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This paper develops a functional relation between Digital Libraries and Confucion Integrated Curriculum Learning systems. We show that under certain properties of Learning Systems which can implement laissez-faire markets under uncertainty, the systems integration is possible in entropy space.

In discussing “Confucianism and Education”, Charlene Tan [

1) Aim of Education

The central place of education in Confucianism is stated in the opening passage of Xueji:

If a ruler desires to transform the people [and] perfect [their] customs, [the ruler] can only do so through education! (Xueji I).

The context of the passage is about good political governance. Rather than merely relying on laws, able officials, or virtuous advisors―all good measures in themselves―the ruler should devote attention to educating the people. The goal is to radically change the people by refining their conventional ways of thinking and doing. The reference to transformation and perfection in the above verse signifies that the scope is extensive, going beyond skills training and cognitive advancement to paradigm shift and character development. The actualization of this aim of education naturally requires a normative standard to guide the ruler in knowing whether and when the people have been transformed and their customs perfected. This standard is revealed in Xueji II to be dao (Way), which is the object of learning: “People who do not learn will not realize dao.” Dao is the Way of Heaven (tian) or “guiding discourse” (Hansen, 1989 in Tan [

2) Curriculum

“Curriculum,” as used in this article, refers to the totality of learning experiences provided to students. This means that the curriculum includes not just the contents to be studied but also all planned activities, programs, events, and functions that take place in a variety of learning sites. Following the aim of education to realize and broaden dao through embracing ren-centered li, a Confucian curriculum should be holistic, broad-based, and integrated. First, the curriculum is holistic, as the spotlight is not just on the students’ cognitive progress but also on their affective and behavioral developments. Cognitively, the curriculum is designed to enrich the learner’s intellect (“broaden their learning”) and content mastery (“know their various subjects and acquire a general understanding”) (Xueji V). As for the affective and behavioral dimensions of the curriculum, the same passage stresses the need for students to “revere their studies,” “esteem their fellow students,” “cherish their teachers,” “be firmly set and not likely to regress” in their learning, and engage in “discourses on their studies” with their teacher and peers. Other passages also highlight a commitment to learning (Xueji V), self-discipline (Xueji VI), enjoyment and diligence in studying (Xueji VI, IX), and respect for and trust in dao (Xueji VI, IX).

A rounded education affirms a Confucian mandate for students to transcend theoretical knowledge of dao by appreciating and abiding in it.

3) Teaching Approaches

A learner-centered education is privileged in Confucianism so that human beings can be equipped and empowered to realize and broaden dao. The pedagogies, resources, activities, and learning environments are customized to produce junzi who are filled with ren and conduct themselves in accordance with li. Xueji X disapproves of didacticism where teachers “chant the [texts on the] bamboos” and “advance [the teaching] rapidly without regard for [the students’ abilities to] accomplish [the learning].” The same passage concludes that these teachers “are not sincere in making others [learn], and do not give [their] utmost to [consider the students’] talents when teaching them.” Such teaching is essentially rote-learning that places the teaching content and the teacher rather than the student at the heart of teaching and learning.

Underpinned by a learner-focused education, Xueji XIV urges teachers to be sensitive to the individual needs of students by “knowing [the students’] heart-minds” (Xueji XIV). The word “heart-mind” (xin) in Confucian parlance refers to the harmonization of one’s thinking and feelings. It is the same word used by Confucius when he urges all to “set your heart-mind on dao” (Analects 7.6). He also testifies that he has followed his “heart-mind’s desires without overstepping the line” (Analects 2.4), i.e., without transgressing li.

4) Contemporary Relevance

Confucian educational thought and practices have had far-reaching and lasting impact on China and other East Asian countries such as South Korea, Japan, and Singapore. Common in these countries are the creation and flourishing of “Confucian pedagogic cultures” (Kim, 2009). Despite variations among them, these cultures share the following primary pedagogic patterns: a premium placed on education, high social status of and respect for teachers, student attention and discipline in class, a firm grasp of foundational knowledge, and repeated practice (Tan [^{st} century (Tan [

Against a backdrop of contemporary education being increasingly determined by neoliberal agendas, Confucian beliefs in values inculcation and social interdependence are particularly salient for policymakers and educators.

The “laissez-faire market Economy model with learning” and the Confucian concept of Integration of curricula:

In a research paper based primarily on my PhD thesis at New York University’s Dept. of Economics but containing the newly developing area of Econophysics and Insurance Medicine, Mallick, Hamburger & Mallick [

Theorem:

If l i * ( p ( s ) ) < K , for all i, in Mallick [

Proof:

To restore the Grossman & Stiglitz [

Suppose as in Mallick [

There are certainly other ways of obtaining separating equilibrium all of which requires changing the market rules in some way by the policy maker, which are not warranted by the definition 1 or by the Rational Expectations equilibrium which Grossman & Stiglitz [

It should be noted that the market structure on the basis of which equilibrium exists in this system can be altered by say changing the rule of consuming endowments in the 0-probability states given by the learning functions of all agents. Such an alteration would result in equilibrium with Finance Pretrading learning not existing in internet driven digital systems economies.

This separating equilibrium has also been solved by Quantum Mechanical Electro-String integrated circuits Econophysics field in Mallick, Hamburger & Mallick [

The central place of education in Confucianism is stated in the opening passage of Xueji:

If a ruler desires to transform the people [and] perfect [their] customs, [the ruler] can only do so through education! (Xueji I).

Proposition 1:

If l i * ( p ( s ) ) < K for all i ≠ j and if l i * ( p ( s ) ) > K , then the rationing condition ∑ i c i s ∗ ( 1 ; ( p ( s ) ) ) = ∑ i w i s for all s > min i l i * ( p ( s ) ) , will not be able to enforce equilibrium for l i * ( p ( s ) ) > K because j will not be able to be matched with any other player.

