My Perspective: Abstractification

As someone who is engaged in philosophy, I opened this blog because I now want to share my ideas with others. I am curious about what people have to say about my thoughts. For this reason, I want to start by sharing the perspective I am currently using. Rather than explaining this perspective from scratch, I will share a philosophical piece I wrote a few months ago, which serves as an introduction to the perspective. This piece not only covers the foundations of the perspective but also includes some ideas that I built using this perspective, which I no longer strongly defend. My main goal is to show how this perspective can be applied. In the future, on this blog, I will be sharing ideas I find intriguing that I have developed using this perspective. However, I don’t plan to only share ideas built with this perspective; I also plan to share ideas that I have developed through other methods. I might even share some older ideas from time to time. Anyway, now I’ll leave you to this perspective.

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First of all, I'd like to mention that I don't have any formal academic background in philosophy. I'm just someone who engages with philosophy at a hobby level in my spare time, and I wouldn't consider myself particularly knowledgeable in this field. So, the ideas that seem logical to me might seem illogical to you. I'm sharing this perspective because I believe many philosophical ideas can be constructed from this point of view. For some time now, I've been compiling small thoughts I've had in the past and organizing them into a coherent perspective. In fact, these are quite obvious and noticeable ideas, yet I haven't seen them examined through a unified perspective before. I believe that a perspective built on these small ideas could provide answers to many questions. Part of this perspective actually contains conclusions that anyone can reach with basic reasoning. Where this part ends should be fairly understandable. The other part consists of my own thoughts, ideas I haven't been able to substantiate very well. In this piece, I've touched on many topics. The ellipses between paragraphs indicate a shift in topic. Since there are many subjects that could be examined through this perspective, I felt the need to do so. You'll come across sections that may seem disconnected from the main idea; I wrote these sections months ago but decided to include them anyway. Because of this, there may be points you don't fully understand until you've finished reading. If you want to understand this perspective, you'll need to read the entire piece and reflect on each point. I haven't written down every detail about this perspective; if I had, it would have been much longer.

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According to this perspective, all things—whether physical or non-physical, thinkable or unthinkable, existing in this universe or not, existent or nonexistent, and even those that cannot be examined through the duality of existence and nonexistence—are positioned along a vast spectrum ranging from the most abstract forms to the most concrete forms. The lower end of this spectrum consists of relatively more concrete forms, while the upper end consists of relatively more abstract forms. The elements within this spectrum are connected to each other and point to one another. This spectrum resembles a peculiar tree with no clear roots or branches that meet at a single point; instead, it branches out in many directions without an end—a vast branching with neither a beginning nor an end. You might say that mentioning branching here contradicts the concept of a spectrum, but once you understand this perspective and think a little more about it, you'll understand why this is the case.

To be more specific: whenever we think of any abstract concept, it inevitably has a physical projection. This concept has a physical representation that can be shown through neurons. Conversely, when we consider anything on the physical plane, we have a tendency to give it meaning and form an abstract version of it in our minds. In fact, all of our perceptions are inherently more abstract than the physical plane itself, because we can’t place the physical object itself directly into our minds. However, an abstract representation of that physical object can exist in our minds. To think about this differently: you’re reading this text on a computer, yet the text itself isn’t literally “inside” the computer, as it doesn’t exist in a form that can be directly placed inside the device. To represent this text, we must abstract it and transform it into data composed of 0s and 1s. This data is then placed on an electromagnetic plane; in other words, we concretize the data by turning it into an electrical signal. Here, two distinct concrete planes—the computer and the brain—are both pointing to one single abstract form, which is this text.

In short, every abstract thing has a physical projection—that is, it has a concrete form. And every concrete thing can have an abstract projection. I say “can” here because we can create an abstract form now, even if it doesn’t currently exist. But if an abstract form already exists, it must have had a prior physical projection and therefore must have a concrete form. Here, I referred to a "physical projection," but this concrete form does not necessarily have to be on the physical plane; it can be another kind of concrete form. I’ll come back to this point later. I’ve mentioned that forms exist on an abstract-to-concrete spectrum. But what exactly am I referring to? To illustrate with a small example: think of the number "3" versus "3 apples." Since "3 apples" is a more concrete form compared to the abstract "3," it would be positioned lower on this spectrum.

I’d also like to mention a detail here. Why are concrete forms considered to be on the lower end of the spectrum, and why are abstract forms placed on the upper end? This detail is included to make the idea easier to understand. For example, in computer science, when you approach the physical plane, meaning when you get closer to Assembly level, it is considered to be at a lower level. Conversely, when you reach a syntax that is more similar to mathematics, such as Python, it is considered to be at a higher level. In any field, when something is described as being at a higher level, it implies a more abstract form, while when it is described as being at a lower level, it refers to a more concrete form.

According to the previous example, "3 apples" might be considered concrete, but the three apples we are holding right now would also be classified as "3 apples," and ten years from now, the three apples we are holding will still be classified as "3 apples." Therefore, we can't call the "3 apples" form concrete in this context, because it has a more concrete counterpart on the physical plane. When we think more generally, if we write these forms as "3, 3 apples, the 3 apples I'm holding right now," we can see that the forms become more concrete as we examine them in order. Conversely, if you examine them in reverse order, you can see them becoming more abstract. The main idea here is this: a form can never be absolutely abstract or concrete. That’s why the abstract-concrete duality should not be examined with classical logic. A form can be abstract in comparison to one form and concrete in comparison to another form. Therefore, it would be more accurate to examine this duality using fuzzy logic.

You may notice that the meanings of the words "abstract" and "concrete" in this perspective are different from the definitions and concepts we are accustomed to. The reason for this is that I wanted to make this perspective easier to understand by relating it to familiar concepts. I could have used entirely different words instead of these two, but I didn’t feel the need to. In fact, the concepts defined here are examples of the abstract and concrete terms commonly used in daily life.

As you may have noticed, an abstract form can refer to many concrete forms. For example, the number "3." This "3" can refer to "3 apples," or it can refer to 3 tables. It can also refer to the 3 apples I am holding right now, or the 3 apples that someone on the other side of the world was holding 10 years ago. There is a branching process here, and this branching moves toward forms that are becoming more concrete. The opposite can also happen. "3 apples" refers to the number "3" and the concept of "apple." In the previous example, I said "can refer," but in this example, I said "refers." The main reason for this difference will be explained later. The number "3" here refers to empty sets, as explained in Zermelo-Fraenkel set theory, or in another abstract algebra concept that forms numbers, "3" refers to something else. To make this clearer, let me give an example. What set does the expression "{1, 2, 3, ..., 10}" remind you of? Isn't it the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}? This is because of the way we've learned it, as well as cultural influences. But the concrete form of the expression "{1, 2, 3, ..., 10}" doesn't have to be the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The concrete form of "{1, 2, 3, ..., 10}" could also be the set {1, 2, 3, -1, 0.5, π, √2, e, i, ω, φ, 10}. In fact, the expression "{1, 2, 3, ..., 10}" could have infinitely many different concrete forms. This process is called concretization. When we think about the opposite, the same is true. If we consider the set {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}, its abstract form could be the expression "the first 10 prime numbers" or the expression "{2, 3, 5, ..., 29}". From this, we can see that the set {2, 3, 5, 7, 11, 13, 17, 19, 23, 29} could have infinitely many different abstract forms. This process is called abstractification.

