The whole existence and the unique existence. There are two meanings to “one.” One as the self (individual) and one as the whole. These two meanings of “one” are the beginning of recognition. One as the self is the one of the self. One’s life is one, one’s body is one, and oneself is a unique and absolute existence. One’s life is also one. One as the whole is the one of existence, the one of the object. Unique and unparalleled. One as the unique existence. One as the whole world. And one as the unique and absolute God.
The one as the whole and the one as the self are originally one as an existing entity. And everything begins from this one as an existing entity. From there, the self distinguishes itself as one from the whole one. At that time, parts arise from the whole, and one gives birth to two. Two becomes three. The two meanings of one give birth to two. One becomes two. And two becomes three. When the one as the unique and unparalleled existence confronts the one as the individual, the one that gives birth to two arises. That is the unit. Beyond two, consciousness gives birth. That is the beginning of differentiation.
∀ “all” one (for all of x) and ∃ “there exists” one (there exists x). (From “Mathematics for a Soft Brain” by Susumu Sakurai, Mikasa Shoten)
The unique existence is the omniscient and omnipotent existence. Omniscience and omnipotence become one. Omniscience is absolute value, and absolute value is undifferentiated. Knowing everything is the same as knowing nothing. If omniscience is perfected, it turns into nothingness. One leads to nothingness. Nothingness is zero.
Zero is nothingness, void, and space. Everything is existence and infinity. One as the individual arises from the self, and the self is one. The self is projected onto the object and becomes a unit, and the object is cut out as a unit and becomes one. The unit is reflected in the self and gives birth to two. Two is reduced to the self and becomes three. God is zero, everything, and infinity. Consciousness arises between zero, one, and infinity.
The self and the whole, the self and the object are in a one-to-one relationship. The self and the whole are unified and become an absolute existence. That is the premise of all recognition.
The essence of things and the words that indicate things exist separately. The essence of things and the words that mean those things exist separately. (From “Lectures on the Philosophy of Science” by Kunihisa Morita, Chikuma Shinsho)
Numbers are words. Therefore, numbers exist separately from the essence of the objects they represent. Monetary value is separate from the essence of things. Monetary value is separate from the essence of things. “Being” and “knowing,” or “acknowledging,” do not mean the same thing. “Being” is a necessary condition for “knowing” or “acknowledging,” but not a sufficient condition.
The first recognition a person has when they are born is an absolute recognition based on intuition. It is a recognition of existence. At first, the whole is recognized as one lump. At that stage, consciousness is still undifferentiated. When the whole is one, existence is absolute and perfect. If the whole is perceived as one lump, individual objects cannot be distinguished. Therefore, differentiation begins immediately after the first recognition. From the moment differentiation begins, all recognition becomes relative, absolute recognition ends, and consciousness begins to act. Therefore, the activity of consciousness begins with dividing the whole.
It is oneself that makes one one, and originally, there is no entity called one. In other words, it is the self’s consciousness that recognizes one as one, and the object called one does not originally exist. The concept of one is on the side of the self.
It is believed that people can distinguish numbers at a fairly early stage after birth. Even if they can distinguish numbers, it is not the numbers that can be counted as one, two, as generally thought. It seems to be the ability to distinguish one, two. In other words, there are two. Something that was one has increased to two. Something that was two has decreased to one. Numbers are distinguished by the relationship and operation between things. From this, it can be understood that the concept of numbers is formed from relationships and operations. Numbers are recognized from phenomena such as dividing, combining, adding, and subtracting. And numbers are used earlier than words are learned. This suggests a fundamental problem of what mathematics is. Furthermore, numbers are distinguished by recognizing the moving part against the static background. The act of separating the basic situation or environment and the object to be focused on itself forms numbers. (From “The Math Instinct” by Keith Devlin, translated by Hoshi Tominaga, Nihon Hyoronsha)
Two is the beginning of differentiation.
Existence or non-existence. One or zero. Good or evil. True or false. Beautiful or ugly. Success or failure. Right or wrong. Positive or negative. Binary is the beginning.
The beginning of numbers is dividing the object. One whole is divided into several parts, forming the recognition of numbers.
Numbers originally arose from counting and measuring. Numbers were born from counting, and quantity was established from measuring.
Numbers arose from counting things. Quantity arose from comparing lengths, sizes, and weights.
The foundation of mathematics was built by systematizing numbers and quantities.
Therefore, mathematics has both numerical and quantitative elements. In modern school education, mathematics is taught based on algebra. However, the foundation of mathematics is rather geometric concepts. Because algebra is taught as the center, geometric elements are often omitted. This becomes a significant defect later on.
The beginning of economic activities is counting, measuring, and dividing. In other words, the beginning of economic activities is mathematical activities.
The first numbers are generally considered natural numbers. When defining natural numbers, there are two ways of thinking: first, defining a set that serves as the standard for numbers and calling it natural numbers, or second, naming the equivalence class of sets equal to the standard set as natural numbers. (From “What is a Number” by Tsuneo Adachi, Kyoritsu Shuppan)
Monetary value is an extension of the latter way of thinking.
