Economics and Mathematics
In school, we are taught numbers and mathematics in a deductive manner. However, numbers are originally concepts derived inductively. The concept of numbers was established through purposes and functions such as counting, verifying, comparing, measuring, exchanging, and distributing. Essentially, numbers are purposeful and functional.
The important characteristics of numbers are their visuality and manipulability. They are visible and can be manipulated, which is why numbers have developed. Extending from this is money.
In the concept of numbers, what is considered the same, or equal, is key. We were taught that the basics of mathematics are addition, subtraction, multiplication, and division, but these operations are only a part of the functions of numbers.
Considering this, the essence of mathematics might lie in geometry and statistics rather than algebra. Economics is directly influenced by the functions of numbers. Without a correct understanding of the essence of statistics, economic problems cannot be elucidated.
We are taught the number system based on the decimal system as a completed entity from the start. However, numbers have been used in binary, ternary, senary, and duodecimal systems depending on their purposes and functions. Numbers have been formed based on their purposes.
Without understanding the origin and history of numbers, one cannot correctly understand the concept of numbers.
In modern economics, it is hard to say that mathematics other than statistics is directly involved in economics. Indeed, it may seem that advanced mathematics is used in economics, but the mathematics used there is different from the mathematics used in natural sciences. In physics, biology, or medicine, mathematics is established by being linked to some reality. Therefore, physics, biology, and medicine can be demonstrated by mathematics.
However, modern economics is not linked to any reality but is derived suddenly from conceptual ideas. Therefore, economic phenomena cannot be mathematically demonstrated and remain in the realm of speculation and conjecture.
Modern economics is more like literature than science.
Prediction, Planning, and Performance
What is certain and what is uncertain? Economics hinges on distinguishing between certainty and uncertainty. Revenue is uncertain. Agricultural products and fish catches are also uncertain. In contrast, the production of industrial products can be calculated with certainty, and the calculation of costs is relatively certain. Nominal accounts like financial costs can be calculated with certainty. Costs can be calculated with certainty, but it is different when resources are procured from overseas. Exchange rates and raw materials can fluctuate unpredictably. However, expenditures are highly certain, while revenues are often uncertain. This makes economics difficult to understand. The certainty of expenditures and the uncertainty of revenues make economic forecasting difficult and hinder economic planning.
Uncertainty is something that cannot be decided by oneself, while certainty is something that can be decided by oneself. Therefore, uncertainty is predicted, and certainty is planned. The result is performance. There are two types of budgets: those based on predictions and those based on plans.
The economy has been swayed by unpredictable, unforeseen, and unexpected events. Situations arise where we think we have predicted and understood, only to be caught off guard, endangering not only the market but society and life in general.
How to deal with unforeseen circumstances is a crucial issue for economics. Mistakes are not allowed, yet the root causes remain unresolved.
Economic policy aims to control uncertainty from certainty.
Revenue is uncertain and cannot be planned. Therefore, it can only be predicted. Certain things must be planned based on uncertain things. This destabilizes the management state. What is uncertain is that revenue is determined by buyers, and the decision to buy or not lies with the buyers. In other words, external factors determine revenue.
The factors that determine revenue lie in the market. The most fundamental revenue for management is uncertain. This is the biggest cause of economic uncertainty.
Revenue is more uncertain and fluctuates more than costs. Although it is often thought that there is little difference in the nature of revenue, differences arise depending on the structure of the industry. These differences are mainly influenced by the nature of costs.
Revenue is based on uncertainty, and expenditure is based on certainty. Revenue is irregular, influenced by the market, production volume, and supply-demand relationships. Consumption is not constant and fluctuates cyclically.
While the amount of necessary funds can be calculated, the exact amount of funds that can be procured cannot be calculated accurately.
The management entity acts as a rectifier to streamline irregularly fluctuating revenue and stabilize expenditure. Without understanding this point, one cannot understand the meaning of profit, nor can one manage and control the management entity through profit. Profit is not a goal but an indicator.
The management entity is responsible not only for production but also for distribution. If only production efficiency is pursued and distribution efficiency is neglected, the economy will become imbalanced and stagnant. Moreover, households are responsible for labor and consumption. The market is the place that connects producers and consumers. The market adjusts supply and demand.
What to Assume
What to assume changes the conclusion. Are we assuming certainty or conceptual products? Modern science is based on verifiability. Economics does not necessarily assume verifiability. It is not clear whether there is a causal relationship or a correlation. This is because the functions of numbers used in natural sciences and economics are different. The assumptions that make numbers valid are different.