Now, I will provide formal definitions for the processes of abstractification and concretization, and try to explain them with other examples. Abstractification is the general term for operations in which something serves as input, and the size of the data within the input decreases relative to the output, scaled by a factor. Concretization, on the other hand, is the general term for operations in which something serves as input, and the size of the data within the input increases relative to the output, scaled by a factor. The "data size" here is related to the scale. In other words, changes in data size that occur without a change in scale do not fall under this definition. Although the thing being examined may be the same, the data size can differ according to the scales. The key point here is this difference.

Now, I will provide an example where the process of abstractification is not involved. At time t1, I have 1 apple, and at time t2, I have 3 apples. The change between these two moments is not a process of concretization. If we did not take the scales into account, we would have to consider this as a process of concretization according to the formal definition. Let me briefly explain the concept of "scale." At time t1, we are only examining the fact that there is one apple. At time t2, we are examining how many molecules the apple contains. The change between these two moments is due to the concretization of what we are examining. The concept of scale I am referring to is related to this. To make this concept clearer, it might be helpful to think of the "scale" concept in map scales. When we use a large scale on a map, the detail of land boundaries will increase, just like how, at time t2, we go into more detail. But we will be aware of less about the thing we are examining. For example, it would be difficult to understand exactly where a region on a large-scale map is in the world. The same situation applies in the previous example. If at time t2 we had examined the molecules without having any idea about the thing itself, it would have been difficult to know what we were looking at. The reason for this difficulty is something I mentioned earlier. Concrete forms, the more concrete they are, the more abstract forms they point to. This is also true in the reverse. In fact, we can think of scale as something like detail, but this wouldn't be entirely accurate for every example; however, we could say that increasing detail is a kind of scaling up.

If you examine the branching I mentioned earlier at a small scale, you could call it a spectrum. However, it's not necessary to only do this at a small scale; if you examine it with a large enough scale and the area you are studying remains small, meaning if you only look at one branch, we can still refer to it as a spectrum.

Let's now turn to the concept of data size in the formal definition. At time t1, the thing being examined was only 1 apple. There was only 1 thing being examined. But at time t2, the things being examined, meaning the molecules, total up to a number with 27 digits. As we can see here, in the process of concretization, the data size increases, whereas in the process of abstractification, it decreases. Let's look at another example from the previous one. Mathematics and physics. According to this perspective, mathematics is the abstract form of physics. Physics is the concrete form of mathematics. When we examine them in terms of data size, the number 3 in mathematics is just the number 3. But when we concretize it, meaning when we examine it with physics, the number 3 can represent mass or energy units. A physical case, where all the details are provided, such as time, location, and all specifications, is 1 in the physical plane. In other words, the case being discussed cannot exist in more than one form in the physical plane. But this is not the case in mathematics; that physical case can be explained by multiple theories. This is because, as I explained earlier, concrete forms point to multiple abstract forms. This is also true in the reverse: a single physical theory can have many examples of cases. In this example, we can see how the scale changes and what consequences this leads to.

Now, let's examine everything I've explained so far through an example. Let's imagine a blank chessboard. We won't think about the pieces on the board, just the colors of the squares. The top half of the board is completely white, and the bottom half is completely black. How many words would you need to express the color arrangement of the board? It can be expressed in one sentence, right? Now, let's examine this situation in more detail. Earlier, we performed an abstractification process. We were able to express the data of 64 squares, meaning 64 different data points, in one sentence: "The top half is black, the bottom half is white." As you can see, in this abstractification process, there is a significant loss of data, but no loss of information. If a brain that can understand this sentence processes it, there is no loss of information as long as an algorithm is in place, but if a brain or algorithm cannot understand this sentence, it would not be able to reconstruct the 64 individual pieces of data, resulting in significant loss of information. In this abstractification process, the processes in the brain are referred to as "algorithms" in this perspective. Algorithms are the set of rules that tell us how to perform abstractification and concretization. When returning from an abstract form to a concrete form, the information loss depends on the algorithm. Now, let's return to our example. This time, let the color distribution of the squares be random. How would you transmit these 64 different data points to the other party? You would list the 64 pieces of data individually, right? Yes, but there is actually one more answer: "Random." I described the condition of the board in the current example just like this answer. If you had listed the 64 pieces of data individually, the abstractification process at the scale we are examining would have been minimal. The reason for the minimal abstractification in this example is that we didn't include the board itself in the data, but only examined the positions of the colors. There would have been data loss, but no information loss. But if you had said "random," the abstractification process would have been much greater. At the same time, there would have been significant data and information loss.

As you may have noticed, in some abstractification processes, there is a loss of information, while in others, there is not. However, there is always a loss of data. In abstractification processes, information loss depends on the magnitude of the abstractification process and the scales involved. Now, let's think about the initial arrangement of the chessboard in the previous example. In this arrangement, by saying "the top half is black, and the bottom half is white," we divide the board into two parts and consider the squares within those parts to be the same. For example, by saying "square 1 and square 2 are the same," we treat them as "unchanging." The concept of "unchanging" is used in this perspective. In the sentence "The top half is black, the bottom half is white," by ignoring the differences between square 1 and square 2, we reduce the scale and treat those two squares as identical. In fact, in this case, we can say that there are only two things on the board: the black section and the white section. As you can see, the scale has been reduced. This is the relationship between abstractification processes and scales.

Now let's think about this chessboard again. We have a time interval, and at the beginning of this period, the top half of the chessboard is black and the bottom half is white. As time progresses, the positions of the colors change, and the number of words required to describe the data on the board increases. By the end of the period, the colors of the squares would need to be described individually. In this time interval, the complexity has increased. If we consider the black squares as areas of high energy, entropy has also increased. However, not every board arrangement with high entropy necessarily requires an increased number of words to describe it. For example, consider the typical arrangement of colors on a chessboard. According to this arrangement, entropy is very high, but it can be described in a simple sentence. In fact, from this, we can see that entropy does not mean disorder. In systems where complexity increases in terms of abstractification, entropy increases as well, but in systems where entropy increases, complexity in terms of abstractification does not necessarily increase. I wanted to show that there is such a connection between entropy and this perspective.

Now that we've reached this point, I would like to talk about symmetries. Symmetry is the property of an object or system where a feature is preserved under a certain transformation. This definition is quite similar to what we've discussed earlier, isn't it? Since we now consider the 1st and 2nd squares to be "the same," we can say that there is symmetry here. The transformation that reveals this symmetry can be taken from anywhere. Abstractification processes that do not involve information loss are also done through these symmetries. In the "random" case of the board, however, these symmetries are ignored, and abstractification occurs. Because this abstractification process disregards the symmetries, information loss happens. I would like to introduce a new concept here: the "abstractification limit without information loss." The abstractification limit without information loss is the highest level of abstractification in which no information is lost during the abstractification process. This limit is defined by scales and symmetries, and different algorithms have different limits.

