Journal of Digital Life 2023,3,3

Secondary publication

Nature Versus Artifact Body II:
Sollen, Central Dualism, and Chameleon Criteria
Masayuki Matsui 1
1

University of Electro-Communications, Kanagawa University, 3-27-1, Rokkakubashi, Kanagawa-ku, Yokohama 221-8686 Japan.

Abstract
Contrary to Wiener’s work, the subject of Sein and Sollen in “nature versus artifact bodies” was logically reexamined using a white-box (pair-matrix) approach and formalized on pair-map (microcosm) under closedearth versus smart-world conditions. This body science and Sollen of 3M&I variety (pair-map) would be
probably developed at the type of ternary SW, which resembles the Eastern danshari concept, and is likely
due to the motion–energy dualism under Newton’s laws (analog type), or equivalently, the amount–value
dualism under Matsui’s law and dualism (discrete type). For this body’s central dualism, a pair map(rotational phase) was characterized in 1983 based on the microcosm of cross-ellipse images in a matrix of
input–output pairs. At the paper, this field theory is physically formulated, solving the pair matrix, ternary
SW and its central dynamism in a body of input-output. The observed underlying condensed structure (timemodel), and the internalized (embedded) dynamism (fractal and wave motion equations), are numericallyclarified based on the expansion of the corporate-producing entity pair maps in Matsui’s theory. Furthermore,
it is demonstrated that the center of the pair-map hyperplane corresponds to a black hole (manifesting in theform of a conical dip that warps spacetime), collapsing the artifact bodies. Finally, interesting issues andfindings are reported regarding the central dualism, progressive physics and chameleon criteria (medium),and are related to pair-map.
Keywords: Body science, Matsui’s dualism, Ternary SW (sandwich), Progressive physics, Look-ahead
logics

1. Introduction
Our study was postwar motivated by the existence of Cybernetics (Wiener, 1961; Ashby, 1956; Ashby, 1960) in
disciplinary academics. Certainly, the world of Cybernetic is unique, universal, and attractive. However, this theory
is not directly applicable to the practical treatment of (discrete/digital) Industrial engineering (IE) & Operations
research (OR) of huMan, material/machine, money/monetary, and Information (3M&I). Thus, there are someconflict stages and a long way to the art of digitalization at body science and realization.
Based on Wiener’s work (Wiener, 1961), we have been observing object shifts and advances in animal, machine, andinformation. Thirty years ago, Nof et al. (2015) presented the PRISM concept, which includes production, robotics,
and integration software for manufacturing and management, and established the PRISM Center at Purdue University.
Conversely, the 3M&I concept and its art was previously named by the author based on the definition of industrial
engineering (IE) in 1948.
Although the value (energy) concept is not positively seen under the PRISM or Cybernetics categories, it would stillbe critical in the modern closed-earth versus smart-world age and toward the art of 3M&I diversity. ClassicalCybernetics would also be critical at the black-box and feedback scheme and desirable to the white-box (pair-matrix)
and look-forward (ahead) scheme toward post-Cybernetics.

Received: 12 December 2022, Accepted: 28 December 2022, Published: 17 January 2023
* Correspondence: matsui@kanagawa-u.ac.jp
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1Nature Versus Artifact Body II: Sollen, Central Dualism, and Chameleon Criteria
Masayuki Matsui
Since 1967, steady progress on the 3M&I concept has been made in fields of factory physics, management, andqueueing systems with losses (Matsui, 2016). This has led to the abyss predicted by Matsui’s equation (dualism) andthe formation of a pair map (rotational phase) at the point corresponding to the maximum profit from the collaborating
manufacturing and sales centers (Matsui, 2002). The problem of profit maximization (W) is similar to that of thecollaboration of sales (Z) and lead time (L) in Matsui’s equation: W = ZL, and is probably reaching to the concept ofternary SW/pair-map at the central dualism of body.
Early research on this topic and progressive physics was motivated by the queueing theory and inventory. Matsui’s
equation was obtained in 1977, look-ahead logics became available, and has recently gained attention as a universal
principle that can be described mathematically via algebra, geometry, analysis, and probabilistic control. Matsui’s
equation (discrete type) is similar to or has a dualism analogy with Newton’s law (analog type) in the interdisciplinary
problems of physics and economics. See Figure 1.