Assuming something unverifiable as self-evident is a bad tradition in economics. Even when talking about demand and supply, it is not clear what is assumed and what is meant. The mathematical basis for what is considered demand and supply should be clarified and defined. In physics, things that cannot be directly measured are not assumed to be self-evident. In economics, what can be directly measured is statistics. Therefore, economic mathematics must be based on statistics.
Even in natural sciences, the range of things that can be directly measured is limited. Even if measurable, the range of phenomena with guaranteed reproducibility is also limited. Therefore, the basis of mathematics can be said to be statistics and sets. In mathematics, proof is a prerequisite because mathematics is supported by logical consistency.
Numbers represent functions. Numbers mean functions. Numbers themselves do not have any reality. Numbers exist because of functions such as counting, measuring, and comparing. Without functions, numbers have no meaning. Numbers mean functions, so they exert their utility by being linked to some real object. Numbers alone cannot exert their utility. Mathematics, which is based on numbers, is logic. The essence of mathematics is logic. Without correctly understanding this point, one cannot utilize mathematics.
Logic is developed based on some assumptions. If the assumptions are different, the answers and results will be different even if the same equations are used. In other words, mathematics is constrained by assumptions.
This is why economics cannot directly relate to mathematics. The assumptions of economics are conceptual, so no matter how much mathematical logic is used, it becomes detached from reality and cannot be demonstrated.
In modern society, mathematics tends to be seen only as an extension of arithmetic and calculation, deviating from its original purpose. Figures are seen only as figures. As a result, the functions and meanings of irrational numbers, rational numbers, fractions, and decimals are lost. Irrational numbers, rational numbers, fractions, decimals, and imaginary numbers have become mere products of concepts. This makes learning mathematics meaningless. The usefulness of mathematics is not understood. Part of the responsibility lies in modern school education and the examination system. Modern school education does not try to teach the most crucial aspects of mathematics. Why is it necessary to learn mathematics? It is not to solve exam problems. The true purpose of teaching mathematics is to understand the truths hidden behind mathematics. Modern school education teaches mathematics only as mathematics, so the essence of mathematics is not understood.
For example, modern sports can be said to be based on mathematics. However, we rarely consciously think about the mathematics supporting modern sports. However, it is not an exaggeration to say that modern sports are mathematics itself.
The functions of numbers include breaking down objects into parts (identification/discrimination), creating collections of several elements (aggregation), extracting specific properties of objects and identifying them (extraction and identification), sorting and classifying objects based on specific characteristics (classification), making objects measurable by some standard (measurement), making objects quantifiable (quantification), making objects countable (countability), making objects operable (operation), making objects comparable (comparison), and making objects verifiable (verification).
These functions of numbers constitute the principle of sets. Mathematics is based on sets because it is based on the above functions of numbers.
Numbers have the property of extracting specific characteristics from objects and classifying and aggregating them. This function makes it possible to break down and classify objects.
Some people equate mathematics with calculation. Mathematics and calculation are not the same. Operations and calculations are just manipulations. If operations and calculations are considered mathematics, the essence of mathematics is lost. If mathematics is taught for exam problems, it becomes hollow and degenerates into mere techniques. The important thing in mathematics is the purpose of learning mathematics. In the Edo period, the purpose of learning reading, writing, and arithmetic was clear. However, modern school education despises the purposes of reading, writing, and arithmetic while not clarifying their own purposes. Why does modern school education belittle reading, writing, and arithmetic? It is because reading, writing, and arithmetic are useful. In other words, the purpose is clear.
Originally, calculus, irrational numbers, rational numbers, and logarithms were also useful. However, because the teachers do not understand the original purpose of mathematics, the practicality of calculus is not conveyed. As a result, mathematics has become sophistry. How many teachers use mathematics such as calculus practically? In reality, very few teachers use mathematics in their daily lives. This means they cannot teach the true role of mathematics. Mathematics is an abstract concept.
The Essence of Mathematics Used in Economics and Natural Sciences
The essence of mathematics used in economics and natural sciences is different. The purposes and uses of mathematics in economics and natural sciences are different, and their formation processes are separate. The foundations that support economics and natural sciences are different.
First, natural sciences are based on given and objective assumptions, while economics is based on arbitrary and subjective desires and motivations. This difference also affects the concept of numbers.
Without clarifying the purposes and methods by which numbers were established, the original role of numbers cannot be seen.
While the mathematics of natural sciences has developed with the primary purpose of measurement, the numbers used in economics are mainly for distribution. Therefore, counting is emphasized more than measuring. When considering the differences between economics and pure mathematics, this characteristic of numbers becomes significant.
