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The Philosophy of Mechanics in Hypertext

    Because philosophy's intrinsic nature involves interactions among its various topics, we should choose hypertext as the appropriate format for writing. For example, we have the following entry:
"The higher order approximation is not just for theoretic interests; there exist practical examples that demand higher order precision [Go2 , p.519, l.−13-l.-9]."
The most appropriate way, perhaps, is to classify this entry under the title of precision. However, this entry also demonstrates that there exist situations that demand generalization or a theory's development. Thus we should repeat the same entry three times under three different titles. Using hypertext, we only need to put it under the single title of precision. For the "Generalization" and "Theory and Its Application" titles, we provide a separate hyperlink to the page titled "Precision" and anchor to where the entry begins. We use a yellow background to indicate the extent of the target content when necessary. This way we not only save space, but also make the discussion of each topic complete.
    In this e-book, there are four types of hyperlinks: the symbol [ ] represents internal hyperlinks, the symbol { } represents external hyperlinks, and the symbol < > represents reference hyperlinks. An internal link will be targeted to a web page of The targeted material will be related to the present context. An external link will be targeted to another web page of However, the targeted material will be related to the present topic but not to the specific context. Once in a while, I search for a term on the Internet and find a web site whose description best fits my purpose. Then I provide a direct link to that web page. We call this type of link a reference hyperlink. Finally, I shall introduce inverse links. If a paragraph's background is yellow, it means that other topics link to this paragraph. I will attach the symbol at the end of the yellow paragraph to represent an inverse link. It helps one trace what topics link to this paragraph. One should look for a purple numeral in the targeted page of the inverse link. Sometimes, one may have to trace to top of the targeted page to find the title of the topic. Although an inverse link is not as effective as a direct link, the inverse link does help one see the big picture.

Table of Contents

  1. Preface
  2. A Guide to Becoming a Good Theoretical Physicist
  3. Solutions
    1. Existence and Uniqueness
      1. Constructions
    2. Comparisons
      1. Analogies
    3. Reductions
    4. Effectiveness
    5. Consistency
    6. Numerical Analysis
      1. Approximations
      2. Precision
        1. Limits
    7. How Eigenvalues Are Affected by a Change in the Operator
      1. Perturbation and Degeneracy
    8. Statistics and Probability
    9. Integration
  4. Origins
  5. Theory and Its Application
    1. Motivating Questions
    2. Viewpoints
    3. Suggestions
    4. Methodology
    5. How Scientists Discover Formulas
    6. Models
    7. Definitions
      1. Nomenclature
    8. Axioms
      1. Mathematical Induction
      2. The Axiom of Choice
    9. Theorems
      1. Equalities
      2. Confusions
    10. Proofs
      1. Reduction to absurdity
      2. Equalities with a Large Number of Terms
      3. Proofs That Are Divided Into a Large Number of Cases
      4. Arguments That Seem True but Are Actually False
    11. Contradictions
  6. Physical Interpretations
    1. Zero, Infinity, and the Empty Set
  7. Designs and Measurements
  8. Isolation from Complexity
  9. Abstraction
  10. Generalization
  11. Examples
  12. Good Illustrations
    1. Classics
    2. Pictures
    3. References
  13. Notation, Formula, Terminology and Language
  14. Coordinate Systems
    1. Symmetry
    2. Duality
  15. Organizing and Fine Tuning
    1. Key Points
    2. Without Loss of Generality
      1. Standardization
    3. Classification
    4. Unification
      1. Leaving differential equations in the same form
    5. Networks
      1. Interfaces
  16. Formalism
  17. Hamilton's Variational Principle
  18. Equilibrium
  19. Exercises (Chinese version)
  20. Questions to Be Studied
  21. Bibliography
  22. Errata of English-Chinese Dictionary of Mathematical terms
  23. Notes (Chinese)