Figure 1. Duality of Newtonian mechanics and Matsui’s law in (Matsui, 2016).
At the beginning of this body’s central dualism, the pair map was first invented from a cooperative game, andcharacterized later by the microcosm of cross-ellipse images in a matrix of input–output pairs. In algebra, the field
theory helps solve the pair matrix in an input–output system, and the ellipse map clarifies the economics of theinvisible collaborations between bodies.
Currently, questions are being raised regarding the relationship between nature and “artifact bodies,” also known as
3M&I bodies. The academic and original nature of the central dualism (Matsui, 2002, 2016) in this topic is a productof developmental research that has yielded middle-phase pioneering results and pair maps. This middle-phasemechanism represents an artificial computer architecture problem, and its boundary (interface) in recent cyber–physical systems remain unresolved.
Pair maps (Matsui, 2002, 2008, 2013) manifest this middle problem in supply and demand systems. They appear to
be two-dimensional representations but are, in fact, three-dimensional miniaturized models (microcosms) of artifact
bodies and are fundamentally governed by the dynamism of Matsui’s equation (Matsui, 2002, 2016) . Recently, thiswas elaborated in (Matsui, 2020).
In addition, in numerous fields ranging from economics to physics, lower micro and higher macro relationships do
not emerge in visible forms. Thus, their boundaries and connecting relationships are overlooked. Matsui’s equation

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Nature Versus Artifact Body II: Sollen, Central Dualism, and Chameleon Criteria
Masayuki Matsui
represents a dual connection, offering a bridge to fields of physics, together with signposts (Matsui, 2013, 2020) andeconomics via interindustry relations entailing table connections and the future information society.
To unravel this middle phase, we must focus on realizing corporate robots (Matsui and Ishii, 2019; Matsui et al, 2021)
as the embodiment of pair maps at an industrial design stage. This task concerns human existence and corporate middle
management and focuses on the nature of the essential scientific role of middle managers.
Important research values that are crucial to the primal state of being (Sein) and ideal human society (Sollen) are thosethat lead to the development of theories and methodologies for management approaches, emphasizing a middle phasethat is neither at the top or bottom (Matsui, 2002, 2008, 2016; Matsui and Fujikawa, 2005). These values contributeto the high and efficient management of the world of artifact bodies and promote sustainability.
With regard to post-cybernetics, the repetitive and cyclic processes of nature versus artifact bodies with delay/loss
can be formulated as shown in Figure 1 by considering the profit equation (cyber/macro level) and progressive
equation (physical/micro level) (Matsui, 2008, 2016). The process can be verified based on Sein, central dualism,
ternary SW and chameleon’s criteria at the physical body.
2. Pair-Map Duality and Matching
2.1. Pair-Map Duality and Mismatching Problems
Herein, consider a 3M&I body as a system consisting of inputs and outputs (with a goal). This system has functions
that maximize the output and minimize the input. Furthermore, a two-term input–output matrix (Matsui, 2008),
referred to as a pair matrix, is considered a collaboration function for the input and output.
Each element of this matrix is a paired element (output gain and input loss). In examples of nature or artifact bodies,various graphic patterns are seen in the pair matrix, though they are all characterized by intersecting ellipses. Thus,an elliptical rotation mechanism generally referred to as a pair map (generic name) is observed Matsui, 2002, 2008,2016; Matsui and Fujikawa, 2005).
Consider the interconnections between manufacturing (input) and sales (output); the aforementioned intersecting
ellipses have intersecting axes, one of which (corresponding to positive correlation) is referred to as economic
efficiency, and the other (corresponding to negative correlation) as reliability. The intersection point of thesefundamentally contrasting axes represents an individual objective (profit maximization) that reaches an equilibriumbalance (win–win or mutation point). A variant of a hyperbolic type is seen in this case, which has an orbit toward thecenter.
Economic efficiency and reliability represent the gain and duration of individual systems, respectively. Here, system
duration negatively correlates with gain, implying that gain size is related to redundancy within the required time.
Thus, no redundancy is present for large gains; if substantial redundancy is present, the gain decreases, increasing theloss and reducing profit.
Furthermore, various forms of map diversity are observed; by discovering the possibility that they may provide a
universal bird’s-eye view (microcosm) of artifact bodies and their clock dynamism, we proceed to verify andcomprehend them, thereby proposing various forms and ideal shapes for artifact bodies.