The difference between the numbers in economics and natural sciences can be described as the difference between “doing” and “becoming.” For example, in the case of money, one can invest ten billion yen. However, when it comes to setting the temperature of water to fifty degrees, the machine is adjusted to make the temperature become fifty degrees. Natural phenomena essentially “become,” while economics “does.” In natural sciences, numbers represent states, but the numbers themselves do not have any function. However, money has inherent power in the numbers it symbolizes. Therefore, in economic mathematics, manipulability is important. By directly manipulating numbers, economics is controlled. This is the decisive difference between numbers in natural sciences and economics.
The origin of numbers and mathematics used in natural sciences lies in division. Irrational numbers, rational numbers, fractions, and decimals were born from division. However, economic mathematics centers on operations excluding division. Therefore, the functions of group theory should be noted.
In nature, one-third is one and three in the market. When distributing to three people, it is important to make one into three rather than one-third. In other words, the numbers used in the market are more direct and tangible. Therefore, indivisible numbers are not necessary in the market. In economics, binary, ternary, and quinary systems have been established if necessary. In economics, mathematics is based on practicality.
Economics is fundamentally based on natural numbers. This is because counting is more important than measuring in economics. Therefore, irrational numbers, rational numbers, fractions, and decimals are not used. The simplicity of economic mathematics, due to the absence of irrational numbers, rational numbers, fractions, and decimals, should not be misunderstood as inferiority to pure mathematics.
Natural numbers do not include negative numbers and are based on discrete numbers. Additionally, additive subtraction is the principle.
The purpose of economic mathematics is distribution rather than measurement. Therefore, it becomes remainder arithmetic and balance principle. For example, the remainder of income after expenditure is savings. Income is the sum of expenditure and savings. Also, profit is the remainder after deducting costs from revenue. The sum of profit and costs is revenue. The value obtained by subtracting profit from revenue is cost. The product of average unit price and sales quantity is sales. Profit is also the remainder after deducting cost from price. Previously, the idea was that price is the value obtained by adding profit to cost, but recently, the idea has shifted to controlling cost within the range obtained by subtracting profit from market price. This change in the concept of profit, i.e., the remainder, signifies a change in thinking.
The Basics of Economics: Remainder Arithmetic
The basics of economics are remainder arithmetic and balance principle. In division, if it cannot be divided evenly, the remainder is produced, or the decimal part is truncated by some principle. This is the decisive difference from mathematics established by division. In other words, the mathematics used in economics and natural sciences are different.
In division, if it cannot be divided evenly, it is left as a remainder without forcing it. The function of the remainder is important.
Leaving a remainder is more important than dividing evenly. How to generate and utilize the remainder is a major issue in economics. The purpose and nature of mathematics are different from natural sciences.
In economics, surplus and shortage are important. Surplus and shortage are phenomena that are two sides of the same coin, but their functions are significantly different. The functions of surplus and shortage differ depending on the elements of people, goods, and money. In short, the total of surplus and shortage of funds is always zero, i.e., zero-sum. In contrast, the total of surplus and shortage of people and goods is not zero. If it becomes zero, it means that hunger or unemployment is occurring somewhere. Therefore, balancing surplus and shortage is the main purpose of economic mathematics.
Today, when we talk about economic loss, it is often a monetary loss rather than a material or human loss. Of course, material and human losses are also economic losses. However, today, monetary losses are enormous. Material and human losses have become secondary in economic terms.
Numbers have been used for economic and political purposes before being used for natural sciences. Pure mathematics developed based on physical objects. Therefore, economic mathematics has been unfairly treated and not given due recognition. Today, when we talk about mathematics, it mainly refers to those based on natural sciences. However, mathematics with economic functions also plays an important role.
Rulers tend to despise “money.” Therefore, they have discriminated against mathematics used in natural sciences as pure mathematics and academic mathematics. The so-called Terakoya (temple schools) distinguished reading, writing, and arithmetic from formal studies, treating reading, writing, and arithmetic as the studies of the common people. This is evidence of that discrimination. In the Edo period, arithmetic was only abacus. Arithmetic was not considered mathematics. However, this is a prejudice. It is similar to the discrimination of positioning computers as calculators today while not recognizing binary as formal mathematics. Commercial mathematics is also legitimate mathematics. There is no need to discriminate against it just because it is for commercial use.
Numbers do not exist on their own.
Numbers and mathematics are established by extracting functions from some entities. Numbers themselves do not inherently exist. The entities that establish numbers are some form of aggregates. By observing these aggregates, the characteristics of numbers are extracted. Numbers are based on some form of aggregates.
