Confucius’s core idea is on humanity. It is the search of factors that shape us human. It proposed an ideal model on dignity and apathy. It proposed the development model and role playing framework for individuals. It is so-called the reappearance of social structure on individuals. It did not give us the principles of formation of social structure. Therefore the social rules were reduced as personal virtues. It cannot help us to lay the foundation of modern society.
Constitution is the law which represents the social contract and governs the government. The spirit of the constitution should be believed by the members of society. The core values are more on public affairs or interpersonal affairs. As we investigate Confucianism, we can find it more on family affairs and intrapersonal affairs. The revival of Confucianism in Sung dynasty revised the relationship between the nature and the human. It left blank in the political aspect. It did not reject absolutism where the government seemed not exist in the traditional Chinese society. The incomplete ideological framework may be able to work with modern constitution. Such cooperation may be similar to the relationship between Christianity and modern constitution.
In the old days, the Protestants in New England regarded making excessive money as evil until the idea of managing business was interpreted as managing the lands given by God. As Benjamin Franklin said, "Industry. Lose no time; be always employ'd in something useful; cut off all unnecessary actions." The economy was geared up. The development of USA was boosted up.
The collapse of original Chinese spirit requires the revival of Confucianism. That's why the traditional Sinologists were searching for a big revision on the ideological framework. For example, the idea of suppressing personal desire may not fit into the freedom of faith. The projection of personal guideline cannot regulate the organizations and institutions. At least, the most precious Confucius values on humanity and dignity must be kept but the old rules and guidelines derived from this idea should be redeveloped in order to fulfill the needs of modern society. The constitution should be revised incorporating with these redeveloped principles. Regulations and education can be revised accordingly.
Unfortunately, PRC has gone far beyond from Confucianism and constitution. ROC still needs to improve its political status quo. Hong Kong is not ready to become the key player of the political reform for Chinese. The Confucianist constitution is just a dream.
Thursday, November 21, 2013
Wednesday, November 20, 2013
Online Social Network
Nowadays the online social network has shortened the distance between you and your friends and also your enemies. We enjoy the sharing but we are not well prepared to resolve conflicts.
Both constructive and destructive messages can go far away. Messages run very fast and evolve very fast. They cannot be checked on time. It really hurts our understanding of the topic.
The bite-size and visualized messages can go viral. All of us are flooded by these advertising messages which simplify the real context and try to move us emotionally. It cannot help us to get the full picture or to go through the discussion on the key aspects of current issues. The opinions and ideas are scattered among the social networks. It is very hard to put them together.
Can we get rid of the problems of online social network? It seems not. Not all of us are clever enough to distinguish the facts from the opinions, the description from the parodies, the black humor from the tragedies. We cannot expect AI can help us a lot. We have more chances to contact with other communities and cultures. Thus we need more effort to relieve our unrest.
Can we learn on the online social network? We may be able provided that we can trace all of our records and we are true to our heart during reflection.
Can we understand how others learn? We know that we have not traced the changes in others’ mind directly. It would become a black hole. However, a black hole does not mean that there is no information at all. The experts in inverse problem could help us on remote sensing of these psychological changes. Reconstruction of models may require us certain assumptions. Is it a self-prophecy? It is probably not because everything will be revised when there is a contradiction.
Both constructive and destructive messages can go far away. Messages run very fast and evolve very fast. They cannot be checked on time. It really hurts our understanding of the topic.
The bite-size and visualized messages can go viral. All of us are flooded by these advertising messages which simplify the real context and try to move us emotionally. It cannot help us to get the full picture or to go through the discussion on the key aspects of current issues. The opinions and ideas are scattered among the social networks. It is very hard to put them together.
Can we get rid of the problems of online social network? It seems not. Not all of us are clever enough to distinguish the facts from the opinions, the description from the parodies, the black humor from the tragedies. We cannot expect AI can help us a lot. We have more chances to contact with other communities and cultures. Thus we need more effort to relieve our unrest.
Can we learn on the online social network? We may be able provided that we can trace all of our records and we are true to our heart during reflection.
Can we understand how others learn? We know that we have not traced the changes in others’ mind directly. It would become a black hole. However, a black hole does not mean that there is no information at all. The experts in inverse problem could help us on remote sensing of these psychological changes. Reconstruction of models may require us certain assumptions. Is it a self-prophecy? It is probably not because everything will be revised when there is a contradiction.
Friday, February 15, 2013
In the search of human meridian system
There are many critics about the human meridian system in Chinese Medicine. It had worked for hundreds of years but the westerners cannot find any evidence.