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Masayuki Matsui
2.2. Body Universal Law of Nature Versus Artifact Bodies
The diversity in form is believed to originate from the duality (Matsui, 2013, 2016) in numerical and monetary(value) equations corresponding to Matsui’s law, similar to the duality in motion and power (energy) equations in
Newton’s laws. The duality of matching and mismatching (skewness) in this middle phase arises in various
phenomena related to the relationship between nature and artifact bodies, as listed in Table 1.
Cycle
Management

Table 1. Cycle duality: nature versus artifact bodies
Lower (movement)
Upper (value)
Work (waste)
Profit formula (addition)

PhysicalMotion (efficiency)

Power (energy)

Information

Symbol (redundancy)

Meaning (knowledge)

Production
Matsui’s law

Thing (flow)
Little’s formula (standby)

Administrative (procedure) Matsui’s equation (job)

Systemic

Scientific
Artifact bodyFirst law (motion)
 Second law (force)
Newtonian mechanics
SchemeDemocracy (people)
Capitalism (money)
Eiichi Shibusawa
Confucianism* (things)
Abacus* (money)*Eiichi Shibusawa, “Confucianism and Abacus” (1916)

Matsui’s equation (W=Z×L) is a universal law (Matsui et al., 1978; Matsui, 2005a) derived by Matsui for artifact
bodies, where Z denotes the cycle time (cycle), W is the waiting time (value), and L is the number of people waiting(quantity).
The multiplication used in this equation is not a simple product but a dynamic adjustment mechanism (role) for
reaching equilibrium. For example, typical physics laws (concept of leverage) and economics (concept of specificgravity) are formulated in a vector space with Matsui’s law as their basis.
Science has advanced by discovering patterns of regularity (cycles) because cyclic phenomena are always considered
reproducible and provable. This cycle (Z) is a summation of Z = regular thing (X) + irregular thing (D).
The latter results from the interaction with the surroundings and is generally regarded as a delay phenomenon (e.g.,reacting, waiting, waste, overflow, margin, error, or profit). Studies on the laws governing this interaction are
relatively new. However, a linear relationship exists between delays and overflows in systems (Matsui et al., 1978;
Matsui, 2005a) and constraints under which cycles stop mid-way (Matsui, 2005b; Yamamoto et al., 2006), as in the
CSPS model (Reis, 1967).
For artifact bodies, L=λW (Little’s formula, where λ denotes the arrival rate) represents the starting point of a queue,
and equations such Matsui’s law, i.e., W=ZL, are later derived for the loss-allowed system. For physical bodies andelectromagnetic systems, Newton’s first formulation of dynamical systems and Joule’s law can be considered,respectively. See Figure 1.
These laws have all been shown to be essentially isomorphic (Matsui, 2011, 2016). Generally, Matsui’s law holds
mathematically (algebraically, geometrically, analytically, and stochastically) in nature versus artifact bodies.
Moreover, the concept of energy in a physical body corresponds to that of money (value) in an artifact body (similarity).

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Nature Versus Artifact Body II: Sollen, Central Dualism, and Chameleon Criteria
Masayuki Matsui
3. Nature Versus Artifact Bodies and Formulation
3.1 Ideal Form and CSPS Model
A nature versus artifact pair body (Ordered-entry, OE, type) was found in (Matsui, 2016), and the pull-type in themerge processes 𝒓 𝒗 → 𝝀 is believed to be a typical ideal form thereof. Figure 2 refers to the Diet–Absorption–
Energy (DAEn) of Ternary SW (sandwich), which resembles the Eastern “danshari” (“refuse–throw away–
separate”) style. The problems with the ideal form in Figure 2 are duality matching, mismatching, and skewness.