In ancient Greece, which is the ancestor of modern mathematics, the tools of mathematics were exclusively rulers and compasses. The rulers were not for measuring lengths as they are today but for drawing straight lines. The purpose of the compass was to draw circles, transfer the length of line segments to other straight lines, and move angles to other places. (From “Introduction to Mathematics for Understanding Infinity” by Hiroyuki Kojima, Kadokawa Sophia Bunko)
Geometrically speaking, numbers are certain line segments. They determine the length of one. Against the line segment determined as one, line segments of two and three are established. Addition is measured by the extension of the line segment of one. That is the beginning of calculation.
Mathematics was formed by converting the quantities established in this way into numbers.
The concept of numbers is not a concept that stands alone. It is a structural concept derived from the relationship and operation between the self and the object. This is the same for language. Therefore, both numbers and language are systems established by operations. When the subjective concept of numbers and the formal attributes of the object are combined, the concept of numbers is established.
In the scales that express the nature of numbers, there are nominal scales, ordinal scales, interval scales, and ratio scales in statistics. These scales well represent the function of numbers. (From “Understanding Statistical Analysis” by Sadami Wakui, Pele Shuppan)
In statistics, the scale that only divides data is called the nominal scale. The ordinal scale has no meaning in the numbers themselves, but their order has meaning. The interval scale has meaning only in intervals, that is, distances. The ratio scale has meaning in both differences and ratios. This is derived from the nature of numbers.
Numbers are symbols. Numbers are shadows. Modern society was established by quantifying phenomena. However, quantification is not the same as mathematization. Many people confuse quantification with mathematization, but they are different. Quantification means simply replacing phenomena with numbers. The subsequent processing is separate. Mathematics provides the means to logically process quantified phenomena. Just because something is quantified does not mean it has been mathematically processed. Some people explain things with numbers in a knowledgeable manner, but simply listing numbers is not mathematical. However, quantification is the entrance to mathematization. In other words, quantification is a prerequisite for mathematization, but it is not mathematization. Modern times can be said to have been established by quantifying phenomena. For example, grades and sports are established by quantified results. And the numbers that make up the numbers are shadows.
The paper stacked on the floor looks like one lump when projected on the wall. However, when the wind blows and scatters the paper, each sheet casts its own shadow.
Numbers are a matter of recognition.
Generally, there is an illusion that numbers are unique and absolute. There is also a misconception that mathematics is rigorous and has only one answer. This misconception tends to be reinforced in current school education. However, numbers are abstract, means, and tools. Abstract, means, and tools, numbers change their appearance and nature depending on the object, purpose, handling, and processing. Therefore, differences such as natural numbers, integers, and real numbers arise. When we handle numerical values, we should confirm the premises and purposes.
The self is the subject and, at the same time, an indirect object of recognition. This state of the self decisively affects the state of recognition. This also applies to the recognition of numbers. In the recognition of phenomena, the distinction between self and others is key. This is because recognition is established in the relationship between the self and others. Numbers are no exception. One is established by corresponding the one of the self and the one of others one-to-one. In other words, the internal one and the external one.
The root of modern individualism is the distinction between self and others. Establishing oneself and accepting others. That is the basis of recognition. The recognition of numbers also begins with the distinction between self and others.
Basically, economics is a matter of recognition. For example, labor, resources, and transactions are all matters of recognition. And what is important in the matter of recognition is when to recognize.
The self that recognizes the whole is one. Therefore, the self that divides the whole is one. However, the self is an indirect object of recognition. Therefore, by dividing the object, the self recognizes its existence. By indirectly recognizing the self through the object, a difference in consciousness arises between the self before recognizing the object and the self after recognizing the object. That becomes two and becomes the trigger for three.
By throwing and projecting the self onto the object, the self is objectified. At that time, the absoluteness and perfection of the object are broken, and it becomes a relative object. This establishes a one-to-one relationship between objects.
There are numbers that count up one, two, and numbers that consider the whole as one, further divide the whole into several parts, consider any part as one, and establish numbers by their ratio. There is no limit to the numbers that count up, and there is a limit to the numbers that consider the whole as one. These two ways of recognizing numbers are not clearly distinguished and are used differently depending on the conditions set. The problem is that the premises set are always arbitrary.
Money is the materialization of numbers. By materializing, money is given not only the attribute of numbers but also the attribute of things. By materializing, money has acquired the attribute of things and, at the same time, is subject to the constraints of things. The attributes of things include owning, holding, carrying, seeing, touching, exchanging, distributing, lending, borrowing, depositing, keeping, giving, saving, storing, handing over, receiving, transferring, discarding, disposing, hiding, and changing. The attributes of things are that they cannot take negative values, cannot represent decimals, cannot use imaginary numbers or irrational numbers, are discrete numbers, must be based on balance, are finite, and do not function as numbers alone. And the attributes of numbers and things regulate the function of money and form the basis of monetary value.