Let’s examine another example: consider the graph of x^2. I’m not talking about the graph of x^2 drawn to show someone else; I’m referring to the ideal graph of x^2 where both the x and y axes are infinite. Such a graph cannot be represented with a certain degree of concreteness because it contains infinities. Since there are no infinities in the physical plane, we can say that, compared to the graph drawn to show someone else, this ideal graph is an abstract form. Now, think about the algebraic representation of this graph. I initially used this representation, x^2, to refer to the graph. What’s the difference between these two forms? Let’s think about this question like this: imagine we have a computer, and this computer somehow performs calculations based on the ideal graph I mentioned earlier. Of course, I’m not sure how such a thing would be possible, but this computer would consume a vast amount of power and resources even for the smallest operation since it would be looking at an infinite graph. However, performing these operations using the algebraic form is much easier, which is why modern computers perform these operations in binary, which is simpler for computers, rather than directly using the algebraic form. In the algebraic form, all we do is multiply the input by itself. But in the ideal graph, we need to find the input along the infinite axes. The ideal graph, the algebraic form, and the binary system—these three forms point to something even more abstract, in the sense that as long as the inputs in these operations remain unchanged, the outputs don’t change, even if the operations differ. Here, we have invariants. Even if we make transitions between operations, that is, perform transformations, invariants emerge. Therefore, these three forms point to a more abstract form. I had previously mentioned that transformations could be taken from anywhere when discussing invariants. That means we can take any input as the input, and for each input, an invariant will emerge, just like when we divide the chessboard in half, make one part black and the other white, and apply a transformation between the 1st and 2nd squares in the previous scale, yielding an invariant.

As the scale decreases, the similarity between the elements within the system increases. At some point, the elements within the system become identical to each other. In the case of Huygens synchronization, this is no different. In fact, Huygens synchronization is an example where we can observe the abstractification process in its most concrete form. In situations where the scale increases, the element within that system is divided into parts according to the concretization algorithm. I had previously mentioned that an abstract form must already have a concrete form. I think what I meant here will now be clearer. That is, when we say that something is divided into parts, we are already implying that it can be divided. In short, in abstractification processes, we reduce the scale and accept that some parts of the concrete form are the same as each other, treating them as "the same" thing. The things we accept as "the same" are invariants, which brings out symmetries. On the other hand, we perform the concretization process by increasing the scale and dividing the abstract form into parts. Abstractification algorithms, being a set of rules that determine which elements are invariant, reduce the scale according to these rules. In other words, abstractification algorithms tell us which parts of the object are invariant with respect to each other. Concretization algorithms, being a set of rules that determine how the object is divided, increase the scale according to these rules. That is, concretization algorithms specify how the object should be divided. Numerous examples can be given to illustrate these concepts.

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I want you to imagine a square in a two-dimensional plane. When you rotate this square by 90 degrees in any direction, what changes? Nothing changes, right? Because there is a symmetry here. Through this symmetry, we obtained invariance. But let's increase our scale a bit. Now, when you rotate the square by 90 degrees, we can no longer say that we obtain the same square. This is because the arrangement of the molecules on the right edge and the top edge of the square is very, very likely not the same. As we can see, we did not get the same square. The symmetry we identified earlier does not hold in this case. Here, I am explaining it from the physical plane, but this larger-scale concrete form does not have to be in the physical plane. The main point I am trying to convey here is that when we increase the scale, symmetries disappear, and this is essentially the concretization process itself. In fact, here we performed an abstractification from the geometric plane to the physical plane, but this concretization process does not always have to be done in the physical plane. I will return to this topic later. As can be understood from this, mathematics is the abstract form of physics. One might argue, however, that mathematics does not show physics and contradicts physics in many cases. Yes, but these are not things that contradict the concepts in this perspective. Abstract forms can be completely unrelated to concrete forms, such as the difference between what has been written about happiness throughout history and the unrelatedness between serotonin, dopamine, and other hormones. One is a literary work, while the other is nothing more than a molecule made up of a few elements. Returning to our topic, the question of whether mathematics is an invention or a discovery is answered by this perspective as "mathematics is the abstract form of physics." In this abstractification process, alongside things that are found in nature, human culture also plays a part. Therefore, it is neither entirely an invention nor entirely a discovery. We could say that the more concrete concepts of mathematics are discoveries, while the more abstract concepts are inventions. However, this classification is not entirely accurate. The reason mathematics produces such accurate results is that it takes into account the abstractification limit where there is no information loss and considers symmetries. In other words, it reduces the scale by considering countable things solely based on their countability and expresses many invariants with numbers. This is why anything countable can be expressed by mathematics and yield consistent results.

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If you're curious about the relationship between complexity and this perspective, I would like to touch on this point. What I previously mentioned about "explaining in one sentence" has a similar counterpart defined by a mathematician for computer science. Kolmogorov complexity is a measure of how a given object, typically a sequence, can be described by the shortest computer program. This concept was developed by the Russian mathematician Andrey Kolmogorov and is generally associated with algorithmic information theory. Kolmogorov complexity refers to the length of the shortest program required to generate a sequence. For example, if a sequence is completely random, the program required to generate it will be long, meaning the sequence has high Kolmogorov complexity. However, a regular and repetitive sequence can be described by a short program and will have low Kolmogorov complexity. This process is an abstractification. Here, Andrey Kolmogorov actually defined complexity by the smallness of the source used to express the object. What Andrey Kolmogorov said here in the fields of mathematics and computer science is not only applicable to those fields. It can be discussed in many other areas and examples as well. And what is being referred to is the abstractification process.

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In physics, the concepts of coarse-graining and fine-graining are actually processes of abstractification and concretization. What I’ve discussed about abstractification and concretization applies to these concepts as well. In fact, many of the concepts we encounter can be defined through the processes of abstractification and concretization. There are many types of processes in the things we’ve discussed. This perspective categorizes these processes. Essentially, what this perspective does is an abstractification process. It divides an uncountable number of process types into two categories, treats their content as the same, and reveals even more abstract concepts. From what we've discussed so far, you can see the relationship between data and information. Information is the abstract form of data, and information is obtained by abstracting data. If the entity acquiring the information were a brain, it would abstract the data from sensory input to obtain knowledge. If it were a processor, it would abstract the data in memory and send it to the screen in RGB format. Here, we can consider the RGB data as information relative to the data in memory. Similarly, if we abstract the data of kinetic energy of molecules in a physical system, we obtain the information about the system's temperature. I mentioned that the abstractification process is carried out with invariants, symmetries, and scales. These symmetries reveal a certain pattern. Information is that very pattern. Science works the same way; it reduces the scale by considering the abstractification limit with no information loss, and then the invariants at that scale form a specific symmetry. These symmetries then reveal patterns. Because the limit I mentioned is considered, there is no information loss.

However, the abstractification processes in social discussions do not consider this limit. Our judgments in social matters often point to abstract forms. In other words, the judgments we place on a social class refer to that abstract class. When making these judgments, we examine the abstract form of the class. That means, most of the time, we do not talk about the individual, their past, what they did, or their nerve cells. The "Sonder effect" is related to this. We often project the judgments we make about abstract forms onto their concrete forms. In social matters, abstract forms tend to exceed the limit of abstractification where no information is lost. This, I believe, is the fundamental cause of most social discussions. A person who dislikes an ethnic group cannot possibly dislike every individual from that group. It is impossible for them to meet enough people from that group in their lifetime. What they truly dislike is the abstract form of that social class. This abstract form of a social class exceeds the limit of abstractification where no information is lost. Because from that abstract form, you cannot even reach the name of any individual belonging to that class. In fact, it is very difficult to even know how many people belong to that class at any given moment. New people are born and die all the time. Here, I gave examples related to social classifications, but what I am saying applies to any classification. Not only for social classes but also for political ideologies. There are countless different political scenarios that could be classified under a political ideology. The chances that the judgments we place on that ideology apply to all those scenarios are very low. Judgments made about such abstract concepts—if the abstractification process does not exceed the limit of abstractification where no information is lost—are valid for their concrete forms as well. But if they exceed that limit, they may not be valid for their concrete forms. Many social judgments exceed this limit, leading to invalid arguments. When we don't know enough about a person and want to make judgments about them, we look at which ideological movements they are close to. We then apply the judgments we have previously placed on those ideological movements to that person. Since there is so much data on that person, and analyzing all that data to make a judgment is very difficult, we abstract that person to a particular ideological movement and apply the judgments we had made earlier about that movement to them. If we used a highly detailed language, such as Ithkuil, the likelihood of not being understood in everyday life would be lower, because Ithkuil keeps the scale very large when naming things. I won’t explain the entire relationship between the Ithkuil language and this perspective here, but with what I've shared so far, you can infer many of the details.