Figure 2. Ideal form of nature versus artifact body (DAE_n): pair body (pull OE type).
From a separation process study (λ → r + v) of the CSPS model (Matsui, 1978, 2005a), the relationship between
delays E (D) and E (η) of a pair-body (push AL/OE type) can be seen in Figure 3. Here, when ρ < 1, the foreseeablechameleon criterion is as follows.
For arrival 𝜆, based on service X and buffer 𝐶 1: 0.7: 0.7 (1), 𝑋: 𝐷 0.6: 0.4, and upper chameleon criterion(medium) (Matsui, 1978, 2013) of 0.6 versus 0.4 is simultaneously satisfied.

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Nature Versus Artifact Body II: Sollen, Central Dualism, and Chameleon Criteria
Masayuki Matsui

Figure 3. Example of Poisson arrival versus constant arrival (Matsui et al., 2021).
In addition, when ρ
1, under a Poisson arrival, 𝑋: 𝐷 2: 1, and a chameleon criterion of 0.6 versus 0.4 is obtained.
Furthermore, in a heat efficiency model, a dual AL-type pair body can be determined.
Moreover, the first case of the merge process is changed to r (X) = λ- v (D), and in DAEn, a better diet (X) would lead
to better absorption (D). Note that this fact in the value type would introduce the opposite criteria.
3.2. Formulation of Nature Versus Artifact Bodies
From Figure 2, the nature versus artifact bodies can be expanded to the cyber–physical body, and formulated byconsidering the profit equation (cyber level): ER = EN + EC in Section 3.1, and progressive equation (physicallevel) in cyclic processes:
Next inflow O

next demand D

standard inventory MI – end inventory I(1)Then, the logical formulation of bodies is seen at Figure 4. According to Figure 4, the formulation implies that thegoal approaches the state variable of the standard inventory (MI) to the next outflow (ER). The standard inventory is
regarded as a control variable that maximizes the marginal profit. This could be reduced to a formulization problem
using the Matsui’s matrix equation (Matsui’s ME) (Matsui, 2018), which partially agrees with a Chinese theory (kisho-ten-ketsu logic).

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Nature Versus Artifact Body II: Sollen, Central Dualism, and Chameleon Criteria
Masayuki Matsui

Figure 4. Logical formulation of nature versus artifact bodies.
Matsui’s ME is a logical matrix product, i.e., (Introduction × Development × Transformation × Conclusion ×
Balance) = Goal. The type II Matsui’s ME is similar to the Ricatti equation in control theory (Bittanti, 1991).
Results should be presented precisely and should not contain material that is appropriate in the discussion. Units,
quantities, and formulas should be expressed according to the International System (SI units). All measurements
should be given in metric units.
4. Physical Body Duality (dualism) and Mismatching
4.1. Physical body cycle and pair-map expansion
For physical body cycles, the following progressive equation (flow control formula) is generally returned, and it issimilar to the wave equation of the discrete type (1). The lifecycle (rotating system) of a physical body according to
the flow control equation is depicted in Figure 5. This is a wave equation of the discrete type. Then, our pair map of
a physical body can be expanded to accompany the rotation cycle in Figure 6.

Figure 5. Physical body cycle (rotating system) versus wave (flow).

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Nature Versus Artifact Body II: Sollen, Central Dualism, and Chameleon Criteria
Masayuki Matsui

Figure 6. Physical body pair map and figure changes (Matsui, 2018).
As shown in Figure 7, the chameleon criteria (Matsui, 2011) introduced in the discussion of duality mismatchingcorrespond to the media. These criteria are based on the linear equations for delays and overflows (Matsui et al., 1978;
Matsui, 2005a)

𝜆𝐷

1

𝜌

𝜂, 𝜌

𝜆 ⁄𝜇 .

