_{1}

^{*}

Toward a balancing (win-win) and sharing world ( Matsui, 2018 ) , there might exist a class of kernels or black-holes at the harmonic cross zone. This article discusses the marginal diversity toward balancing, integration (win-win), and a sharing equilibrium, and obtains the relative or Chameleon’s condition of the correlation coefficient at the lower level, and the information amount at the upper level, on the dualism of artifacts. Instead of Simon’s bounded rationality, the new concept of a pair (diversity, integration) is introduced, and there are the relative pairs with a lower correlation coefficient of 0.8, and upper marginal diversity with a ratio of 0.6 at the knowledgeable or higher society. Finally, this pair map (microcosm) of the body is obtained for the win-win and sharing world and its harmony, and the Chameleon’s existence (marginal diversity) is ascertained and positioned at the hyperboloid of the pair-map (integration, sharing).

The world of artifacts ( Matsui, 2016, 2019) is progressing from being concerned with the tangible (material) toward being more concerned with the intangible (knowledge). This world is closer to that of invisible artifacts and the related black box, and as a result we are faced with the design problem of this new normal, or smart life, and the extent of diversity within the intangible, risky, and rapid world under globalization.

Matsui (2018) provided a few construction examples of a harmonic world, with the pursuit of growing social wealth, and found a harmonic condition for the balancing (win-win) vs. sharing issues (4.6) for the Chameleon Criteria ( Matsui, 2013, 2019). Matsui, Yamada, and Takanokura (2019) formulated the integration (win-win) vs. sharing issue for certain collaborations from a scientific and economic perspective.

However, the cross or equilibrium zone at the balancing, integration (win-win) vs. sharing center might have a kernel or a black-hole ( Matsui, 2019, 2020) on Chameleon’s correlation, criteria, and diversity issues. The problem occurs under uncertainty, is especially critical for knowledge or higher society under closer correlation, and is considered numerically based on three sample correlation tables.

This article discusses marginal diversity toward balancing, integration (win-win) vs. sharing, and could obtain the relative or Chameleon’s condition of a correlation coefficient at the lower level, and an information amount at the upper level. This is referred to as the dualism of artifacts ( Matsui, 2019). Instead of drawing on bounded rationality in economics, the new concept of a pair (diversity, integrity) is introduced, and there is the relative pair of a lower correlation coefficient of 0.8 and upper marginal diversity with a ratio of 0.6 for knowledge or higher society.

Finally, these facts are systemized as a pair-map (microcosm) of artifacts for the win-win and sharing world, and its harmony ( Matsui, 2018). The pair-map first originated in 1983 ( Matsui, 1983, 1988, 2002, 2008), and is simplified here as a sandwich or composition of the pair (diversity, integrity) at the lower level, and the pair (integration, sharing) at the upper level.

From the 3-skyme (S = W) sandwich principle ( Matsui, 2016), we have developed the pair-hierarchy theory of nature vs. artifacts body as a pair-like type (

For the artifacts, this pair-hierarchy shows the tangible stages with weight at the lower level, and the intangible stages without weight at the upper level. Each level in the six pair-hierarchy in

In

Recently, the relationship between the pair of bodies A and B has been formulated using a Venn diagram from a scientific and economic perspective. For example, this relationship is represented by the profit equation shown in

In

( E N A + E N B ) / 2 ≥ E N A × E N B (1)

The inequality presented in Equation (1) shows that balancing (win-win) would be better than integration, and if the profits of A and B are equal, then both sides of the inequality are equal.

Regarding collaboration issues, the relationship between balancing, sharing, and integration are presented in

Based on previous research ( Matsui, 2018; Matsui, Yamada, & Takanokura, 2019), this three-way relationship can be outlined as presented in

Generally, the artifacts body would be characterized by the dualism of materials vs. value. This refers to the value of some function of material or data, and money (profit) is representative of value and the information amount. Under the lower level, the relationships between balancing, sharing, and integration are shown in

The fundamental equation [

H ( X , Y ) = H ( X ) + H ( Y ) − T ( X , Y ) (2)

In Equation (2), H(X) and H(Y) are the information amounts of A and B respectively, and H(X, Y) and T(X, Y) are the information amounts of integrity and integration, respectively.

At the upper level, several information amounts are available for the three correlation tables. An additional information amount is the sharing amount of information, and is introduced below.