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According to this perspective, classical logic is an abstract form of fuzzy logic. In classical logic, there are definite classifications. For example, if you examine an element within a classification using classical logic, you can definitively say that the element belongs to that class. But when we increase the scale, that element may not definitively belong to that class. In fact, it might not belong to any of the classes we’ve defined. According to fuzzy logic, the element could be at the intersection of classes. It's similar to a virus. The philosophical debate about whether a virus is alive or not is still ongoing, but it doesn’t have to be strictly alive or non-living. It can occupy an intermediate form. Ultimately, the concepts of "alive" and "non-living" were created by us. These abstract concepts are a product of our abstractification. We abstract a system made up of molecules and then label it as either alive or non-living. Any system that does not engage in this abstractification process cannot make such a simple and instinctive distinction between alive and non-living systems, nor even recognize this distinction. And this instinct is nothing more than another form of an abstractification algorithm. By the way, I mentioned that the debate over whether a virus is alive or not is still ongoing, but in most literature, viruses are considered non-living. The discussions I refer to are mainly philosophical debates. In short, when we examine something that involves classification, we use classical logic to assert that the element definitely belongs to that class. We can create more classes to obtain more consistent results. Increasing the number of classes is a form of concretization. In fact, when we examine something using fuzzy logic, we are performing this concretization. It is better to examine the difference between classical logic and fuzzy logic in terms of scales. The judgments that classical logic can make are either 0 or 1. It cannot make judgments for any values between 0 and 1, because it does not have a scale that accounts for those values. Fuzzy logic, however, makes judgments by considering the necessary scale values. Essentially, what is done in this perspective is to increase the scale in order to examine the values between abstract and concrete, and it suggests that the abstract-concrete duality should be examined using fuzzy logic. It could be argued that it’s not reasonable to examine everything in detail using fuzzy logic. Yes, that’s true. What I’ve emphasized so far applies to abstractifications that exceed the limit where no information is lost. In situations already analyzed with classical logic, where no problems arise, symmetry can be clearly observed. For example, "2 is a prime number," where the property that makes the number prime gives us a definite idea about whether the number is prime. But this is not the case with examples like "the weather is hot."

To make the concept of the abstractification limit with no information loss and information loss clearer, I will provide two examples. In our first example, let's consider a society, and we have all the data of this society in the physical plane. A general election is held in this society, and we have the data of the vote counts as a result of this election. There is an abstractification process here. The society is abstracted, and the data of the vote counts are obtained. Now, let's imagine all the possible societies, whether they exist or not, that would result in these vote counts, and group them into a set. The number of elements in this set is vast, and the society we initially considered is one of the elements in this set. If we select any society from this set, the degree of concreteness of that society will be the same as the initial society we considered, and if we apply the same abstractification process that I mentioned to obtain the vote counts, we will get the same results. The number of elements in this set is directly proportional to the amount of information loss. Now, let's examine a different example with less information loss. Consider a system with a known volume that contains molecules. When we measure the average kinetic energy of the molecules, we obtain the temperature of the system. Again, there is an abstractification process here. Let's take all the systems, both existing and hypothetical, that would result in this temperature value within the given volume, and group them into a set. The number of elements in this set is still large, but it will be noticeably smaller than in the first example. Of course, the size of this number can change proportionally with the volume, but since we are talking about a system of normal volume here, this number will be smaller than the one in the first system. Therefore, the amount of information loss in the abstractification process of the second system is less than the amount of information loss in the abstractification process of the first system, and for this reason, the abstractification limit with no information loss is exceeded to a lesser degree in the first system.

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We create meaning through the process of abstractification. To give the simplest example, select a pixel in the middle of a video you're watching. Now, imagine that the entire row and column of that pixel disappear. You will still be able to extract the same meaning from the video. Of course, the size of the pixel matters in this example, and that is related to scales. This abstractification process is a fundamental part of human perception and mental processes. The human brain, when interpreting the data it sees, hears, or experiences, often disregards details and focuses on extracting the general patterns and meanings. Here, I am referring to our experiences. For instance, when we look at an object, we don't analyze the exact tone of its color or from which angle we are viewing it in great detail. Instead, our brain categorizes the object: a car, a tree, a face, and so on. In fact, I believe there is a strong similarity between reducing scale in our understanding and how, when maps reduce scale, the location of a point in the world becomes clear.

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I will make additions to the branching concept I mentioned earlier, as I believe this will make it easier to understand. When you reduce the scale of something while examining it—meaning you treat some of the things within it as interchangeable—you are accepting that it has an abstract form. The opposite is also true. If you increase the scale of something—meaning you break it down and talk about its components—you are accepting that it has a more concrete form, according to this perspective. You can apply this concept to anything you can think of in the paragraph I just described. This will lead to the branching I mentioned at the beginning. To illustrate this with a narrow example, when we use the phrase "it doesn't matter" in daily life, we are actually performing an abstractification. As a result of this process, we point to an abstract form. By saying "it doesn't matter" to multiple things, we claim that those things are invariant and reduce the scale. For the phrase "it matters," we increase the scale and perform a concretization process by breaking down the things we've mentioned and showing that they are not invariant. As a result, we point to a concrete form. When you use the phrases "it matters" or "it doesn't matter" in very different things, concepts, or words, you will be able to see this branching. The abstractification or concretization processes you perform here may lead to incorrect results, but the details of that aren't important at this point. I will address that issue later. The important thing is that the branching can still be obtained, even with incorrect abstractification or concretization processes. You can apply and think about this point wherever words like "similar," "dissimilar," "like," "exactly," or "irrelevant" are used. You can even apply this within this text itself.

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The projection of an abstract form onto the concrete plane, that is, its projection onto the physical plane, means that the more abstract the form is, the more complex its concrete form must be. As you can see from this definition, some of the best examples of this are genes and culture. What is the effect of a gene on culture? Questions like these are very difficult because the culture being referred to here is in a very abstract form. Therefore, the gene that is linked to this culture in a cause-and-effect relationship is very complex. In fact, such topics are so complex that they are almost impossible to discuss, but we can talk about their abstract forms. Since the abstract forms in these topics exist as a result of abstractification processes that go beyond the limit where no information is lost, I’m not sure how possible it is to say anything accurate. Therefore, when we need to make a decision about such complex forms, we perform an abstractification process using systems like numbers and voting systems, and this abstractification process exceeds the limit where no information is lost by a large margin. It could be said that averages are also taken in voting systems and in temperature measurements, yes. However, in temperature measurements, the scale we reduce to treat molecules as the same is not reduced in the same proportion as the scale in a voting system, where we treat people as the same to consider them as the same individual. The information loss comes from these scales.