(2)

The design criteria of CSPS artifact bodies satisfying this relationship is known as conditional expressions (chameleon
criterion), given by the following equation:

𝜆 𝑣 :𝑣 𝜇 :𝑐 𝜂

1: 1.4 𝑙𝑛2 : 1.4 𝑙𝑛2(3)This problem in physical bodies can be seen in Figure 7, where 𝜆 corresponds to the initial velocity 𝑣, service rate
𝑣 corresponds to velocity 𝑣, and 𝑐 corresponds to acceleration 𝑎 (Walker, 2001). In addition, from a duality
perspective, earnings ER corresponds to energy (Hamiltonian), and lead time 𝐿 corresponds to motion p (= v L ).

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Nature Versus Artifact Body II: Sollen, Central Dualism, and Chameleon Criteria
Masayuki Matsui

Figure 7. Three-dimensional physical body (𝜆, 𝑣, 𝑍) system.
4.2. Economic Efficiency Versus Reliability in Physical Body
Here, Figure 7 is an expansion of the pair map for a physical body provided in Matsui, 2002; Matsui and Fujikawa
2005). The relationship of economic efficiency (energy) versus reliability (gravitational pull) is further clarified. In
general, the artifact body (money) is a Hamiltonian (energy) of a physical body.
𝐸𝑅 𝑍

𝐸𝐶 𝑋

𝐸𝑁 𝐷 .

Moreover, 𝐸𝐶 𝑋 is equal to the motion energy 𝑚𝑣/2 . When 𝑋 → 𝑍

𝐸𝑅 𝑍

𝜆

𝜇, 𝐷

𝜂, and 𝐷

𝑋

𝑋: 𝐷

𝑋

𝐷 , the following equations hold:

𝐿𝑍 or 𝑍𝐿 ,𝐿𝑋 or 𝑋𝐿

In particular, when 1(4)

𝐿𝐷 or 𝐷𝐿 .

(5)

(6)

1, then

0.5: 0.5 𝑍

1 ,

(7)

where 𝜆 and 𝜇 are different 𝜆: 𝜇 1: 1.4 , and X: D
0.6: 0.4.
In addition, for reliability (gravitational pull), if 𝐺 is the gravitational constant, then𝐹

𝐺𝑀𝑚/𝑟 .

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Nature Versus Artifact Body II: Sollen, Central Dualism, and Chameleon Criteria
Masayuki Matsui
Here, if we consider 𝐺𝑀/𝑟 → 𝑍 𝑑 , 𝑚/𝑟 → 𝐿, then the gravitational force matches the lead time.
On the other hand, the Hamilton (4) could be represented at the ternary SW in Section 3.1 and Figure 5 as follows:
EC 𝑋
EC 𝐷 → ER 𝑍 . Also, some relaxation problem of ternary SW with allowance (buffer) is geometricallyseen at the progressive equation (1), Figure 6., and could be simultaneously displayed by 3D-like pair-map at Figure
7. Probably, this would result in the advanced field theory with ternary and pair-map at the central dynamism of body.
5. Pair maps and black holes
5.1. Artifact Body Wave Motion Equation and Conical Surfaces
Recently, the wave motion equation for the clock system of artifacts body type was obtained from a pair-map threedimensional polar display 𝜽, ∅ (Matsui, 2018). From this, the conical surface in Figure 8 was obtained at thecenter of the pair map. From the geometric relationship in (9) (Matsui, 2018), we derive (10) based on a
trigonometric theorem.

Figure 8. Pair-map kernel and black hole.

𝑅 sin 𝜃Then, we assume 𝜃𝜃𝜑 and 𝜃

𝜃

𝜑

sin 𝜃

𝜑 ,

(9)

𝜑, which implies that

𝑅sin𝜃

𝑅sin𝜃

.

(10)

Furthermore, if u → y, then 𝑥, 𝑦 are as follows:

𝑥

𝑅sin𝜃

𝑅sin𝜃

,

(11)

𝑦

𝑅sin𝜃

𝑅sin𝜃

.

(12)

Here, (2) is as follows:

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Nature Versus Artifact Body II: Sollen, Central Dualism, and Chameleon Criteria
Masayuki Matsui

𝐿
𝑍
From the above, 𝑥

𝑦

(13)

𝑦.

𝑅 cos 𝜑, and from 𝑑cos 𝜑,

𝑦

𝑑 .