Monetary value and money are different. That is the premise. Monetary value is a set of natural numbers, so monetary value is the former, counting up one by one. However, money originally has a limited amount as a thing, and money also deals with finite objects. Therefore, it is the latter, a number with a whole. Money deals with finite objects, but monetary value itself has no limit. Without some restriction, monetary value will spread infinitely. Today’s economy is based on a finite world. However, the monetary economy continues to expand indefinitely. That is one of the contradictions of modern society.
Information is intangible. Monetary value is a type of information. Money is the tangible form of intangible information and monetary value. Money represents the numerical unit of monetary value.
Monetary value is effective within a closed space called a currency zone. Money does not exist in nature. Money is an artificial thing and only works within an artificial space.
Numerical data related to people, things, and money are primary data, and monetary value is secondary data. For example, people (population and population composition, age, height), things (production volume, consumption volume), and money (money supply) are primary data, but asset values like land prices are secondary data. Numbers are abstract concepts, but for numbers to be established, there must be some substantial thing under the numbers. It did not take a day to abstract the common element of two from phenomena such as two apples, two trees, and two people. It took many years just to establish the number two. Furthermore, it took even longer to add monetary value, such as two hundred yen. Moreover, monetary value was established by combining substantial numbers and monetary units, such as one apple for two hundred yen.
Numbers are not real things but concepts established by abstracting functions. The functions that established numbers are counting, measuring, and confirming. To develop these functions into numbers, there is a function of extracting common equal parts from objects and distinguishing them from others. From the functions of counting and measuring, functions such as arranging, gathering, combining, dividing, indicating, marking, and informing arose. Furthermore, functions such as aligning, ordering, adding, subtracting, multiplying, and dividing were established. From confirming, functions such as indicating and marking arose. These are the basis of numerical representation. In the concept of numbers, numerical representation and numbers are inseparable. And numerical representation is replaced by money, forming monetary value.
The beginning of numbers is natural numbers that do not include zero. The concept of zero and minus is a very modern concept. It is a newer concept than rational and irrational numbers.
The function of counting numbers became the basis of algebra, and the function of measuring numbers became the basis of geometry. In any case, the beginning of numbers is natural numbers that do not include zero.
Numbers have characteristics. The characteristics that make up numbers, such as even numbers, odd numbers, divisors, multiples, and prime numbers, form the basis of the nature of numbers. The characteristics of numbers that form the base of positional numeral systems, such as binary two and ternary three, characterize the system of numbers. For example, in binary, multiples of two are the basic unit, and in ternary, multiples of three are the basic unit. The duodecimal system can be divided by two, three, four, and six. In other words, multiples of two, three, four, and six form a group. Why are these characteristics of numbers important in economics? Because the root of economics is distribution. Therefore, divisors and multiples have important meanings in economics. Numbers also affect combinations. For example, combinations of numbers that add up to ten can represent states. Seven-three, six-four, fifty-fifty, and so on. These base numbers also have important functions in economics.
The basic units of sports are nine for baseball, eleven for soccer, six for volleyball, and five for basketball. These basic units of sports numbers seem meaningless at first glance, but they shape the nature of sports. They are elements that form the format and appearance of sports. Similarly, the basic units of economics work in the latent part of the nature of economics. The nature of numbers works at the base of economics. Especially prime numbers may work in unexpected places in economic phenomena. Twin primes and Mersenne primes are good examples.
Numbers developed by combining individual functions such as counting and dividing, counting and combining, or measuring and dividing, measuring and comparing. Furthermore, measuring, dividing, and comparing, counting, dividing, aligning, gathering, counting, dividing, and combining operations gave birth to basic operations such as adding, subtracting, multiplying, and dividing. Counting, measuring, dividing, comparing, combining, and aligning basic actions form the algorithms of operations. These are also inherited in accounting systems.
Numbers can express quantity by being ordered. By ordering numbers, it becomes possible to express position with numbers. Position represents distance. As a result, if positional relationships are established, it becomes possible to express quantity. Distance gives rise to the concept of length. By comparing positions, concepts such as length, size, and weight are established. By combining the concept of distance with equality, units are established. These are established by relating objects and numbers through order.
When we count things, we sometimes make piles of ten, gather those piles into tens, and count the remaining ones to total the number. At this time, the pile can be considered as one unit. Conversely, the pile can be perceived as a pile without the need to arrange it in order. However, it is difficult to calculate that way. By combining the concept of order with numbers, operations become possible.
The nature of numbers includes the property of being attached to the objects to be counted or measured, that is, being related. This property plays a decisive role in the function of numbers.
Numbers exert their utility after the system of numbers is established and related to other objects. In other words, numbers are universalized and generalized in relation to others. By being universalized and generalized, numbers exert their power.
The key concept is equality. Equality also leads to the concept of sameness or commonality. The important thing is what is considered equal, what is considered the same, and what is considered common. This determines the nature of the object. Furthermore, when equality is linked to time, concepts such as constancy, fixedness, and stillness arise.
