December 20, 2018
The preprint will show that most of the sciences for hundreds of years have lived with the mathematical formulas that are “half-correct” and offers a solution to find the formulas that are one hundred percent correct.
Here we show that the existing mathematical formulas so far are only “half-correct” since philosophically they have applied bad habits of humans who only judge the goodness of people or things that they loved, and only judges the ugliness of things they did not like. On the other hand, the formulas are one hundred percent correct if they are willing to assess both the goodness and ugliness of things.
Here is give a proof that only the formula of Harmony in Gradation or the formulas that contain its spirit are one hundred percent correct because of they able to show the level of perfection of everything being assessed accurately and precisely.
Keywords: “half-correct” mathematical formula; the Harmony; the Gradation; the Harmony in Gradation; the level of perfection.
1. PREFACE: EXISTING FORMULAS Are the “Half-Correct” Formulas
Here we show that the mathematical formulas used in the most of the sciences so far have applied bad habits of humans who only judge the goodness, kindness, favor, virtue, merit, benefit, courtesy, good deed, charity, or cordiality of people or things that they liked or loved. The same mistake was made when they were only judging the ugliness, badness, disrepute, infamy, deterioration, meanness, wickedness, degradation, malignancy, or shabbiness of people or things they did not like. As a result, these two types of formulas will only be half-correct.
As an example of the above statement, we present an analysis of the existing formulas which two formulas representing groups of formulas that only consider the goodness of others which we refer to as the Harmony, and two formulas representing groups of formulas that only consider the ugliness of others we call the Gradation.
1.1. Examples of the Half-correct Formulas that only consider the Goodness of Things
We call the formula that only considers the Goodness of things as the Harmony. In the following, we describe the weaknesses of the two examples of Harmony.
1.1.1. Herfindahl-Index for Competition Law
The purpose of the Herfindahl Index is to measure the Concentration Level. Then, if it is found that the Concentration Level in an industry for a certain period of time is already very high, the Economic Judge can decide to do a merger or the unification of several companies that have a low market, with the aim of saving the assets of small companies that will no longer be able to withstand an unfair competition. Unfortunately, so far as the existing formula is not able to prove that if the merger is carried out it will reduce the Concentration Level so that Economic Judges are hesitant to take action. In other words, this formula is not able to provide indexes that are significantly different in the two groups that have different nature.
1.1.2. Shannon’s Information Entropy
As an existing formula that belongs to the same group as the Herfindahl Index, Shannon’s formula for calculating information entropy also has the same weakness, which is not able to provide indexes that are significantly different in the two groups that have different nature. Thus, this formula is not accurate when used in the field of cryptography since it cannot accurately represent a significant change in the entropy of a deliberately altered population of information groups.
1.2. Examples of the Half-correct Formulas that only consider the Ugliness of Things
We call the formula that only considers the Ugliness of things the Gradation. In the following, we describe the weaknesses of the two examples of Gradation.
1.2.1. Gini Index for Income Inequality Assessment
The weakness of the formula that only consider the ugliness is to give the possibility that some random variables (or sets) of a different nature that have same sample populations will get the same index. So, the Gini Index is not accurate when used to assess very many countries where the likelihood is greater for the weaknesses of this formula.
1.2.2. Pearson’s Linear Correlation
Pearson’s Linear Correlation was chosen as an example in this preprint because there are millions of studies that use the existing formula and result in the greater possibility of errors in research conclusions. In a Pearson’s Linear Correlation, the regression process is done by finding the regression line in such a way as to cause the minimum value of the resultant deviations of all sample points to its regression which represents the condition of the maximum correlation level. So, there are two possible mistakes. First, the regression equation is correct as produced by the Pearson formula, but the level of confidence in the correlation is wrong. And second, besides the level of correlation, the regression equation is also wrong.
Figure 1. Proposed Roadmap of Mathematical Formula
2. The Future Formulas That Simultaneously Consider the Harmony and the Gradation
The future formulas are mandatory to simultaneously consider the goodness and the ugliness of others, which we call the Harmony in Gradation. Let see figure 1. In detail, the existence of “the harmony” and “the gradation” at the same time on a formula when used to analyze a Union or a random variable is to produce an index that accurately and precisely represents the “perfection level” of the Union or random variable regardless of the population. This means that an index equal to one is showing the perfect conditions, a value equal to 0.95 means that the level is 0.95 of the perfect, a value equal to 0.75 indicates the level is equal to 0.75 of the perfect, and so on. The consequence, the Harmony in Gradation will produce an index that represents the nature of the union or the random variable very accurately and precisely.
There are two ways to use the Harmony in Gradation formula.
- First, is to replace the existing formula. For example, figures 2, 3 and 4 are shown that Harmony inGradation is worth considering as a substitute for existing formulas such as the Herfindahl Index for Competition Law, the Gini Index for income inequality assessment, and Pearson’s linear correlation.
- Second, the spirit of Harmony in Gradation is utilized, in the sense that the existing formula is modified in such a way so that in the same time it has the two elements which“the Harmony” and “the Gradation”. For example, the proposed modification of Shannon’s formula for Information, Entropy measurement, as presented in Figure 1.
This preprint, not only contains a new insight but also provides homework for all researchers in the world to review the existing formulas they use today, starting with the formula used that causes the research being carried out to have a deadlock. Signs that your formula must be corrected are when decades of theory appear dubious when faced with another theory, or when years of research do not find the right solution. And, more obvious signs are when practitioners begin to question the theories made by academics
Sigit Haryadi (born in Indonesia on May 13, 1959) is a telecommunications engineer. The discovery of the concept and formula of the Harmony in Gradation on April 28, 2016, in preparation for retirement as an Associate Professor at the Bandung Institute of Technology (2015 – 2024). It is estimated that efforts to promote this concept until it is successfully recognized worldwide require 9 years to 25 years