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In Zermelo-Fraenkel set theory, numbers are constructed using empty sets. Empty sets are sets that contain no elements. The number 0 is considered as the empty set. The number 1 is obtained by a set that contains 0, which is the empty set. The number 2 is obtained by a set that contains 1 and the empty set. This is how numbers are constructed in Zermelo-Fraenkel set theory. If you've noticed, the numbers only contain the empty set. In fact, this situation is no different from abstract forms and the abstractification process. For example, when counting apples, we treat them as empty sets and do not concern ourselves with the contents of the apple, such as what molecules are inside it. This is because our scale is not large enough to deal with such concrete forms. This perspective explains the formation of numbers in this way. When it comes to questions like "Do numbers really exist?" these are abstract forms, but this perspective also contains further details which I will explain later.

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What I am about to explain is not necessarily what this perspective says, but rather what I have been thinking using this perspective. We are able to show the physical projections of the things we experience. We can talk about the physical projections in the concrete realm of our experiences, which are abstract forms. However, we cannot always make sense of everything we experience, even though we can see the physical projections of those experiences. In my opinion, the things we can make sense of are the experiences that are closer to the level of concreteness of our experiences, and the experiences that are closer to the branches in the branching process I mentioned.

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Imagine any photo frame. This photo is blurry, and now try to imagine its clear version. Most likely, you won't be able to guess the real version of the photo because the blurry photo acts like an abstract form compared to the clear one, referring to many different clear photos. Therefore, with this blurry photo, you would choose one form with a certain level of concreteness from a large number of potential clear forms and think about that form. You might ask, isn’t the blurry photo as concrete as the clear one? This would be true if the clear photo was blurred by a computer algorithm. This computer algorithm takes the blurry photo, an abstract form, and brings it into the concrete realm of the clear photo. Essentially, the algorithm averages the values of certain pixel groups in the photo and accepts those values as constants. This process is nothing but an abstractification algorithm. By using these constants, it places the resulting values in the same positions without changing the pixel size. This brings the blurry photo’s plane to the same plane as the clear photo. This process is not only about blurring a photo but also about sharpening it using a specific algorithm. As the photo sharpens, the scale increases, and therefore, the pixel size must decrease, and the pixels must divide into smaller parts. These split pixels must then take values according to the algorithm. These processes show that it should be on a more concrete plane. However, since the pixel size cannot change, photos produced by sharpening algorithms move to a more abstract plane as their width and height increase. This plane is the same as the plane in the original photo. If you notice, the resolution of the photo and the concept of scale in this perspective are very similar to each other. In fact, we don’t need to think about abstract forms in very different contexts; even in physical realms that we all agree on, we encounter these abstract forms. Many paradoxes actually arise here.

When paradoxes similar to the Sorites Paradox are examined from this perspective, the common issue in these types of paradoxes becomes quite clear. The relationship between the heap of sand made up of grains of sand and the grain of sand itself is discussed, and these are attempted to be observed in the same level of concreteness. However, "grain of sand" and "sand heap" do not share the same level of concreteness. A sand heap is a more abstract form than a grain of sand. Therefore, the fundamental cause of paradoxes like this is examining different forms of things in the same plane. In fact, the "sand heap" is not in the physical plane but refers to the fundamental particles that make up the grains of sand, which are a more concrete form than the abstract form of the heap. If we examine another paradox, Theseus' Ship, in this context, the ship's name and the ship's planks are considered to have the same level of concreteness. However, the ship’s name and the planks do not have the same concreteness; the ship’s name is a more abstract form than the planks. Trying to examine an abstract form, like the name of the ship, alongside something directly in the physical plane, like the planks, is a significant mistake, in my opinion. This is not just true for Theseus' Ship, but there is no real connection between things and their names. This connection can only be seen when examined in the realm of human culture. However, this connection is not a physical one. These names are not directly connected to the things themselves, but when we have appropriate abstractification algorithms and abstract the physical plane with these algorithms, we can see what humans have named them within their culture.

Let's consider another example: is the infinity of positive integers greater than the infinity of all integers? The fundamental issue here is the same. It is trying to evaluate things of different forms within the same plane. One number can be greater than another, but one infinity cannot be greater or smaller than another because in order to compare sizes, we need a certain level of concreteness. Of course, in mathematics, sometimes comparing infinities can be useful, but that's not the point here. In short, infinity is a more abstract form than numbers, so comparisons of size don't work for infinities. This leads us to Hilbert's hotel. In Hilbert's hotel, we weren't discussing the physical projection of numbers but the physical projection of infinity. This is impossible, and the problem of Hilbert's hotel begins here. I had mentioned earlier that abstract forms must have a projection into a concrete plane, but infinity does not have a physical projection; there is a projection of infinity in the electromagnetic plane of our brain. An abstract form doesn't necessarily need to have a direct physical projection. It can have a projection in another concrete plane, which is beyond the physical plane.

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In this perspective, algorithms are actually forms within this perspective itself. For example, species are abstract forms. The symmetries and similarities between these species have emerged as a result of evolution. The algorithm here is evolution. The reason we can distinguish these species is because of our own evolution. These evolutionary processes have occurred entirely in the physical plane and have resulted in the emergence of abstract forms that we can perceive. It has done so through evolution. The evolution, which is the algorithm here, is also an abstract form because it is not a form that can be shown at a specific position in the physical plane. It exists due to the statistical representation of certain cases, and it has physical projections.

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I want to talk about the concept of "degree of concreteness." The degree of concreteness is a value that roughly indicates how concrete a form or a plane is. This value can vary depending on reference points, but by default, it shows the distance from the most abstract form. In other words, the physical plane has a certain degree of concreteness, and forms and planes that are more abstract than the physical plane have a degree of concreteness that is greater. In short, this value is used to compare how abstract or concrete forms are and to compare their abstractness and concreteness with other forms.

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When we examine "reality" from this perspective, we get the impression that the more abstract forms, which are examined in a way that decreases their degree of concreteness, have a lower sense of reality. For example, when it comes to numbers, debates often arise about the reality of numbers. And these debates become even more intense when we discuss more abstract forms. In fact, almost all debates are dependent on the degree of concreteness of the form being discussed. When the degree of concreteness decreases, we can observe how the reality of more abstract forms drops compared to the physical plane by examining a few examples. For instance, consider any fictional work. Fictional works are not real, but they contain some level of reality. To give an example: which is more real, the city of Zion in *The Matrix* or the Matrix itself? The reason Zion’s reality is considered higher is that the Matrix is just a program running on a computer. From this, we can easily see that the Matrix is more abstract than Zion. The reality of the Matrix has a projection in the plane of Zion’s concreteness, as it exists in the computer’s memory and processor as electromagnetic data. But the experience within the Matrix and the Matrix itself are in a more abstract form. From this, we can understand how this perspective can explain which forms of reality are considered more real.

For something to be real, it must exist even without any observer observing it. Now, when we examine this in the context of *The Matrix*, it appears that when there are no humans in the Matrix, nothing would be processed, and therefore, everything in the Matrix would be considered non-existent. However, if we consider what I explained earlier, a memory in a more concrete form still contains the data of the Matrix, and even if the Matrix does not exist in abstract form, it still maintains its existence in the concrete plane where Zion exists. The part that retains its existence is not the abstract form, but the concrete form. In fact, the example I've discussed so far comes from a fictional work — namely, Zion, the Matrix, and the processor running the Matrix. None of these exist in our physical plane; they are all fictional. However, within their own context, we accept them as real and acknowledge the reality they contain. In fact, I have used them as examples, treating them as if they were real. In this reality, which exists in a more abstract form than our physical plane, there is gravity, just like in our physical plane, and we can observe the effects of gravity in the scenes we watch. Many similar phenomena are drawn from the physical plane.