The total sample number is denoted as follows:

N = N + + N − + N 0 , (3)

In Equation (3), N + = ∑ f k + is the area of the upper half, N − = ∑ f k − is the area of the lower half, and N 0 = ∑ f k 0 is the diagonal area, in which f k is the frequency of cell k, k = 1 , 2 , ⋯ .

The information, H, is defined as follows:

H = − ∑ ( f k / N ) log ( f k / N ) (4)

More specifically, the information amounts of integration and sharing are defined and calculated as follows:

Integrity (joint) amount:

H ( X , Y ) = H + + H − + H 0 (5)

N = 250 ( N + = 18 , N − = 19 , N 0 = 213 ) ,

Sharing amount:

H ( X Δ Y ) = H + + H − → 0.6111

H + = ( N + / N ) log N − ( 1 / N ) Σ f k + log f k + = 0.3975 − 0.0916 = 0.3059 (6)

H − = ( N − / N ) log N − ( 1 / N ) Σ f k − log f k − = 0.4196 − 0.1144 = 0.3052 (7)

in which N + → H + , N − → H − and N 0 → H 0 .

From

Through examining the correlation and information amounts,

summary | correlation coefficient | diversity** | integration | sharing | integrity | diagonal (H^{0}) | ||
---|---|---|---|---|---|---|---|---|

0.95 | 3.3 | 1.197 | (0.7) | 0.6111 | (0.4) | 2.113 | 1.502 | |

0.83 | 2.9 | 0.6382 | (0.4) | 1.0933 | (0.6) | 2.252 | 1.159 | |

0.79 | 3.1 | 0.3983 | (0.2) | 1.6588 | (0.8) | 2.718 | 1.059 | |

chameleon’s criteria | 0.83(0.48)* | 2.9 | 0.369 | (0.4) | 0.631 | (0.6) | 0.4 versus 0.6 |

*concise result ( Isotani & Matsui, 1969) **H(X) + H(Y).

the pair-map of knowledgeable and intelligent artifacts.

According to

From

cycle* type | Z ( = X + D ) | constraints (redundancy) | marginal diversity (MP) | ||
---|---|---|---|---|---|

processing (X) | delay (D) | integration (Muda) | sharing(efficiency), EN | ||

cost system | variable cost | (marginal) profit | variable cost (EC) | fixed cost | value (profit) |

diversity (Z) | H(X) 1.609* | H(Y) 1.691** | T(X, Y) 1.197** | H^{0} 1.5019** | H (X, ∆Y) 0.6111** |

integrity ( L ¯ ) | H(X, Y) 2.113** |

*cycle (revenue): E R ( Z ) = E N ( L ¯ ) + E C ; **case of

from

From these results, we can ascertain the equilibrium inequality of knowledge and intelligence as follows:

0.4 vs. 0.6 (upper)

Integration (Muda) > (Chameleon’s diversity) < Sharing (efficiency). (8)

R = 0.83 (lower)

The inequality presented in Equation (8) shows that Chameleon’s diversity can be understood as being conceptually similar to, or updating, Simon’s concept of bounded rationality ( Simon, 1947). That is, for the industrial or real world, the boundness of rationality would be result in the lack of diversity at the finite time and space.

By utilizing correlation tables and pair-maps, this article approached and investigated the existence of kernels or black-holes at the harmonic cross zone of the balancing (win-win) and sharing world. Under uncertainty, a Chameleon’s harmonic correlation was found in criteria and diversity, instead of bounded rationality in economics, for knowledgeable and intelligent artifacts.

We should notice the existence (zone) of Chameleon’s diversity in dualism at the industrial or real system, probably escape of GAFA, CONVID-19 and so on.

However, our article might not yet reach the visible quantification or mechanism of bounded rationality at the view of marginal diversity.

Further research should investigate the harmonic progress on win-win and the sharing world toward smart supply chain and city. A critical problem would be resolved by using the dualism of artifacts and its skewness in the gap between things (lower) vs. value (upper), and/or motion vs. energy, at body.

This research is now advancing from factory physics, economics ( Matsui, 2008, 2014) and artifacts science ( Matsui, 2016, 2019) to the new academic discipline of indivisibility/body (Matsui, 2020). Some characteristics of the discipline would be mainly seen on pair body, indivisibility and marginal diversity.

The authors declare no conflicts of interest regarding the publication of this paper.

Matsui, M. (2020). A Chameleon’s Harmonic Correlation, Criteria, and Diversity for a Win-Win and Sharing World. Theoretical Economics Letters, 10, 735-744. https://doi.org/10.4236/tel.2020.104045