The fact that numbers can be related to any object and that objects can be equalized by numbers, and that this is done by arbitrary procedures, are important elements in the development of mathematics. (From “What is a Number” by C. Lanczos, translated by Keizo Yoneda, Kodansha Bluebacks)
The important things about numbers are visibility and operability. Numbers are established and developed because they are visible and operable. Replacing invisible functions such as counting and measuring with visible forms is the beginning of numbers. By replacing them with visible forms, the equality of the objects behind the numbers becomes clear. Also, by making them visible, it becomes possible to operate numbers. That equality becomes the basis of units. Also, by replacing them with visible forms, it becomes possible to replace them with visible forms, it becomes possible to relate them to others. By relating them to others, it becomes possible to compare the related things through numbers. Comparison brings order to numbers. By being ordered, numbers can measure position. This eventually leads to economic value. By connecting to economic value, the concept of numbers further develops.
It should be noted that the system of numbers is an independent system separate from the system of objects to be measured.
When numbers are connected to value, monetary value is established. Monetary value is not connected to numbers from the beginning. Monetary value was established by connecting objects and numbers through the medium of money.
Monetary value consists of three elements: the recognizing subject, the object indicated by money, and money. These three elements are people, things, and money. Money is an indicator of monetary value. Monetary value works neutrally towards the object indicated by money. This supports the objectivity of monetary value. Different objects, such as things and labor, time, can be calculated by converting them into monetary value. This is because money is neutral towards the object.
What the objects indicated by numbers or money are does not matter mathematically. Only numerical values and monetary units are abstracted.
Numbers are not necessarily neutral towards the attributes of the objects they indicate. Numbers can be constrained by the objects they indicate. For example, when saying five apples, the number means specifying the object of apples.
In contrast, monetary value is neutral towards the object indicated by money. If one apple is two hundred yen and one mandarin is one hundred yen, it is possible to calculate three apples and one mandarin together. That is the utility of monetary value.
Numbers themselves have no smell, weight, color, or taste. Numbers are not the objects being counted or measured, nor are they part of the objects. Numbers are added marks. This is where the potential for the development of numbers lies. Therefore, even if objects are quantified, it does not affect the nature or function of the objects. And the nature of numbers also transfers to the nature of money.
もちろんです。以下の文を英訳しました。
Numbers are inherently tied to economics.
Numbers are extremely economical and rational. Firstly, numbers have no waste. All unnecessary elements are eliminated. In this sense, numbers are economical and rational. Numbers are indeed economical.
Historically, mathematics has been a tool of control for those in power. In other words, mathematics was initially on the side of the rulers. When mathematics became the property of the people, democracy deepened. Democracy can be said to be a system that stands on numbers.
Mathematics is history itself. It is a product of history. Therefore, if one aspires to learn mathematics, the history of mathematics is essential. Mathematics has developed along with history. At the root of history is economics. Therefore, mathematics has significantly influenced human history, and conversely, mathematics has been shaped by history.
Economics has developed alongside mathematics.
Numbers originally came into existence by being tied to real-world entities. Therefore, the system and function of numbers have significant meanings based on what they are tied to. This importance remains unchanged today.
Numbers can be said to have originated for the purpose of counting livestock or game, and many cultures linked units of numbers and lengths to parts of the body such as fingers and arms. Furthermore, taxes and units were inseparably related.
When agriculture began, the system of numbers is thought to have been established by organizing standards for measuring harvests such as bundles and grains of barley, wheat, and rice, and tools for measuring harvests such as bushels.
Such systems of numbers were not necessarily based on the decimal system. It is reasonable to think that they were influenced by the social systems and living environments of their times.
We often think of area in terms of shapes. Area is recognized as the product of lengths. However, in ancient societies, area was derived more as a quantity based on harvests or labor rather than the product of lengths. Area was sometimes determined by weight. For example, in Japan, area was considered based on harvest quantities such as dan, bundles, and bushels. In Korea, an area was defined as the size that one ox could plow in four days. The British acre was defined as the area that two oxen could plow in one day. (From “Discovery of Area” by Toru Muto, Iwanami Shoten)
In Babylonia, the volume of 180 grains of barley was called one shekel, and the area of a field sown with 180 grains of barley was also called one shekel. In the Hebrew Bible, the price of one shekel of silver was one shekel. Thus, one shekel was both a unit of weight and a unit of currency. (From “Discovery of Area” by Toru Muto, Iwanami Shoten)
Thus, units of area, weight, and currency are intricately intertwined. This also hints at the relationship between mathematics and economics. What elements were combined to create units? This provides important insights into the relationship between mathematics and economics.
However, it is important to note that area is not necessarily derived as the product of lengths. This is evidence that mathematics has developed as practical wisdom.
Originally, mathematics arose from the necessities of life. Economics is the activity of living. Therefore, mathematics and economics are inseparably related.
Today, mathematics is often thought of as an abstract concept detached from reality, but originally, mathematics was a discipline based on the realities of life. Therefore, clarifying what entities numbers symbolize is a key to understanding mathematics. The significance of what elements combined to form mathematics is hidden in this. And this is also related to the fundamentals of today’s economy.