Numbers and currency share fundamental similarities. Firstly, both currency and numbers do not exist on their own. Originally, the value of currency is expressed in numerical terms. Both numbers and currency are fundamentally based on numbers. Therefore, the characteristics of numbers are crucial. Essentially, mathematics and economics are well-suited to each other.
The foundation of mathematics, which is numbers, was originally established by linking to purposes such as counting, measuring, verifying, and comparing. The essence of numbers is their purposeful function, and numbers themselves have no inherent meaning. Since numbers are established by their purposeful function, they presuppose some objects to become numbers.
Comparison, verification, and validation are fundamental functions of numbers and are important functions. In economics, comparisons such as year-on-year and forecast vs. actual are important functions, and one of the motivations for the emergence of numbers was to verify livestock, which is evidence of this. However, such functions are often overlooked in pure mathematics.
In natural sciences, numerical values arise from the functions of objects, but in economics, the functions that numbers exert on objects are important. In natural sciences, equations represent the laws and changes of phenomena, but in economics, numerical values signify the value and function of objects.
The functions of numbers in economics include comparison, verification, validation, measurement, exchange, classification, calculation, and preservation, and these functions also impose constraints. The purpose of economics is distribution, and the functions of numbers ultimately relate to distribution.
Economic mathematics has a strong connection between numbers and objects, and numbers are often strongly constrained by objects.
The characteristics of numerical values include: firstly, extracting specific characteristics from objects for identification; secondly, classifying objects into several aggregates; thirdly, defining objects by numerical values by setting arbitrary standards, i.e., establishing units; fourthly, unifying values; fifthly, quantifying objects to make them calculable; and sixthly, dividing and systematizing objects. The concept of groups holds significant meaning in relation to these characteristics of numerical values.
A typical example is bookkeeping. Bookkeeping involves a series of functions such as transactions, sorting, recording, aggregation, and settlement through numerical manipulation. Accounting numerical values essentially drive the management organization. In contrast, machines like boilers and airplanes are different. Numerical values merely indicate states and do not drive the mechanisms.
Profit and loss are fundamentally based on additive subtraction. Economic accounts build the overall framework by accumulating numbers. Additive subtraction and balance principle perform operations within a certain framework, which forms the prototype of double-entry bookkeeping. In other words, calculations are based on transactions and adjustments. Instead of directly adding or subtracting, addition is calculated by accumulating in the balance display column, and subtraction is calculated by accumulating in the opposite column of the balance display column.
Economic Space
Economic problems arise from the inconsistency between the whole and the parts. The distortions of people, goods, and money disrupt the economy.
The economy is established by the balance of workload, production, and income. When the expansion of disparities and the accumulation of debt reach an extreme, social systems collapse. Such distortions are spreading worldwide. In China, ghost towns called “鬼城” are spreading on one hand, while capsule apartments are emerging in urban areas, and people known as “鼠族” are increasing. These distortions destabilize society.
Indeed, economic conditions appear on the market surface as monetary phenomena. However, it is impossible to elucidate the economy by looking only at monetary phenomena and monetary aspects. The root of the economy is human activities for survival. The economy is established by earning income as some form of compensation and obtaining necessary resources from the market for survival. Money is not everything. Behind the monetary phenomena that appear on the surface, there is a real economy. Consumption and population determine the direction of prices.
Ultimately, the economy is about what and how much consumers need, how to produce what consumers need, and how to distribute it to those who need it. This issue has been replaced by the problem of money. Since the replacement, the essence of the economy has been lost, and we have been swayed by “money.”
Space is a collection of distances.
A collection of distances forms space. The distortion of space appears in distances.
Euclid begins his “Elements” by stating that there are three things: one is a point, another is a line, and another is a plane. Developing logic through three points is one form.
Numbers are composed of three points: the self, the object, and the unit. In other words, the basic structure of numbers is the triangular relationship created by the self, the object, and the unit.
The foundation of dimensions is created by triangles. Triangles relativize positions. When positions are relativized, it becomes possible to formulate relationships mathematically. By adding a time axis that represents change, space that represents position, motion, and relationships is constructed.
Triangles create space. Triangles form the smallest unit that constitutes space. Triangles create topology.
By assuming a four-dimensional space that adds a time axis to the three dimensions of people, goods, and money, economic space is formed. In other words, the collection of human distances, material distances, monetary distances, and temporal distances constitutes economic space. The triangles and spaces created by people, goods, and money form the basis of the economy.
