mass of pieces. After some time, people realized that it was possible to grind sugar for sale, and sell it in the form of piles, like sand. Thus, accounting for sugar turned into accounting for many small pieces that no one already considered, but took into account the total mass. That is, now counted a lot, but not objects. In the final passage of grinding, we get powdered sugar. Powdered sugar is also a lot of small parts. And we take it into account as a set by weight. More interesting: fluid is also a multitude. And we take it into account like sugar. It turns out that water is a lot.
Now a little linguistics. We say: give me nails, and we can also say: give me water. Nails are in the plural, and water is in the singular. Water in this context is plenty. Therefore, it is in the singular. We can come up with a name for many nails: a bunch. And then we can say: give me a bunch. A heap is also a designation of a multitude.
Therefore, I conclude: if we are talking about uncountable nouns, then we are talking about sets. And if about countable, then about objects. But the one and the other accounting method is equally accessible to us.
You will say that a substance is a substance and that it can be divided. You are wrong. You can share everything, would be technology. For example, you can divide a spoon. But not the way you are used to. But in a different way. Imagine that the technology of splitting a spoon into parts was invented. Let these parts occupy a volume, they can be used as spoons, but these spoons have the property of being less durable, because they are more loose. However, for some purposes it is permissible to divide a spoon into two equal looser parts, but for some purposes not. If we can divide the spoon into parts in an arbitrary proportion, we get an analogue of dividing the substance into parts. But now we were able to divide not a substance, but a functional object into many functional objects. So it all depends on the technology available to us and the accounting method.
In how many ways can water be divided into parts, assuming that the smallest part of the water does not exist? In answering this question, we must commit violence against common sense: we must move on to the concept of a point and the concept of continuum. There will be a huge number of ways to divide water into parts. The power of so many divisions is M3, or the continuum continuum. It seems to me that the complexity of this design led the Greeks to a version about the molecular structure of matter.
So, if we hear the question: How many?, Then we are talking about objects. If: How Much ?, then we are talking about classes of objects! Will we discuss it?