For economics, mathematics is purposeful. Because it is purposeful, the nature of mathematics is influenced by its purpose. Because it is purposeful, it is arbitrary, and human will is important.
Economics is a phenomenon based on artificial systems. Economics does not operate on given laws like natural phenomena. Naturally, the premises of thinking about mathematics differ between natural science and economics.
Economic systems are complete as systems. Therefore, they can become uncontrollable and run amok. If economic phenomena are based on arbitrary systems, it is necessary to clarify the premises that constitute these systems to control economic phenomena. Economic phenomena do not occur naturally; they occur because they are meant to occur.
The flight of an airplane and the flight of a bird are fundamentally different, even though both involve flying. A bird is born from an egg if it is incubated, but an airplane does not come from an egg. A bird learns to fly on its own once it is born, but an airplane needs to be designed to fly.
The symmetry in accounting is artificially created symmetry.
The essence of mathematics lies in abstraction. By abstracting natural and social phenomena into numbers and shapes, then replacing them with equations, deriving laws and principles, generalizing them, and then re-materializing them to verify, this process becomes mathematics. (From “Mathematics Book to Develop Thinking Skills” by Koji Okabe, Nikkei Business Publications)
And this process is precisely economics itself. Therefore, mathematics and economics can be said to be one and the same. However, when we generally speak of mathematics, we often limit it to phenomena that originate from natural or material phenomena. In contrast, mathematics in economics targets social phenomena. Therefore, even in abstraction, the subjects and conditions assumed differ. Naturally, there are subtle differences in the process of development and history.
The difference between natural phenomena and social phenomena is that the former assumes given subjects, while the latter assumes arbitrary subjects. Given subjects mean objective reality, while arbitrary subjects mean subjective, conceptual subjects. Therefore, mathematics targeting natural phenomena is based on definitions, while mathematics targeting social phenomena must be based on consensus. In other words, the former is based on assumptions, while the latter is based on agreements.
Monetary economy is an economic system that reduces economic value to exchange value, converts it into monetary value, and utilizes it for activities through the market. An economic system is the structure of the economy. In other words, monetary economy quantifies one’s utility to society by utilizing one’s resources, converts it into monetary value as income, and sustains itself by exchanging the acquired money for goods and services necessary for living in the market.
Saying that a 1,000,000 yen suit is expensive and saying that 1,000,000 people are many have different meanings. One million people have a tangible existence, but one million yen is nominal and has no tangible existence.
Mathematics did not start from lofty philosophical motives. Numbers and quantities arose from the necessity of living. Mathematics is originally a part of life. Because it is a part of life, when mathematics is abstracted, it can be connected to profound thoughts about life, the universe, and mysteries.
Mathematics was originally created to be useful to humans. Therefore, mathematics has always been part of people’s lives and continues to be indispensable to people’s lives today. However, as mathematics established itself as a field of pure mathematics and became abstract, the mistaken notion that mathematics is useless or that it is good because it is useless spread.
However, economics is so intertwined with mathematics that one could say economics is mathematics. And mathematics only demonstrates its significance when it is useful to economics, especially in pure mathematics. The foundations of economic mathematics lie in number theory, set theory, and group theory.
Humans did not create numbers from pure mathematical motives or profound philosophical thoughts. Numbers were fundamentally created from practical, utilitarian motives, such as marking notches on a stick to count livestock or dividing harvests fairly, or measuring the area of fields. In other words, the creation of numbers was driven more by economic motives than academic ones. And monetary value arose as an extension of this.
Monetary units are sets of natural numbers. Therefore, they strongly reflect the characteristics of natural numbers. This means that number theory plays an important role in considering monetary economy. For example, the characteristics of cardinal and ordinal numbers constitute the fundamental characteristics of monetary units.
In considering the relationship between money and numbers, the key lies in the one-to-one correspondence between numbers and objects. And the exchange of money and goods based on this one-to-one correspondence.
Monetary value is an infinite set of natural numbers. Therefore, the density of monetary value is equal.
The set of natural numbers is closed under addition. (From “Introduction to Prime Numbers” by Shozo Serizawa, Kodansha Bluebacks)
Monetary value is closed under addition.
By replacing the economic value created by human concepts with money, it becomes universal and quantifiable. And monetary value is activated through the exchange of money and non-monetary goods. The monetary economy is based on this monetary value.
If one thinks of economics as just counting money, one loses sight of the essence of economics. Economics is the activity of living. It is life. The essence of economics is not the relationship of money but human relationships and the relationship between people and things. This is the same for the essence of numbers.
Numbers are purposefully set standards. When defining a system of numbers, there are two ways: either the set of elements that serve as the standard for the system of numbers is considered natural numbers, or the set of equivalence classes equal to the set of elements that serve as the standard for the system of numbers is considered natural numbers. (From “What is Number” by Tsuneo Adachi, Kyoritsu Shuppan)
Monetary value is fundamentally the latter. Numbers, that is, monetary value, refer to the set of equivalence classes equal to the set of elements that serve as the standard.
