Image Mathematics—Mathematical Intervening Principle Based on “Yin Yang Wu Xing” Theory in Traditional Chinese Mathematics (I)

Affiliation(s)

School of Finance and Statistics, East China Normal University, Shanghai, China.

The College English Teaching and Researching Department, Xinxiang University, Xinxiang, China.

School of Finance and Statistics, East China Normal University, Shanghai, China.

The College English Teaching and Researching Department, Xinxiang University, Xinxiang, China.

ABSTRACT

By using mathematical reasoning, this paper demonstrates the mathematical intervening principle: “Virtual disease is to fill his mother but real disease is to rush down his son” (虚则补其母, 实则泄其子) and “Strong inhibition of the same time, support the weak” (抑强扶弱) based on “Yin Yang Wu Xing” Theory in image mathematics of Traditional Chinese Mathematics (TCMath). We defined generalized relations and generalized reasoning, introduced the concept of steady multilateral systems with two non-compatibility relations, and discussed its energy properties. Later based on the intervention principle in image mathematics of TCMath and treated the research object of the image mathematics as a steady multilateral system, it has been proved that the mathematical intervening principle is true. The kernel of this paper is the existence and reasoning of the non-compatibility relations in steady multilateral systems, and it accords with the oriental thinking model.

By using mathematical reasoning, this paper demonstrates the mathematical intervening principle: “Virtual disease is to fill his mother but real disease is to rush down his son” (虚则补其母, 实则泄其子) and “Strong inhibition of the same time, support the weak” (抑强扶弱) based on “Yin Yang Wu Xing” Theory in image mathematics of Traditional Chinese Mathematics (TCMath). We defined generalized relations and generalized reasoning, introduced the concept of steady multilateral systems with two non-compatibility relations, and discussed its energy properties. Later based on the intervention principle in image mathematics of TCMath and treated the research object of the image mathematics as a steady multilateral system, it has been proved that the mathematical intervening principle is true. The kernel of this paper is the existence and reasoning of the non-compatibility relations in steady multilateral systems, and it accords with the oriental thinking model.

Cite this paper

Y. Zhang and W. Shao, "Image Mathematics—Mathematical Intervening Principle Based on “Yin Yang Wu Xing” Theory in Traditional Chinese Mathematics (I),"*Applied Mathematics*, Vol. 3 No. 6, 2012, pp. 617-636. doi: 10.4236/am.2012.36096.

Y. Zhang and W. Shao, "Image Mathematics—Mathematical Intervening Principle Based on “Yin Yang Wu Xing” Theory in Traditional Chinese Mathematics (I),"

References

[1] Y. S. Zhang, “Theory of Multilateral Matrices,” Chinese Stat. Press, Beijing, 1993.

[2] Y. S. Zhang, “Theory of Multilateral Systems,” 2007. http://www.mlmatrix.com

[3] Y. S. Zhang, “Mathematical Reasoning of Treatment Principle Based on ‘Yin Yang Wu Xing’ Theory in Traditional Chinese Medicine,” Chinese Medicine, Vol. 2, No. 1, 2011, pp. 6-15. doi:10.4236/cm.2011.21002

[4] Y. S. Zhang, “Mathematical Reasoning of Treatment Principle Based on ‘Yin Yang Wu Xing’ Theory in Traditional Chinese Medicine(II),” Chinese Medicine, Vol. 2, No. 4, 2011, pp. 158-170. doi:10.4236/cm.2011.24026

[5] Y. S. Zhang, “Mathematical Reasoning of Treatment Principle Based on the Stable Logic Analysis Model of Complex Systems,” Intelligent Control and Automation, Vol. 3, No. 1, 2012, pp. 6-15. doi:10.4236/ica.2012.31001

[6] Y. S. Zhang, “Mathematical Reasoning of Economic Intevening Principle Based on ‘Yin Yang Wu Xing’ Theory in Traditional Chinese Economic(I),” Modern Economics, Vol. 3, No. 2, 2012, pp.

[7] Y. S. Zhang, S. S. Mao, C. Z. Zhan and Z. G. Zheng, “Stable Structure of the Logic Model with Two Causal Effects,” Chinese Journal of Applied Probability and Statistics, Vol. 21, No. 4, 2005, pp. 366-374.

[8] C. Luo, X. D. Wang and Y. S. Zhang, “Orthogonality and Independence—New Thinking of Dealing with Complex Systems Series Three,” Journal of Shanghai Institute of Technology (Natural Science), Vol. 10 No. 4, 2010, pp. 271-277

[9] C. Luo, X. P. Chen and Y. S. Zhang, “The Turning Point Analysis of Finance Time Series,” Chinese Journal of Applied Probability and Statistics, Vol. 26, No. 4, 2010, pp. 437-442

[10] Y. S. Zhang, X. Q. Zhang and S. Y. Li, “SAS Language Guide and Application,” Shanxi People’s Press, Taiyuan, 2011.