Here, I would like to introduce a new concept: the "reality set." A reality set consists of things that are considered real only within that set, and where reality is discussed within that set. For example, when we think of two different reality sets, one reality set does not have to be real for the other. In fact, within one reality set, even the concept of a "reality set" may not be real. These are isolated realities, and only things within them are real according to that reality set. These reality sets do not always have to be isolated, but I will address that later. In fact, our physical universe is like this. Things that cannot be explained by the physical plane are considered "not real." The reason for this is that the physical plane itself is a reality set. For instance, any thought we have does not have to be real in the physical plane. But in the plane of that thought, it is real. Its projection is just the electromagnetic data in our brain. The thing we are thinking of is not real in the physical plane because it does not refer to anything in the physical realm; however, in the concrete plane of our thoughts, it is real. Therefore, anything in the abstract form is real within that plane but does not always have to be real in relation to the concrete plane. As you can infer from this, abstract planes are reality sets themselves.

In this perspective, how can abstract reality sets be discussed in relation to the physical reality set? The answer to this is again in the algorithms; our culture, our history, which are considered algorithms in this perspective, and certain events that have occurred, have led to the representation of these abstract reality sets in the form of fictional works. Here, we can observe that two different reality sets are connected to each other. Therefore, not every reality set has to be isolated. However, one is in a more abstract form. The reason for this lies in the definition of a reality set. If two different reality sets were connected in the same degree of concreteness, they would not conform to the definition of a reality set and would behave as one reality set. The abstract reality set could have a more concrete form, and this concrete form could have a higher degree of concreteness than the physical universe. Nothing prevents this. However, as I mentioned, for the reality set we are in, that concrete form is not real. This is not only true for fictional works but can also be applied to mathematics as a reality set. Mathematics is a more abstract form compared to the physical plane, as I explained earlier. There is no reason why we should not speak of a reality set in which mathematics has a concrete form similar to the physical plane. In fact, this plane could be more concrete in the physical plane. Ultimately, the degree of concreteness of the reality set does not matter. If there are multiple connected reality sets, the connected reality set must be in a more abstract form for the reality set it is connected to. The scale of the data transferred will be reduced. I use the term "transferred" here for easier understanding, but "transferred" is not exactly the right term. After all, think again: if the data from the connected reality set were in a more concrete form than the degree of concreteness of the current reality set, which data would be real? The data from the connected reality set or the data of the current reality set? When we think about the reality set of mathematics a little more, we can examine the concept of infinity. According to recent research, infinity is not real for the physical plane, but in the mathematical reality set connected to it, infinity is real. However, mathematics, being the connected reality set, is in a more abstract form. Therefore, infinity is real for that abstract plane. In fact, things that are not real in the physical plane can be real in more abstract forms, and this is something we encounter almost all the time. Like whether something is true or false. A person's truths are true only within the plane of their thoughts, i.e., in an abstract form. They do not necessarily have to be true for our thoughts or for the physical plane. But when we call something true or false, our reference point is often the physical plane. Because this is the reality set closest to us in common. What I am talking about here is also true for the existence-nonexistence duality. Does a character exist in a fictional work? If not, how can we talk about them? The existence of that character is also dependent on the degree of concreteness. When a fictional work is processed by an algorithm, which could be the human brain, for example, a connection forms between two different reality sets. From here, you can see that questions like "Does knowledge exist?" can easily be answered. If there is an algorithm that processes the data with a concrete form of that knowledge, then yes, that knowledge exists. But if that data is not being processed right now, then no, that knowledge does not exist. If that knowledge has been concretized and "written" somewhere and is not being processed, it still does not exist. But whenever that written data is abstracted and processed, meaning it is read and understood, that knowledge exists. The concepts I explained here are based on fictional works, but what I have explained is not limited to fictional works; it applies to anything that can be considered a reality set.

Now I will talk about the concept of "degree of reality" and its differences from the degree of concreteness. As you can understand, the degree of reality is a value that shows how real different reality sets are in relation to the current reality set. If there is a reality set that is connected to the current reality set, it can be said that the degree of reality of the connected reality set is greater than 0. The more the connections increase, the greater the degree of reality becomes. For example, mathematics is more real than fictional works. Although both reality sets are in abstract form, the reason for this is that the mathematical reality set has more connections with the current reality set. The field of physics also studies these connections mentioned in the previous sentence. However, the connections in fictional works are not as numerous. Most of the time, the reality set of a fictional universe is connected to the current reality set through ink marks in a book. However, an abstract form of the physical plane does not have to have another concrete form on the physical plane. Examples from fictional works actually fit this situation exactly. Therefore, the degree of concreteness and the degree of reality are different levels. Although the degree of concreteness may be greater than the degree of concreteness of the reality set of the physical plane, the degree of reality can still be 0. This means that there is no connection between these reality sets and the current reality set. Despite the degree of reality being 0, the degree of concreteness may be the same as, or even greater than, the degree of concreteness of the physical plane.

I will now show the relationship between Leibniz's Principle of Identity and these concepts, and how we can talk about a plane in a more concrete form than the physical plane. According to Leibniz's Principle of Identity, if two different things have the same properties, then those two different things are actually the same thing. This gives us a way to show the scale value of the physical plane. However, by discussing situations where two different things with the same properties are not the same, we can talk about a plane in a more concrete form than the physical plane. But this plane would not be real for the current reality set, because it would belong to a different reality set. In fact, we can see a similar situation by examining the relationship between mathematics and physics. Let's consider the properties of the number 2. In the physical plane, there are many things that can be defined by these properties. All of these things have the same mathematical projection, and in mathematics, they are not different things. For mathematics, they are all the same thing, the number 2. In fact, by using the terms "different" or "same," I may have reminded you of things I previously explained. What I discussed there is also applicable here.

In fact, in abstractification examples, a reality set is always obtained. I think you can see why from what I have explained and the examples I’ve provided. I won’t explain it again here. In short, the things we abstract don’t necessarily have to be real according to the current reality set. So, are there infinitely many different reality sets? After all, an infinite number of abstractification processes can be made. I haven’t discussed the existence of reality sets here. That’s why I’m not saying "there are infinite reality sets." I’m only saying that reality sets can be discussed. Based on what I’ve explained earlier, we can say that the universe outside of our observable universe is in a more abstract form, relative to our reference. The universe outside of the observable universe is still in the physical plane, but in our reference, it is simply a reality set shown by science. Since science takes into account the abstractification limit where there is no information loss, it can be said that there is a strong connection between the reality set of the current observable universe and the reality set of the universe beyond the observable universe. In fact, similar concepts can be examined in a similar way with this perspective. For example, parallel universes are reality sets. If we consider the probabilities in the wave function as an abstract form, and the collapse of those probabilities as their concrete form; when we observe the physical plane where the probabilities have collapsed, we can say that another probability has collapsed in a different reality set with the same degree of concreteness as the physical plane. However, the collapse of this other probability is not real, due to the definition of the reality set.