Monetary value is a set of natural numbers. However, what sustains this monetary value, which is a set of natural numbers, is human daily activities. If daily activities are lost from the economy, the economy loses its essence. Monetary value is not the substance of the economy. The economy refers to people’s way of life and daily activities.
Therefore, thinking about economics is thinking about life and living. Therefore, economics is philosophy and thought.
Making money is a means, not an end. Earning money is for the purpose of living. If life collapses for the sake of money, it is putting the cart before the horse. However, in modern economics, it even seems that making money has become an end in itself. We must not forget that the essence of economics lies in human dignity. Living with human dignity is essential; without it, the foundation of human economics would crumble. Yet, today’s economy only deals with issues related to money. Therefore, economic problems cannot be solved. Even under hyperinflation, during the Great Depression, in wartime, or after disasters like earthquakes and tsunamis, people’s daily activities continued without fail.
From this perspective, economic collapse originally refers to a state where physical survival activities and life become unsustainable, such as droughts, famines, and wars.
If we think of economics as merely counting money, we lose sight of its essence. Economics is the activity of living. It is life itself. The essence of economics lies not in monetary relationships but in human relationships and the relationships between people and things. This is also true for the essence of numbers. Numbers are purposefully set standards. When defining a system of numbers, there are two ways: either the set of elements that serve as the standard for the system of numbers is considered natural numbers, or the set of equivalence classes equal to the set of elements that serve as the standard for the system of numbers is considered natural numbers. Monetary value is fundamentally the latter. Numbers, that is, monetary value, refer to the set of equivalence classes equal to the set of elements that serve as the standard.
Monetary value is a set of natural numbers. However, what sustains this monetary value, which is a set of natural numbers, is human daily activities. If daily activities are lost from the economy, the economy loses its essence. Monetary value is not the substance of the economy. The economy refers to people’s way of life and daily activities. Therefore, thinking about economics is thinking about life and living. Hence, economics is philosophy and thought.
Originally, numbers were directly connected to life, that is, economics. Numbers developed from the act of counting, eventually evolving into calculations such as addition, subtraction, multiplication, and division. Additionally, the act of measuring land, that is, measuring, developed into shapes and geometry. This marks the beginning of today’s mathematics.
Therefore, in its primitive stages, agriculture played a decisive role in the formation of mathematics. The origin lies in the economic activities of calculating harvests and determining the distribution of game. And the act of distribution is also the fundamental significance of economics. Herein lies the essence of mathematics and economics.
Adding, increasing, subtracting, decreasing, multiplying, and dividing are mathematical concepts. And these concepts are also connected to the fundamental concepts of economics, such as production, consumption, and distribution. Calculations began as economic activities.
Even in ancient societies, when unified dynasties were established, the unification of units was sought. This unification of units is called weights and measures. “Do” refers to a ruler, representing length. “Ryo” means a measure, representing volume. “Ko” refers to a scale, representing weight. Units are based on the concept of equality. Therefore, the system of numbers is based on some substantial activity, such as counting or measuring. Units are constructed based on elements like a measure, a certain amount, or a certain number.
The basis of units was determined by the number of family members, the length of an arm, the size of a foot, the number of fingers, the size of a measure, and other environmental conditions, premises, and purposes of actions at that time and place. Therefore, units varied depending on time, place, and situation.
The system of numbers established in this way is somewhat different from the universal system of numbers we consider today. The system of numbers of that time was more realistic and substantial. For example, we accept the decimal system as a matter of course. However, the establishment of the decimal system is not that old. Evidence of this can be seen in the remnants of the sexagesimal and duodecimal systems in time units, and the use of 360 degrees as a unit of angle.
In considering the system of numbers, for example, monetary units sometimes mixed or coexisted with the decimal and quaternary systems. Until the decimal system was established, humans lived in a rather complex world of numerical systems. Even today, the binary system is common in the world of information and communication, and it is permeating various fields.
Furthermore, the system of monetary value is established as an extension of the system of numbers. Monetary value is one of the systems of numbers.
Economics is a matter of perception. Economics is an activity, not a reality. The essence of monetary value is numerical.
In economics, principles such as competition are often mentioned, but the laws of nature and the laws and regulations of society are fundamentally different. Natural laws are propositions established through observation and experimentation of natural phenomena, while the laws, systems, and regulations of society are based on definitions established through consensus and contracts. Natural laws are based on givens and self-evident truths, while the laws, systems, and regulations of society are based on arbitrariness and consensus.
For numbers to exist, the existence of objects or phenomena is a prerequisite. To count numbers, a motive for counting is necessary, and this motive arises from necessity. To distribute game fairly among a large family, it is necessary to correspond the game to the family members one-to-one. This is the beginning of counting numbers.
The premise of monetary value is the existence of money, the premise of money is the act of exchange, and the premise of exchange is the existence of goods to be exchanged. In a monetary economy, the fundamental necessity is the existence of goods to be exchanged. The function of money is the function of numbers, meaning it serves as a standard for exchange. This is the peculiarity of money. Therefore, monetary value is realized through money. The ultimate form of this is fiat money. Hence, the monetary economy is mathematics.