Economic space can form a space similar to physical space by using people, goods, and money as coordinate axes. People and goods are constrained, and money is relatively determined by the relationship between people and goods. However, numerical values are open upwards. For example, the constraint on people is the constraint by population, and the constraint on goods is the physical constraint of production volume. The numerical system of people and goods is closed, but the numerical system of monetary value is open upwards.
The purpose of constructing economic space with the three dimensions of goods, people, and money is to enable operations between objects with different properties. For example, operations are possible by combining labor, cars, time, and other heterogeneous objects with money. For example, the formula unit time × number of people × unit price × average sales volume = sales revenue holds. If an average of two customers per hour buy five apples at 200 yen each over six hours, the sales revenue is 12,000 yen.
Monetary economic space forms a four-dimensional space by adding a time axis to the three axes of people, goods, and money. The vector of monetary value is formed and shaped by people, goods, and money. For example, gas sales form a market space and transaction space by the number of cases × unit consumption × unit price, and by adding a time axis, the revenue for a unit period is determined by the number of cases × unit consumption × unit price × unit time. Food sales form a transaction space and market space by the number of consumers × unit consumption × unit price, and by adding a time axis to the formed transaction space, the revenue for a unit period is determined by the number of consumers × unit consumption × unit price × unit time.
The vectors that arise in these spaces, the state of position, direction, and function determine the overall trend of the economy.
The vector formed by population, consumption, and currency flow determines the direction of prices.
In physics, length, quantity, quality, weight, heat, volume, area, speed, and force are important, while in economics, the whole, average, maximum value, minimum value, range, variance, bias, and composition are important. This is because the essence of the economy is distribution, and the currency that represents numerical values is a means for distribution.
The structure, distribution, and bias of income, production, consumption, population, and finance (debt and capital, revenue, savings) determine the movement of the economy.
The numbers used in economics are countable numbers.
Numbers make it possible to measure and calculate objects by converting them into countable values and quantities.
The numbers used in economics are countable numbers. The foundation of economic space is countable sets.
Monetary value is a countable set. The fact that money is a countable number means that money is a medium.
Money is a medium for unifying exchange value.
In a monetary economy, the economy is driven by the flow of “money.” The economic system is a mechanism driven by the flow of “money.” Therefore, to clarify the state of the economy, it is necessary to clarify how the flow of “money” affects people and goods.
The function of “money” is expressed in numerical terms. This is because the characteristics of numbers play a decisive role in the function of “money.”
“Money” emerged as a means of transaction. In other words, “money” is used to obtain necessary resources, exchange them, and accumulate value. Therefore, “money” must be something that can be owned, exchanged, and counted.
“Money” is something that can be exchanged and represents numbers. “Money” must be countable and exchangeable. “Money” must have exchange value and represent the characteristics of numbers. “Money” cannot function without interchangeability, countability, and realizability. Such “money” is required to have a direct function. The numbers represented by “money” are given a direct function. This is the decisive difference from the numbers used in natural sciences.
In other words, while the function of numbers used in natural sciences is indirect, in economics, they are given a more direct and practical function. The numbers used in economics represent exchange value and can be exchanged for goods, sold, bought, saved, paid as rewards, and used for investment and speculation.
Moreover, for “money” to function, a certain amount of “money” must be circulating in the market. Today, we can easily obtain “money.” However, “money” did not exist and circulate as “money” from the beginning. “Money” was initially something that could be exchanged.
“Money” is created through debt and supplied to the market through investment. Therefore, for the supply of money to increase, there must be demand for debt and investment. For “money” to be created and spread in society, there must first be a motivation to invest in something, which creates the need to incur debt. In a self-sufficient society, neither debt nor investment is necessary. So, what was there a need to invest in?
The most common uses of “money” are for war and satisfying vanity. Another use is for social capital. Education was added to this later. These are still the basics of public investment today.
We must not forget that the trigger for money to circulate in the market was war and the government bonds issued to procure funds necessary for war. This built the foundation of the market economy.
The units used in economics are not uniquely determined values like physical units.
The units used in economics cannot be uniquely determined like physical units. This is because economic units have quality, and density is an issue in economic units.
Therefore, the key lies in the average unit consumption and variance. If the absolute amount necessary for living can be secured, the economy can function. As long as it falls within the range of the maximum and minimum values, the economy can avoid collapse. The issue is whether the averages and variances of income and consumption are balanced. When the balance between income and consumption is lost, the economy becomes uncontrollable.
However, unit time, unit population, unit price, and unit production are not uniquely determined but are based on representative values. For example, the number of people, the number of sales, and even prices are not uniformly constant but have biases and fluctuations. When defining the units of people, goods, and money and measuring distances, the important factors are the average and deviation. In other words, the distances of people, goods, and money are determined based on statistics, which is a characteristic of economic space.