𝑥

(14)

Therefore, point 𝑀 𝑥, 𝑦 is on a circumference of a circle of diameter 𝑑 centered at the origin, and the value of 𝑦is the 𝑦 coordinate value at this time. In addition, because 0 𝑑 𝑅, according to (5), 𝑑 is a function of 𝑥, 𝑦 and𝑑𝑥
𝑦 , we express a conical surface in three dimensions 𝑥, 𝑦, 𝑑 , as shown in Figure 8.
5.2. Artificial black holes versus Chameleon’s criteria
Normally, when a kernel (black hole) is produced in the middle of an artifact body pair map, the risk of system
divergence from the queueing theory increases as the input (demand) and output (supply) speeds converge. The riskof variations in the input and output may be avoided by providing a buffer (time) for demand matching. A stable(robust) operation of global artifact bodies is necessary to avoid the bankruptcy at managing of enterprise (artifacts)
type, and this may be achieved by adjusting the demand versus supply mismatching with a look-ahead
forward/feedback approach.
6. Conclusion and Outlook
The contribution of the paper is the findings of similarity and identification on nature (physics) vs. artifacts body,and the findings could be unified to the field of Newton’s Little formula, Matsui’s law, and Matsui’s ME at the pairmap microcosm. Probably, this material might also be applicable and useful to a class of the twin systems (cycles) at
the cyber (upper)-physical (lower) system.
This study began with a queueing matrix for the production of artifact bodies. Noting that our artificial society
consists of input (demand), output (supply), and queueing/inventory systems, we devised pair maps as tools(strategic tables) for sublating the dilemma facing manufacturing integration (sales maximization versus cost
minimization), starting with Matsui’s system as a basis for input and output. This has proven beneficial in providing
a core basis for subsequent research and allowing for the fabrication of miniaturized models of artifact bodies toprovide a microcosmic view.
Currently, inquiries have been made into artificial society. Microcosms of artifact bodies within this are miniaturized
models consisting of 3M&I objects. These miniaturized models (from 3D to 2D) are considered as pair-map categories(created in 1983). The format (compass) of these pair maps has been found in corporate-producing entities andphysical bodies in the natural world and economics; this format is expected to be verified and proven even further.
The observed underlying (deep) condensed structure (time model), and internalized (embedded) dynamism (fractal
and wave motion equation), are numerically clarified from the expansion of these corporate-producing entity pairmaps (Matsui’s theory). In addition, they also showed that the center of the pair-map hyperplane corresponded to a
black hole (cone) in the universe, leading to a collapse of artifact bodies.
A nature-versus-artifact-body pair-body (OE) phenomenon is seen in (Matsui, 2016, 2018), and the pull-type in themerge process is believed to be a typical type of this ideal form. This type of ternary matrix (Maurus and Plant, 2014)is referred to as DAEn in Ternary SW, which resembles the Eastern danshari concept. DAEn bodies have duality
matching and mismatching (skewness) problems in pair maps. A buffer based on proper delays (overflows) is expected
to resolve this mismatching dilemma.
Thus, based on our research, a desirable measure (that does not reach a black hole) is a dual chameleon criterion(medium) according to input 1:output In2:buffer In2 in the upper part of a body (quantity/motion) with an efficiencyof 0.6 versus a waste of 0.4 pull balancing in the lower part (money/energy system).

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Nature Versus Artifact Body II: Sollen, Central Dualism, and Chameleon Criteria
Masayuki Matsui
Finally, other than stochastic differential equations with numerical delays, Matsui’s ME type approaches may also bepractical in the nature versus artifact world. We believe this will lead to the solutions found in classical analects,
democracy, abacus, and debates on capital.
Acknowledgments
This paper is a translation into English of the following research paper, which has already been published inJapanese .Matsui, M., (2021) Bodies Science, Hyperboloid type and Nested Economics Sollen, Central Dualism andChameleon’s Criteria in Nature vs. Artifacts Body (II), The 9th OHKAN Conference of NPO: Transdisciplinary
Federation of Science and Technology, Tsukuba University, Japan.
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