Some common persons argue that it is a lymph system. Some said it is nerve system. Unluckily they are wrong.
From another point of view, any physiological phenomenon should rely on matter. It can be organic molecules or inorganic ions. Some researches state that the accumulation of calcium ions happens at needle point.
Does it mean that science existed in the history in China? Science is not the output of a process. It is the mindset and the methodology. We may gain it from experience but it is not guaranteed.
It was a common practice to give an interpretation if the answer had not yet found. But they thought their interpretation was the truth later on and ignored the inconsistency. The same pattern happened in the society. The officials may blame the people. The rulers and the people would restart the system instead of finding out the cause of problems. That's the reason of spiral history evolution.
Tuesday, January 15, 2013
Cohomological Amplitude of Moduli Spaces of Curves
A trial analysis of the following topic from Conference on [Algebraic Groups] and [Representation Theory].
Topic: Cohomological Amplitude of Moduli Spaces of Curves
For a scheme one has [a notion of [cohomological excess]]. The speaker first defines and discusses this notion and then he states the main result which says that the [universal curve of genus] g > 0 has cohomological excess at most g-1. The speaker shows that this is an [algebro-geometric] strengthening of [Harer’s theorems] on the [[virtual cohomological dimension] of the [mapping class group]] and implies a [theorem of Diaz] on the [maximal dimension] of a [complete subvariety] of [a moduli space of curves]. He also discusses some ingredients of the proof.
Step 1: Determine the main theme.
Main Theme: Mathematics
Step 2: Find out the meaning of unknown terms. (What is it?)
T1.1 An algebraic group is a [group] that is an [algebraic variety], such that the multiplication and inverse are given by [regular functions] on the variety.
T1.2 Representation theory is a branch of mathematics that studies [abstract algebraic structures] by representing their elements as linear transformations of [vector spaces], and studies modules over these [abstract algebraic structures].
T1.3 The cohomological excess of a nonempty [algebraic variety] X, denoted ce(X), is the maximum of the integers ccd(W)−dimW, where W runs over all the [Zariski closed subsets] W ⊂ X.
T1.4 Genus: A [topologically invariant property] of a surface defined as the largest number of non-intersecting simple closed curves that can be drawn on the surface without separating it. Roughly speaking, it is the number of holes in a surface. The genus of a surface, also called the geometric genus, is related to the Euler characteristic X.
T1.5 Algebraic geometry is a branch of mathematics, classically studying properties of the sets of zeros of polynomial equations. Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry.
T1.6 Harer’s theorems (I am not quite sure about it.)
T1.7 In abstract algebra, cohomological dimension is an invariant which measures the homological complexity of representations of a group. It has important applications in geometric group theory, topology, and algebraic number theory.
T1.8 In the sub-field of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a discrete group of 'symmetries' of the space.
T1.9 theorem of Diaz (I am not quite sure about it.)
T1.10 In algebraic geometry, a moduli space is a geometric space whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. A moduli space of (algebraic) curves is a geometric space whose points represent isomorphism classes of algebraic curves.
T1.11 complete subvariety => An algebraic variety is an irreducible algebraic set, i.e. one which is not the union of two other algebraic sets which are the sets of solutions of a system of polynomial equations.
T2.3 Geometric space is a special topological space. Topological space is a mathematical structure that allows the formal definition of concepts such as convergence, connectedness, and continuity. Examples of mathematical structure are order, measure, metric, geometry, topology.
T2.4 Algebraic curves are the simplest objects of Euclidean geometry (T2.3) that cannot be defined by linear properties.
T2.5 Cohomology is a general term for a sequence of abelian groups (T2.1) defined from a co-chain complex. Chain complex is an algebraic mean of representing the relationships between the cycles and boundaries in various dimensions of a topological space. (T2.3)
T2.6 Algebraic geometry is a branch of mathematics, classically studying properties of the sets of zeros of polynomial equations.
T2.7 Geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.
T2.8 A vector space is a mathematical structure (T2.3) formed by a collection of elements called vectors, which may be added together and multiplied by numbers, called scalars in this context.
T3.1 A manifold is a second countable Hausdorff space that is locally homeomorphic to Euclidean space. e.g. curve and line (1-manifold), sphere and torus (2-manifold).
Step 5: Try to reduce the key statement.
The cohomological excess (of nonempty irreducible algebraic set)
is a theorem on the dimension of the discrete sets (with binary operation) of 'symmetries' of the topological space and
implies another theorem on the maximal dimension of a irreducible algebraic set of a geometric space whose points represent isomorphism classes of algebraic curves.