Units are omitted in equations because they are reduced to ratios, which implies the essence of numbers. A unit is something that identifies and extracts a part of the whole. Furthermore, by setting units, distances can be measured. In other words, units are based on some whole. Distance is a part, and because it is a part, there is a starting point and a focal point. Units are determined by where the starting and ending points are placed. Therefore, units are reduced to ratios.
Units constitute dimensions. Units represent dimensions.
The space created by people, goods, and money constitutes the dimensions of production, consumption, etc. The space created by production consists of production volume, labor population, and income. The space created by consumption consists of consumption volume, consumption population, and price.
The distribution of the labor population, production bases, and consumption areas is biased, and the economy stagnates due to distribution inconsistencies and distortions.
Considering this, in economics, averages, distributions, and densities hold the key. Furthermore, it is the structure of changes over time. The funds needed throughout a person’s life do not occur uniformly. There are several peaks in the supply and demand of funds according to age and life progression. The waves of income and expenditure do not match. Spatial and temporal changes cause economic fluctuations.
The total value of money does not represent the total physical quantity.
Economic activities are based on position, movement, and relationships. Representative relationships include causal relationships and correlations.
While the value of money is infinite, physical space is limited. When the value of money, which tends to diverge infinitely, reaches the physical limit of the market size, it begins to contract.
Even if it appears to be expanding, phenomena occur where the reality is contracting. Therefore, it is necessary to always relate the actual movement of goods and the movement of money. Nominal movements and real movements do not necessarily coincide.
Taking land prices as an example, land is finite, and there are limitations on usable land. Not all land is effectively utilized, and there is land that is not effectively utilized. The use of land changes according to its purpose. As the population increases and the economy grows, the effective use of land is promoted, and usable land decreases. When building houses, there are restrictions on the site area per house. This is a premise. The economy is about how to effectively use land, not about how much profit can be made from the land.
When the housing market matures, the site area expands, and the quality of housing improves. Moreover, good quality housing is provided to everyone. That is the land policy sought by the economic system.
Whether land is effectively utilized is summarized in the distribution of land.
The correlation between land prices and actual site areas differs during periods of market expansion and contraction.
If the total amount of land does not change, land is subdivided according to the increase in the number of households as the population increases. Land prices are determined by the supply and demand of land. However, when the population starts to decline, the site area should naturally expand. Also, housing should shift qualitatively from new construction to renovation.
In reality, land transactions fluctuate wildly unrelated to the actual demand for land, causing bubble phenomena. On the other hand, while the population is declining, there is an unprecedented condominium boom, creating a situation far from the effective use of land. Moreover, while there is an excess inventory of housing on one side, the number of homeless people is increasing on the other.
The issue of land prices in an economic sense is about maximizing the effective use of land, not about expanding land transactions or maximizing profits from land transactions. Misunderstanding this point leads to significant errors.
The economy plays an important role not only in quantity but also in quality, that is, density.
The market size is constrained not by money but by people and goods. This is because money is a number, has no substance, and is infinite. In contrast, people and goods have substance and are finite. Therefore, the real conditions that constrain the market size are formed by people and goods. Money units are only quantitative. In contrast, people and goods consist of quantity and quality. Therefore, the real economy has mass and density.
To understand the reality of the economy, it is necessary to understand this density.
Economic value is deeply related to density. Therefore, if the economy is only viewed in two dimensions as it is now, the whole picture of the economy cannot be grasped. Also, physics cannot be applied. If economic phenomena are deeply related to density, economic phenomena can be said to be more like statistical thermodynamic phenomena.
Physical distance can be simply reduced to quantity, but economic distance involves qualitative elements. Moreover, economic distance has subjective elements and variations, making it difficult to measure linearly. Basically, economic distance is based on statistical data, and its reliability varies with the average and deviation.
The reality of the economy lies in people and goods. Money is just a tool that mediates people and goods for distribution. People and goods, which are the reality, are limited, but money, which is the medium, has no upper limit. At the root of economic phenomena are people and goods. The mechanism of the economy is to distribute necessary goods to necessary people. The basics of the economy are people and goods. Monetary phenomena appear on the surface. However, what drives the reality of the economy are people and goods. The essence of the economy is how to distribute production goods to people, and the mechanism of the economy is the mechanism of distribution. To distribute, it is necessary for the necessary people and necessary goods to be balanced. The market is where the value created from human resources and the produced goods are exchanged through money.
There are always physical and human constraints in the market. Prices are different. Prices can vary two or three times even under the same conditions, premises, and situations, depending on time and place.