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We give names based on scale. That is, when we consider everything in the universe as the same thing, the name of that thing becomes "existence." However, as we increase the scale, the number of things to be named increases, and therefore the number of names increases. The number of names used in everyday life is fewer than the number of names used in technical fields. For example, the thing we call "molecule" in daily life can have thousands of different names when the scale is increased, such as "amino acid." When we concretize this naming, we get names like glycine, lysine, and phenylalanine. To give another example, the word "glass." If we keep the scale small, we call all glasses "glass," but when we increase the scale, names like "water glass," "tea glass," "coffee glass" (which actually has another more commonly used name, "cup") appear. The differences between these glasses are often cultural, meaning you can drink coffee in a tea glass. Sometimes these differences can be functional. For example, cups generally have handles because coffee is usually hot. But this is not observed in water glasses. If you notice, the functional differences are in a more concrete form than the cultural ones. To explain these two classes of differences in the physical plane, we would have to scale up the cultural differences much more than the functional differences. The reason for these differences is explained through the concept of algorithm in this perspective. What I’m trying to convey here is that throughout history, we have named things based on certain scales, and we continue to do so. In everyday life, when we keep the scale large, multiple names we use are often met with the question "Aren’t they the same thing?" The fundamental reason for this question is that individuals use scales with different values.

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I’ve talked a lot about abstract and concrete forms, so what can be said about the most abstract or most concrete forms? When we examine the most abstract form, in order for it to be the most abstract, it must contain as little data as possible. This is because, according to this perspective, as the degree of concreteness of forms increases, the amount of data within them must also increase due to scales. Therefore, in my opinion, the most abstract form is "nothingness." Because we cannot say anything about nothingness itself, we can only talk about the name we give it, "nothingness." The reason for this might be that nothingness contains no data. I believe that after enough abstractification, we would end up with nothingness, but I’m not entirely sure about this. In the most concrete form, however, we can say that it must contain infinite data. But, unlike nothingness, I don’t think there will be a limit to the amount of data, so I don’t believe it would have an end. In other words, the most concrete form might exist at the very bottom of the spectrum I mentioned earlier. If the most abstract form is nothingness, then the branching I mentioned earlier would resemble the branches of an inverted tree. The root of the tree would be nothingness. So, there would be a point at the very top, and from that point, a branching extending infinitely downwards. Of course, I’m not entirely sure about these ideas.

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We can encounter many common patterns across different disciplines. These common patterns point to an abstract form. For example, the similarity between an electrical circuit and a water system. The electrical current is similar to the flow rate of water; voltage is similar to water pressure; resistance is akin to the friction in the pipes or the narrowing of the pipes in a water system. In fact, these concepts can be explained through topology, and if you notice, topology is a more abstract form than these two fields. By examining the invariants in these two systems at a certain scale, applicable theorems can be derived for both areas.

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If my consciousness is experiencing this moment and it was uploaded one second ago, how can I distinguish this reality from the reality I believe to be true? I cannot distinguish it, because my consciousness is a system built upon abstract forms of experiences. This system derives its reality by abstracting the reality it is in. When we concretize these experiences, as in the first question, we can reach judgments that are different from the ones we believed. What we believed, something we have been conscious of since childhood, can, according to the new judgment, be the case that this consciousness was uploaded to us one second ago. All newly formed judgments represent their own reality set.

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The existence of complex systems can be discussed if the abstracted forms' concrete parts are transferred over time. For example, human intelligence: at a large scale, it is made up of nerve cells. At an even larger scale, it is made up of atoms. We cannot determine the state of the system one second later with all the information from these elements, but when we abstract the system one second later and if the same system emerges, then that system exists. Changes are ignored here because the scale is smaller, and the abstractification process has been applied. Since these systems are abstracted, the information we receive gives us the "existence" of the system. If we are considering preservation over time, we cannot say something "exists" in just one Planck time. The virtual particles in quantum foam exist and vanish within a Planck time, meaning they cannot exist until the next Planck time, so we cannot consider them "existing." If they were considered "existent," they wouldn't be called "virtual." Thus, the condition for existence is that when the system is abstracted over time, the same system must emerge, and this must occur over more than one Planck time. The system obtained here is in a more abstract form than the system itself.

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When defining a name, such as "cat," we specify characteristics for that name. For a cat, one of its characteristics might be having four legs. But if we only examine the characteristic of having four legs, we will encounter many more forms than just the cat. This is because the number of characteristics of a cat is greater than just the characteristic of having four legs. The more characteristics there are, the higher the degree of concreteness, and it points to fewer concrete forms in a more concrete plane, such as the physical plane. Therefore, the definition of all four-legged creatures is a more abstract form than the definition of cats, as four-legged creatures encompass cats. By considering all four-legged forms based on the scale where they are only defined as "four-legged," we create a symmetrical situation in the forms. Now, all the forms we examine are the same, all being four-legged. The number of legs is the same across the forms, independent of the specific forms. When we apply this to all the characteristics of the name, we obtain that name. This name is in an abstract form relative to the physical projection of the name. Not every name has the same degree of concreteness.

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Let's imagine watching a 10-minute video, and if we watch it by skipping 10 seconds at a time, we could finish the video in about 5 minutes. If we do this, the scale at which we don't skip (the parts we watch fully) will be larger than the scale at which we skip 10 seconds. Therefore, the version of the video where we skip 10 seconds is a more abstract form of the video itself. In fact, if we analyze this in more detail, we could say that skipping through the video results in an abstractification of 2, because we are effectively watching the video twice in 10 minutes. In some cases, abstractification values like this can be calculated. We can observe that the data size of the video in its concrete form is larger, but even if we skip through it, we can still extract information from the video. That means information loss doesn't have to occur in every video. The information I’m referring to here is small-scale information. I’m not talking about large-scale information, such as the RGB value of a pixel at x = 342 and y = 109 in the 2-minute, 37-second mark of the video. In fact, you could argue that this value isn’t information, but data. This is entirely dependent on the scale being examined. So, if we analyze the video at a binary format scale, that value would be considered information.

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Since I wrote these parts months ago and discussed some bold ideas, I’m not entirely sure about the validity of what I’ve said here. However, I still wanted to add this section to the writing where I explained this perspective. In this part, I tried to explain what consciousness does from this perspective and also explained why consciousness was inevitable in the evolutionary process through this explanation.

Let's consider an 8 x 8 matrix where the entire upper half is filled with 1s, and the remaining part is filled with 0s. Now, let's think of an operation and call it "A." This operation takes the matrix we initially thought of as input, and it sets the right half of the matrix to 1s while leaving the rest as 0s, essentially rotating the matrix.

When we consciously think about this operation, we abstract the groups of 1s and 0s and no longer think of it as an 8 x 8 matrix, but instead as a 2 x 2 matrix, performing the operation on this 2 x 2 matrix and considering the result as a 2 x 2 matrix as well. In fact, when we first see the 8 x 8 matrix, we no longer think of it as an 8 x 8 matrix, but as a 2 x 2 matrix. This is because the patterns in the data within the matrix and the patterns required by the operation itself can be reduced to the size of a 2 x 2 matrix. Let’s call the number of commands the reduced operation uses to perform operation A "B." The total number of commands that work at the lowest level in the human brain, that is, at the most concrete form, we’ll call "C."

If a computer processor were to perform this operation, it would work directly on the 8 x 8 matrix without any reduction or abstractification. This is because computer processors do not have a mechanism to "detect" patterns within the data they are given. If such a mechanism existed, it could perform the abstractification process. Let’s call the number of commands the computer processor executes to perform operation A "D." The sequence of B, C, and D is: B < D < C. The number "B" is much smaller than the others because the operation involving abstractification is performed on the 2 x 2 matrix in its abstract form, meaning the number of commands it executes is very small, and I was able to express the total number of commands in just one sentence.