Mathematics is a technique that arose from the necessity and practicality of living. As its abstraction deepened, it reached a philosophical realm. We must not forget the beginning and essence of mathematics. Mathematics has always been part of people’s lives and has developed along with people’s lives. Mathematics is not a transcendental discipline but the most secular one.
The act of counting is inseparably related to economics. Counting is a cultural act.
In schools, they try to teach arithmetic and mathematics. However, they do not teach the origins of arithmetic and mathematics, the motives for their establishment, what they tried to express through mathematics, or what they tried to elucidate. Therefore, mathematics ends up being superficially interpreted. The same goes for economics. If we only chase the phenomena that appear as numbers and overlook the lives of people behind those numbers, economics cannot be established. That is the logic.
What is important in numbers and formulas is visibility and operability. Numbers are not inherently visible. However, it is possible to replace them with visible forms. By replacing them with visible forms, it is possible to perform operations such as addition, subtraction, multiplication, and division. This ability to replace and operate with visible forms is the foundation of the development of mathematics. The extension of this is formulas, shapes, and graphs.
By making the number of objects visible and manipulating them, it is possible to manage, divide, exchange, and compare the objects. This awakened the basic sense of economics.
Mathematics developed from counting numbers and measuring quantities. Numbers are concepts derived from the act of counting. The act of counting numbers is based on three actions: managing, distributing, and exchanging. In other words, counting is a necessary act for living, an economic act. Measuring quantities includes measuring time with a calendar, measuring length, height, width, and thickness with scales, measuring volume and capacity, measuring weight, and measuring heat. Measuring quantities also arises from the necessities of life. The word “measure” includes meanings such as measuring, weighing, calculating, and planning. Mathematics developed from these acts of measuring, weighing, calculating, and planning.
The foundation of mathematics was established by linking inherently discrete numbers and continuous quantities through the arbitrary setting of units. By setting units, continuity was added to discrete numbers, and discontinuity was added to continuous quantities. This is quantity.
The foundations of numbers are management, distribution, and exchange. The foundations of quantities are measuring, weighing, calculating, and planning. These actions are also the foundations of economics. The units of time, length, height, weight, and heat are elements that sustain the economy. From these extensive quantities, intensive quantities such as speed and concentration were derived, forming economics and mathematics.
Numbers are infinite, but quantities are finite. Quantity is composed of infinite numbers and finite quantities. Economic units and economic value are expressed by numbers and quantities, that is, by quantity.
Many people think that talking about economics means talking about making money. Many also think that economic mathematics is about counting money. However, economics is not about making money. The problem of money is not the only problem in economics. Environmental issues are a good example. If we only pursue monetary profit, environmental problems will not be solved but will worsen.
To solve environmental problems, we first need to clarify what kind of environment we want. Then, based on this clarity, we need to develop a plan. Based on the plan, we need to clarify where and how much cost will be incurred. Then, we need to build a system that can realize the fundamental plan, including not only the social system but also the economic system. Money is a means, not an end. Money alone does not sustain the economy. Economic mathematics exists to understand the reality of the economy behind the numbers through the numbers.
Economics is the activity of living. To live, we need things necessary for living. The things humans need to live are limited. The living space for humans is finite. However, land prices are not limited. Once land prices start to rise, they become limitless. Economic value is based on the harmony of these two elements.
In contrast, monetary value is limitless. Monetary value can rise indefinitely. Economic value is composed of the quantity of goods and the numbers indicated by monetary value.
Economics is the activity of living. The fundamental activity of living is eating. Humans are living beings and cannot live without eating food. And humans cannot live alone. At least, a newborn baby cannot eat or even move without someone taking care of them. There is no child who does not trouble their parents.
To live, humans must assume human relationships that support them. In other words, humans assume obtaining food and relationships with other humans to live. Living is the premise. Therefore, the activity of living precedes everything.
In the past, people lived by sharing the game and harvests they caught. How to share them fairly was the beginning of economics. Therefore, numbers and economics have been inseparably related from the beginning.
To share game and harvests fairly, it is necessary to count how many to divide and how many there are. How many to divide is the subjective number, and how many there are is the objective number. The establishment of numbers requires both subjective and objective numbers. This is because numbers are concepts derived from recognition. Numbers are abstract concepts. Being derived from recognition means they are relative. Being abstract concepts means they assume some substance and consensus.
To live, it is necessary to distribute game and harvests. In other words, numbers and quantities developed from the necessity of fair distribution.
The necessity of distributing goods established numbers and quantities, and numbers and quantities were positioned and systematized. Eventually, the four arithmetic operations of addition, subtraction, multiplication, and division were established, forming the foundation of mathematics. The necessity of exchanging goods gave rise to money. Therefore, money is purely mathematical.