Inflation and deflation appear as prices of goods. In principle, prices inherently reflect the shortage or excess of goods. The imbalance between the distribution of people who need goods and the distribution of production goods causes this. The rise in energy prices, land prices, and the wild fluctuations in prices are caused by the bias in the distribution of goods and people. However, there are times when price fluctuations occur seemingly unrelated to the shortage or excess of goods. This is because money operates in places far removed from its original function. This is because money itself has no substance and therefore has no upper limit. The attempt to impose an upper limit on money is like the gold standard. However, the gold standard also ultimately failed to determine the upper limit of money.
Thus, the fact that money has no upper limit is one of the reasons why the economy is swayed by the movement of currency. The second reason is the inconsistency between the whole and the parts. There are differences in the value scales of individual industries. The imbalance of parts destabilizes the structure of the whole. When unreasonable disparities expand, consumption is unduly distorted. As a result, the balance between flow and stock is broken. The fact that entertainers and athletes receive higher rewards compared to other labor is due to differences in industrial structure. Even with low unit prices, high income can be obtained if there is high customer attraction. If such disparities become abnormally high, the consumption structure is also distorted. The third point is that there are qualitative differences in production means, income structure, and consumption structure. Each person’s income does not necessarily match their individual living needs. The economy is affected by such imbalances. When income disparities widen excessively, the consumption structure is distorted. The typical example of this is the bubble phenomenon. When there is an excess of money, more money than necessary flows into the stock market, causing asset prices to soar, and speculation pushes aside actual demand. The fourth point is that the economy relies too much on market competition. What is important is the appropriate price, not just being cheap or pursuing competitiveness. In other words, it is an example of how changes in the economy are amplified by institutional inconsistencies. Conversely, in a state of oligopoly or monopoly, appropriate price formation cannot be achieved. The economy is a purposeful activity, and competition without purpose is harmful. The purpose of the economy is distribution. The fifth point is that local fluctuations amplify overall fluctuations. This is a phenomenon where the overall price level loses control and soars when a certain good becomes extremely scarce or expensive, like the oil shock.
Today, money is used as a means of distributing necessary goods. Money is distributed to individuals in exchange for some consideration. People use their money to procure necessary resources from the market.
The problem is that the means to obtain money, goods, and life are not uniform. Also, production means are not uniformly distributed. Moreover, the quality of production means is not uniform.
To obtain money, it is necessary to own some means of production. The simplest is labor. Labor is one of the means of production.
The quality of labor is not uniform. Because the quality of labor is not uniform, the rewards and income as consideration are not uniform. There are differences in the quality of labor. The quality of labor varies by occupation. For example, there are qualitative differences between simple manual labor, skilled labor, intellectual work, and managerial work. They cannot be treated uniformly. Also, the quality of labor varies depending on how it is evaluated. Differences arise based on the results, quality, and working hours of labor.
Differences in the quality of labor lead to differences in rewards. Therefore, density is important in labor. Differences in income arise from differences in production means and outcomes. Also, differences arise depending on how labor is involved. Differences in the quality of income arise from how knowledge, experience, skills, achievements, and abilities are evaluated.
Moreover, there are differences in the quality of goods.
For example, in the case of housing, there are qualitative differences in housing based on site area, buildings, and convenience. Also, the people involved in construction are diverse, including plasterers, carpenters, architects, plumbers, and furniture craftsmen, and there are differences in skills and proficiency. Housing consumers also differ based on living standards, lifestyles, and income. These cannot be treated uniformly. Differences also arise based on the housing life cycle, depreciation, and financial planning.
Assuming there are people who need 60,000 houses, first, the materials needed to build those houses are required. Also, it is necessary to secure the workers needed to build the houses, including workers by occupation. And consumers must have the funds to buy the houses. In other words, the market cannot be established without the materials, workers, and income needed to build the houses. All these elements have quality, and averages, distributions, and densities are issues. Moreover, for the market to function, it is necessary for elements such as housing prices, wages, material prices, disposable income, and interest rates to be balanced. Furthermore, if these are not balanced over time, the market and industry cannot be sustained. Therefore, the economy is a function of housing prices, wages, material prices, disposable income, and interest rates.
Budgets and forecasts are based on Bayesian statistics.
I like the program “Otakara Haiken” and watch it often. When I think about it, the program “Otakara Haiken” seems to hide the basic idea of Bayesian statistics. “Otakara Haiken” is a program where people have their treasures appraised by professional appraisers. The person requesting the appraisal first presents the amount they predicted, and then the professional appraiser appraises it. The viewers also predict whether the actual purchase price and the predicted amount match the appraiser’s appraisal or not. This seems to be the reason why it has remained popular for a long time.