The number "C" is much larger than the others because this process occurs in the biological brain, and it can be abstracted all the way down to the jumping of electrons, or even the processes of fundamental particles in the Standard Model. The number "D" is somewhere in between because a computer processor is much simpler compared to a biological brain, and the number of commands can be abstracted down to Assembly code or even binary format. The computer processor executes "D" commands, the biological brain executes "C" commands, but where do the "B" commands execute? In consciousness. However, the word "working" in consciousness has a different meaning than in the processor. The "working" in consciousness is not as concrete as the "working" we are familiar with. In fact, the "working" here refers to the awareness of the abstracted form of the processes in the biological brain, meaning nothing is actually "working" in the conventional sense. Inputs are given to the brain, outputs are taken, and consciousness is aware of these outputs, but not in all their details — only in their abstract form. Consciousness emerges from the abstractification of the brain's inputs and outputs according to the processes. If we could build a mechanism that detects patterns in the data coming to and from computer processors and performs an abstractification process based on that, we could create artificial consciousness. The level of consciousness can be measured by the difference between "B" and "C." For the human brain, this difference is quite large, but for a computer processor, the difference is zero. Therefore, according to what I've explained, the level of consciousness in today's artificial intelligence algorithms is zero.

Imagine a robot trying to survive in nature. For such a robot to exist, a very complex system is necessary. Any malfunction in such a complex system would affect its life and prevent it from reproducing. If there were an abstractification mechanism, these malfunctions would be ignored due to data loss, and even if there were an error in the system, it would still respond. The incorrectness of these responses wouldn't matter for survival, because the system would continue to function. Evolution, on the other hand, tends to eliminate organisms that haven't developed consciousness. Evolution developed such a complex mechanism, using inputs and outputs, that abstracts these processes, and consciousness emerged as a result. When we define consciousness, the term "awareness" is often used. So, what is this awareness of? In my opinion, it’s the awareness of the inputs and outputs. As Donald D. Hoffman mentions, without consciousness, there wouldn’t be a system dealing with basic processes for survival. If that were the case, it would be very difficult for any organism to survive. Therefore, consciousness is an inevitable feature gained through evolution. Consciousness is an interface that makes survival easier. What this interface does is abstract the inputs and outputs to make the necessary decisions for survival. The reason we ignore small probabilities and treat their likelihood as zero is that we reduce the scale when analyzing probabilities. Smaller probabilities, when the scale is reduced, approach zero. The reason we reduce the scale might be related to what I explained earlier.

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Let's consider two sets of realities: the Physical Reality Set (F) and the Mathematical Reality Set (M). The reality set we are currently in is the Physical Reality Set (F). The Mathematical Reality Set (M) is in an abstract form compared to the reality set we are in. Let's experiment with some operations performed in axiomatic sets, such as intersection and union, on these reality sets.

F ∩ M = M

Here, the intersection of F and M is M. This is because the entire M can exist within F, but there is not a single element of F in M. In simpler terms, mathematics exists in an abstract form within physics, but physics is not contained within mathematics.

F ∪ M = F

Here, the union of F and M is F. This is because when we consider all the data within F and all the data within M together, we end up with F. In simpler terms, the physical realm contains mathematics and the algorithms that generate mathematics, but mathematics does not contain physics. The total sum of the data within them is still physics.

If we were to generalize this example:

A → B

A ∩ B = B

A ∪ B = A

The symbol "→" here means that the reality set on the left is the abstracted form of the reality set on the right.

In a union, the reality set that is preserved is more real within itself than the other reality set. In an intersection, the reality set that is preserved, if it is also preserved in other reality sets, points more to a concrete form. Identifying these kinds of reality sets is more difficult within the reality sets they can exist in.

I use similar representations and concepts to determine whether one form is in an abstract or concrete form compared to another. In fact, the most important concept in this perspective is the concept of "scale." Other concepts are derived from scale, and I use these additional concepts to make the explanation easier. Therefore, referring to abstract forms as "small-scale" and concrete forms as "large-scale" does not change anything.

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Relatively concrete forms can be represented by rational numbers, but more abstract forms, such as growth or circular motion, cannot be expressed by rational numbers. This is because the abstract form of irrational numbers is the formation of rational numbers. Between all rational numbers, there are infinitely many irrational numbers. The reason for this is that when it comes to numbers, there is no limit to the process of concretization. The reason why many phenomena that occur frequently in the physical realm, such as growth or circular motion, are expressed by irrational numbers is that these phenomena do not have a sufficient degree of concreteness. When discussing these phenomena, we often think of the most ideal, i.e., the abstract form. However, in the physical realm, there is no perfect circular motion, and there is no perfect growth. Therefore, the exact values of π and e do not have a place in reality. But the reason these numbers still work is that we never actually use the numbers themselves. Instead, we use their abstracted form, which is the first 10 decimal places. This happens because, when we reduce the scale enough, things do not change according to the reduced scale.

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In this explanation, we kept the area of examination constant. That is, we examined things by enclosing them in a square of a specific size. When we place a human inside this square, the scale value will be smaller than when we place any molecule of that human inside the square. If we keep the area of examination constant, as the scale increases, the amount of data will also increase. If we keep the scale constant, as the area of examination increases, the amount of data will also increase. This is actually quite understandable. If we keep the amount of data constant, as the area of examination increases, the scale will decrease. For example, let's examine an atom. As we expand the area of examination, meaning as we look at more atoms, or even more molecules at the atomic scale, the amount of data will increase. If we want to keep the amount of data constant, as the area of examination increases, the level of what we are examining should not remain at the atomic scale but should continuously decrease. Initially, it should drop to the molecular level, and later, perhaps to the human level, or possibly to a level of something else that we can't even predict.

If we take the area of examination into account, it becomes clear that studying a culture through its physical dimensions does not constitute reductionism. In other words, understanding why the elements of a culture exist and tracing these reasons back to very ancient times, with those ancient reasons being closely related to something like evolution, is not reductionism. However, if the cause-and-effect chain of an element of a culture is ignored and only the result is examined, that would be reductionism.

To briefly explain this perspective, scale is like detail. As the scale increases, the details increase. The opposite is also true. The states of a system at all scale values are separate reality sets. One reality set does not have to be considered real according to another reality set. Reality values are expressed on a spectrum between what is real and what is not. The state of systems at different scale values can be the same as each other. When we represent this with a diagram, it results in an incredibly large branching. The processes of scaling up and down are carried out by algorithms, and algorithms represent the different or same system at different scale values.

In daily life, I believe scales should also be specified at the points where we say "the same" or "not the same." Because at the smallest scale, everything is the same, but at the largest scale, everything is different. For this reason, I think this perspective could be useful in any debate. It is enough to use the fundamental arguments of the perspective for this. We have already explored the basic arguments of the perspective and some examples. There are many topics that can be explored with this perspective, but I didn’t want to make it longer. Once you become familiar with the concepts of this perspective, it will be much easier to analyze any topic with this perspective. Moreover, the basic arguments of this perspective are open to development and should be developed. In my opinion, this perspective is not complete. There may even be parts where it is incorrect. You can help me create a better perspective by correcting these mistakes. See you in the next perspective.