Proof:

Hence, only a “command rationing system” which is “benevolent and participative” by all players including the outsider j such that L i * ( p ( s ) ) < K , can implement the Grossman & Stiglitz [

Thus in terms of the adapted Mallick [

However, if this process is repeated over time the String of Command and Control is created over space and time with periodic review i.e. every K periods and over history develops into laissez-faire customs because the method of solution is learnt universally. Q.E.D.

Following the aim of education to realize and broaden Dao through embracing Ren-centered li, a Confucian curriculum should be holistic, broad-based, and integrated.

Proposition 2:

If l i ( p ( s ) ) = 0 for all i, then the states of the world (learning) will extend to the entire states of Nature, and laissez-faire contingent commodity markets will satisfy the Confucian concept of curriculum being inclusive of all unknown contingencies and hence fields of knowledge.

Proof:

In the entropy formula of Theorem 2 in chp. 2.4. of Mallick [_{i}) will converge by Cauchy’s criterion and L’Hospital’s rule, if limit w i / L i → 0 for all i, which has to be implemented by the Confucian curriculum covering the Field of all unknown states of Nature. This program which exists generically (Mallick [

This satisfies the scientific judgment on Learning contained in my thesis Mallick [

Corrollary:

The systems integration of the heart and mind of the learner is achievable as Confucian policy.

Proof:

Mallick [

The “learning technology” works as follows. It uses the consumption good as input and produces a forecast of the possible state-space at date 1. In fact it partitions the initial infinite statespace to a finite set which contains the true state and the residual infinite set. Each agent i knows that the first set i in (1)) contains the true state but does not know which one it is. They therefore attach probability 1 to the first set and probability zero to the other. These sets are as given in (1). However, the identity of the sets is not known to the agent before the investment. The agent knows the learning technology subject to some random error, i.e. the agent knows, subject to a random error with mean 0, how close to the true value the forecast will be consequent to a given level of input for e.g. suppose for some value of i viz. i^{*}, L i ∗ ( l i ∗ ) = 4 , the agent expects that the technology will churn out 4 integers (for notational simplification we assume this to be 4 consecutive integers starting at 1) and the true state will be one of these but does not know which 4 consecutive set of integers the machine will churn out, nor does he know which one out of these four is the true state. However, given the rational expectations framework of this paper the agents will be optimizing with respect to a set of states which consists of a consecutive set of integers starting at 1 the true state, in making the learning-investment decision which we will narrate in the next section.

The learning technology has the following properties:

L i ∈ I + − { 1 } (1a)

if l ′ i > l ″ i then L ( l ′ i ) ≤ L ( l ″ i ) (1b)

∃ , ∞ > l ′ i > l ″ i such that L ( l ′ i ) = L ( l ″ i ) − 1 ∀ L ( l ′ i ) ≥ 3 (1c)

π i ( s ) = 1 L i ⇒ ∑ 1 L i = 1 (1d)

I_{+} refers to the set of positive integers. Assumption (1a) is made so as to keep the choice model in discrete time and exhibit “Quantum Science” and satisfy the convention of numbering states. It also implies that s = 1 being the true state (which we know but the agent does not know) it is never possible to have perfect knowledge priori. Assumption (1b) implies that an increase in learning reduces the size of the state space (see (1)) and (1c) imply that the exogenous learning technology which agent i uses to learn about the possibility of various states occurring is a step function. (1d) implies that the Learning Function is a String Function which results in Group Homology and the “Copenhagen” criterion of probabilistic Quantum Science.

This results by the balancing of “Quantum Forces operating on Laissez Faire Market Group Homology over spacextime of market actions” in the Shannon Entropy of Computer Science (Theorem in Chapter 2 Mallick [

Reading, Writing and Arithmetic in Curriculum Groups satisfy the Principles of Laissez-Faire education systems (Beckerian concept of Market Value based education systems as we have String Matching Field Theoretically developed into the Learning Field Theory (Mallick [

The estimated basic equation obtains as: S^{^} = 524.73 + 9.39 * Factor where, S^{^} is the number of subscribers after estimation and Factor is the simple impact factor. The t-statistic on the Factor variable is significant at a two-tailed probability of 0.40, R = 0.10 and R^{2} = 0.01 and significance of F = 0.40.

This shows that a broad-based curriculum contained in the Repec digital library consisting of scientific fields of interest to researchers in Economic Sciences spread across 63 countries in 82 fields and 3926 subscribers contained in statistically complete hence naturally complete curriculum reflecting the States of the world satisfies the concept of Dao and Confucian integrated curriculum and also satisfies the notion of laissez-faire market based holistic participation based economic value based demand for scientific fields as simple impact factor satisfies both the cardinal concept of quality of fields and the ordinal criterion for ranking of fields and hence is the integration of forces which drives the subscriber data.

This also verifies the fundamental theorem of RHMHM Functor Algebra Calculus implicitly developed in Mallick, Hamburger, Mallick [

The author thanks L. Susskind, T. Krichel, M. Novarese, for helpful comments and R. Dharchakraborty and the IISWBM Faculty Research Fund for financial assistance and the participants of WED 2018, Jinan, China for helpful discussions and comments. The usual disclaimer applies.

The author declares no conflicts of interest regarding the publication of this paper.

Mallick, S.K. (2018) Subscription to Digital Libraries and Corresponding Journal Impact: A Value-Based Approach to Demand for Digital Research Data―Confucian Integration of Curricula and “Market String” Digital Education Systems. Journal of Applied Mathematics and Physics, 6, 1988-1996. https://doi.org/10.4236/jamp.2018.610170