The contrast between the joy when a higher-than-expected appraisal is given and the disappointment when the prediction is off is amusing.
What is important here is that the person judges the authenticity of the antique and purchases it, and then predicts the current price and makes the appraisal amount public. The professional appraiser then makes an appraisal.
By repeating this process, the ability to discern is developed. This is Bayesian statistics. Bayesian statistics have recently gained attention because they seem to be the closest to the logic of human prediction algorithms.
The key to mathematics lies in algorithms.
Bayesian algorithms can be seen in forecast performance management and hypothesis testing. Predictions or hypotheses are made, executed or experimented based on those predictions or hypotheses, and the results are compared with the predictions or hypotheses to make adjustments or prove them. These algorithms are common in science.
Ordinary people make predictions, execute based on those predictions, reflect on the results, and use them as references for the next decision. This ordinary logical process is based on Bayesian statistics. By comparing results and predictions, correlations are found, and causal relationships are derived. However, just because there is a correlation does not mean it immediately leads to a causal relationship. Even natural laws that are taken for granted were not clear from the beginning. Everything starts with careful observation. That is science. Even if it is said to be based on derived laws, that is after the laws have been proven.
The problem with modern economics is that this logical development is not done. In other words, it cannot be called positivism. Economics is full of hypotheses that cannot be verified. It is treated as an economic law without any proof, just because it is probably correct. The principle of competition, which says that everything will go well as long as there is competition, is a typical example. Many economists claim that competition is a principle without comparing the differences between when the principle of competition is working and when it is not. This kind of principle is like a divine oracle. It has no rationality or logic.
What is certain and what is uncertain
Everything was vague and ambiguous at first. Ultimately, the origin of science lies in statistics.
What is required in mathematics is certainty. Mathematics is a symbol of certainty. Therefore, in mathematical logic, ambiguity and uncertainty are thoroughly disliked. Strictness that does not allow compromise is required.
What is certain and what is uncertain, economics holds the key to distinguishing between certainty and uncertainty. Revenue is uncertain. Agricultural and fishery yields are also uncertain. In contrast, the production of industrial products can be calculated with certainty, and the calculation of costs is relatively certain. Nominal accounts like financial costs can be calculated with certainty. Although it was said that costs can be calculated with certainty, it is different when resources are procured from overseas. This is because exchange rates and raw materials can fluctuate unpredictably. However, expenditures are highly certain, while revenues are often uncertain. This makes the economy difficult to understand. The fact that expenditures are certain and revenues are uncertain makes economic forecasting difficult and hinders economic planning.
When it comes down to it, the real world is full of uncertainties. It can only be said that things happen because they happen. This is why life is considered a gamble.
Even so, gambling can be explained if results are obtained. For the time being, the probability of winning or losing is fifty-fifty, assuming there is no cheating. Also, assuming there are no biases or distortions in the dice. It is believed that the probability of getting a winning side is fifty-fifty if repeated many times. This is called the law of large numbers.
However, the real economy does not work that way. Complex factors intertwine, and even if results are obtained, there are no rules on how to evaluate those results. The same result can be seen as a success by some and a failure by others. Most people are vaguely aware that the real world does not go according to theory. Therefore, when something happens, they are often admonished by saying that the world does not work according to logic.
People know that the events of the world do not go as they wish. Predictions do not come true. That is why gambling exists. If it were clear that stock prices fluctuate according to some theory, stock investment itself would not be viable.
For example, the birth ratio of males and females. The ratio of males to females is not exactly fifty-fifty. There are slightly more males. The law of large numbers does not apply here. However, it is generally accepted that there are roughly equal numbers of males and females. Moreover, it is often easier to assume that there are equal numbers of males and females. The precision of mathematics is sufficient for this level in the real world. It is meaningless to derive hundreds or thousands of decimal places. People also have their own strengths and weaknesses. It is rough to treat people uniformly as the same.
Modern economics sounds plausible but is not reasonable. It sounds probable but is not certain.
The events of the world are vague and uncertain. That makes life difficult. Therefore, people predict the future and make plans. Mathematics is the basis for this.
However, numbers are just numbers, and predictions are just predictions. There are always errors. It would be best if the world went exactly as predicted and planned, and plans were realized without any differences. Predictions and plans often do not match. Science has developed from correcting the errors between hypotheses and results, predictions and actuals, plans and results. Therefore, the root of mathematics is error correction, sets, statistics, especially Bayesian statistics, and probability. And further, approximation.