Modern pure mathematics cannot do without the concept of infinity. However, phenomena related to economics are fundamentally finite. They are finite, relative, and distributive. If we forget this, economic mathematics cannot be established. Therefore, the monetary value that forms the basis of economics is a set of natural numbers, and the concept of negative numbers has only recently been used. The concept of negative numbers is accepted without question by modern people, but historically, it is a very new concept and was not easily recognized. This is strongly reflected in the world of economics.
In any case, economic mathematics is different from pure mathematics. It is based on finiteness, relativity, and a distributive system. Especially in economics, ratios are important because the root of economics is distribution.
Inner Numbers and Outer Numbers
Subjective numbers refer to one’s own numbers, inner numbers, while objective numbers refer to the numbers of objects, outer numbers. The function of numbers differs depending on whether the object is a physical entity or a subjective existence. If the object is a physical entity, it forms physical units, and if it is a subjective existence, it forms economic units, that is, monetary units.
In other words, numbers are established through two actions: the act of recognizing the object and the act of reconstructing the object. This leads to inductive logic and deductive logic. Numbers have two elements: the element of counting and the element of being counted.
Objective numbers are existing numbers, while subjective numbers are positioned numbers. Existing numbers become cardinal numbers, and positioned numbers become ordinal numbers.
The act of calculation develops economic activities. It involves breaking down captured game or harvested crops, reconstructing them, and distributing them. This forms the basis of the act of counting numbers. A whole is considered one, and the divided parts are also considered one. By comparing the whole one with the part one, units are established. This is the beginning of one, and numbers start from one.
Therefore, the act of dividing is the premise of the concepts of economics and numbers. And dividing also means the beginning of recognizing the object, because recognition means differentiation.
The beginning of numbers is dividing objects. This is because numbers start with recognizing objects. Recognition is differentiating objects. Differentiating means dividing objects. Therefore, numbers arise from dividing objects.
Dividing is ratio. Counting is quantity. Ratio is subjective numbers. Quantity is objective numbers.
Objects are continuous entities, and numbers are discrete recognition.
Objects consist of mass and form. Objects are made of quality and quantity, and quality refers to the inherent characteristics of the object. Numbers are concepts abstracted from the quantitative part of the object’s form. Objects have material and appearance. Material is substance, and appearance is form. Humans consist of soul and body. The soul is quality, and the body is form. For humans, spirit and posture are important. Spirit is quality, and posture is form. Numbers are derived from form.
When counting numbers, we do not just count one, two, three. We count one animal, two animals, one book, two books, or one item, two items, assuming something behind the numbers. Quality and quantity are undifferentiated. Numbers do not exist solely as numbers. The concept of numbers is abstracted by separating from objects.
Objects are originally continuous. Differentiation arises from recognition. By dividing the whole into parts, objects are differentiated and recognized. Recognition relativizes objects. It is the self that relativizes objects, not that objects are relative from the beginning. The self relativizes objects to recognize them. This is differentiation. And differentiation arises from recognizing objects.
The objects we count are originally continuous. We divide them to count. From this, the concept of quantity is formed. Quantity exists between continuity and division. Therefore, there are continuous quantities and discrete quantities. Think of a drink. A drink has a whole as a liquid. It is divided into drinking amounts in cups and distributed to each person. The drink is a continuum. By dividing it into containers, it forms a unit and is converted into discrete quantities.
Numbers arise in the process of recognition. Recognition is established as a result of the interaction between the self as the recognizing subject and the object being recognized. Numbers are established by the internal matters of the subject and the external objects of the subject.
Probability is an event in the world of matters, and statistics is an event in the world of objects.
The world of objects is finite, and the world of matters is infinite.
Numbers are extracted as attributes from arbitrary objects, events, masses, and sets. Arbitrary objects are not necessarily some kind of aggregate. For example, multiple numbers can be extracted from the attributes of a single person, such as the number of fingers, eyes, and ears. By associating these numbers with actions or behaviors, different numbers can be added.
Several characteristics are added to the set of extracted numbers through the relationships between numbers. By adding characteristics, numbers are classified. We must not forget that the connection between numbers and objects shapes the characteristics of numbers.
The system of numbers is not constructed by a single system of numbers but by combining multiple systems of numbers.
Monetary phenomena are extremely mathematical phenomena. If it is a person or an object, it has substance. Infinite or boundless numbers are not fundamentally handled. Even if we say we divide objects, there are physical limits. However, there are no limits to money. This is because money is a mathematical matter. And the problems of the monetary economy are essentially mathematical problems.
Having substance means having not only quantitative aspects but also qualitative aspects. In other words, economic numbers generally involve quality. For example, even if we say we cut meat into four equal parts and distribute it to four people, the meat slices are different, and the four people also have individual differences. Besides the number four, there are qualitative differences and variations. However, once converted into monetary value, these differences are lost. An item worth 400 yen has only the value of 400 yen.
Originally, numbers are established by combining inner numbers and outer numbers, but once converted into monetary value, they only have the characteristic of quantity. This is the feature of the monetary economy.
Therefore, monetary phenomena are extremely mathematical phenomena.