Step 6: Simplify the key statement.
A theory on the dimension of the discrete sets with binary operation in topological space
implies
another theorem on the maximal dimension of a irreducible algebraic set of a geometric space.
Can we understand it?
Topic: Cohomological Amplitude of Moduli Spaces of Curves
For a scheme one has [a notion of [cohomological excess]]. The speaker first defines and discusses this notion and then he states the main result which says that the [universal curve of genus] g > 0 has cohomological excess at most g-1. The speaker shows that this is an [algebro-geometric] strengthening of [Harer’s theorems] on the [[virtual cohomological dimension] of the [mapping class group]] and implies a [theorem of Diaz] on the [maximal dimension] of a [complete subvariety] of [a moduli space of curves]. He also discusses some ingredients of the proof.
Step 1: Determine the main theme.
Main Theme: Mathematics
Step 2: Find out the meaning of unknown terms. (What is it?)
T1.1 An algebraic group is a [group] that is an [algebraic variety], such that the multiplication and inverse are given by [regular functions] on the variety.
T1.2 Representation theory is a branch of mathematics that studies [abstract algebraic structures] by representing their elements as linear transformations of [vector spaces], and studies modules over these [abstract algebraic structures].
T1.3 The cohomological excess of a nonempty [algebraic variety] X, denoted ce(X), is the maximum of the integers ccd(W)−dimW, where W runs over all the [Zariski closed subsets] W ⊂ X.
T1.4 Genus: A [topologically invariant property] of a surface defined as the largest number of non-intersecting simple closed curves that can be drawn on the surface without separating it. Roughly speaking, it is the number of holes in a surface. The genus of a surface, also called the geometric genus, is related to the Euler characteristic X.
T1.6 Harer’s theorems (I am not quite sure about it.)
T1.7 In abstract algebra, cohomological dimension is an invariant which measures the homological complexity of representations of a group. It has important applications in geometric group theory, topology, and algebraic number theory.
T1.8 In the sub-field of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a discrete group of 'symmetries' of the space.
T1.9 theorem of Diaz (I am not quite sure about it.)
T1.10 In algebraic geometry, a moduli space is a geometric space whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. A moduli space of (algebraic) curves is a geometric space whose points represent isomorphism classes of algebraic curves.
T1.11 complete subvariety => An algebraic variety is an irreducible algebraic set, i.e. one which is not the union of two other algebraic sets which are the sets of solutions of a system of polynomial equations.
Step 3: Find out the unknown common terms or categories in the first round of elaboration.
Directly Connected to the Topic
- Group
- Algebraic structure
- Geometric space
- Algebraic curve
- Cohomology
Indirectly Connected to the Topic
- Algebraic set => Algebraic variety
- Algebraic geometry
- Topological space
- Geometric topology
- Vector space
Step 4: Elaborate the unknown common terms. (What is it?)
T2.1 A group is an algebraic structure consisting of a set together with a binary operation.
T2.2 An algebraic structure generally refers to an arbitrary set with one or more finitary operations defined on it.
T2.3 Geometric space is a special topological space. Topological space is a mathematical structure that allows the formal definition of concepts such as convergence, connectedness, and continuity. Examples of mathematical structure are order, measure, metric, geometry, topology.
T2.4 Algebraic curves are the simplest objects of Euclidean geometry (T2.3) that cannot be defined by linear properties.
T2.5 Cohomology is a general term for a sequence of abelian groups (T2.1) defined from a co-chain complex. Chain complex is an algebraic mean of representing the relationships between the cycles and boundaries in various dimensions of a topological space. (T2.3)
T2.6 Algebraic geometry is a branch of mathematics, classically studying properties of the sets of zeros of polynomial equations.
T2.7 Geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.
T2.8 A vector space is a mathematical structure (T2.3) formed by a collection of elements called vectors, which may be added together and multiplied by numbers, called scalars in this context.
T3.1 A manifold is a second countable Hausdorff space that is locally homeomorphic to Euclidean space. e.g. curve and line (1-manifold), sphere and torus (2-manifold).
Step 5: Try to reduce the key statement.
The cohomological excess (of nonempty irreducible algebraic set)
is a theorem on the dimension of the discrete sets (with binary operation) of 'symmetries' of the topological space and
implies another theorem on the maximal dimension of a irreducible algebraic set of a geometric space whose points represent isomorphism classes of algebraic curves.
Step 6: Simplify the key statement.
A theory on the dimension of the discrete sets with binary operation in topological space
implies
another theorem on the maximal dimension of a irreducible algebraic set of a geometric space.
Can we understand it?
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