[11] Y. S. Zhang and S. S. Mao, “The Origin and Development Philosophy Theory of Statistics,” Statistical Research, Vol. 12, 2004, pp. 52-59.

[12] N. Q. Feng, Y. H. Qiu, F. Wang, Y. S. Zhang and S. Q. Yin, “A Logic Analysis Model about Complex System’s Stability: Enlightenment from Nature,” Lecture Notes in Computer Science, Vol. 3644, 2005, pp. 828-838. doi:10.1007/11538059_86

[13] N. Q. Feng, Y. H. Qiu, Y. S. Zhang, F. Wang and Y. He, “A Intelligent Inference Model about Complex System’s Stability: Inspiration from Nature,” International Journal of Intelligent Technology, Vol. 1, 2005, pp. 1-6.

[14] N. Q. Feng, Y. H. Qiu, Y. S. Zhang, C. Z. Zhan and Z. G. Zheng, “A Logic Analysis Model of Stability of Complex System Based on Ecology,” Computer Science, Vol. 33, No. 7, 2006, pp. 213-216.

[15] C. Y. Pan, X. P. Chen, Y. S. Zhang and S. S. Mao, “Logical Model of Five-Element Theory in Chinese Traditional Medicine,” Journal of Chinese Modern Traditional Chinese Medicine, Vol. 4, No. 3, 2008, pp. 193-196.

[16] X. P. Chen, W. J. Zhu, C. Y. Pan and Y. S. Zhang, “Multilateral System,” Journal of Systems Science, Vol. 17, No. 1, 2009, pp. 55-57.

[17] C. Luo and Y. S. Zhang, “Framework Definition and Partition Theorems Dealing with Complex Systems: One of the Series of New Thinking,” Journal of Shanghai Institute of Technology (Natural Science), Vol. 10, No. 2, 2010, pp. 109-114.

[18] C. Luo and Y. S. Zhang, “Framework and Orthogonal Arrays: The New Thinking of Dealing with Complex Systems Series Two”, Journal of Shanghai Institute of Technology (Natural Science), Vol. 10, No. 3, 2010, pp. 159-163.

[19] J. Y. Liao, J. J. Zhang and Y. S. Zhang, “Robust Parameter Design on Launching an Object to Goal,” Mathematics in Practice and Theory, Vol. 40, No. 24, 2010, pp. 126-132.

[20] Y. S. Zhang, S. Q. Pang, Z. M. Jiao and W. Z. Zhao, “Group Partition and Systems of Orthogonal Idempotents,” Linear Algebra and Its Applications, Vol. 278, No. 1-3, 1998, pp. 249-262. doi:10.1016/S0024-3795(97)10095-7

[21] J. L. Zhao and Y. S. Zhang, “The Characteristic Description of Idempotent Orthogonal Class System,” Advances in Matrix Theory and Its Applications, Proceedings of the 8th International Conference on Matrix and its applications, Taiyuan, Vol. 1, No. 1, 16-18 July 2008, pp. 445-448.

[22] X. P. Chen, C. Y. Pan and Y. S. Zhang, “Partitioning the Multivariate Function Space into Symmetrical Classes,” Mathematics in Practice and Theory, Vol. 39, No. 2, 2009, pp. 167-173.

[23] C. Y. Pan, X. P. Chen and Y. S. Zhang, “Construct Systems of Orthogonal Idempotents,” Journal of East China University (Natural Science), Vol. 141, No. 5, 2008, pp. 51-58.

[24] C. Y. Pan, H. N. Ma, X. P. Chen and Y. S. Zhang, “Proof Procedure of Some Theories in Statistical Analysis of Global Symmetry,” Journal of East China Normal University (Natural Science), Vol. 142, No. 5, 2009, pp. 127-137.

[25] X. Q. Zhang, Y. S. Zhang and S. S. Mao, “Statistical Analysis of 2-Level Orthogonal Satursted Designs: The Procedure of Searching Zero Effects,” Journal of East China Normal University (Natural Science), Vol. 24, No. 1, 2007, pp. 51-59.

[26] Y. S. Zhang, Y. Q. Lu and S. Q. Pang, “Orthogonal Arrays Obtained by Orthogonal Decomposition of Projection Matrices,” Statistica Sinica, Vol. 9, No. 2, 1999, pp. 595-604.

[27] Y. S. Zhang, S. Q. Pang and Y. P. Wang, “Orthogonal Arrays Obtained by Generalized Hadamard Product,” Discrete Mathematics, Vol. 238, No. 1-3, 2001, pp. 151-170. doi:10.1016/S0012-365X(00)00421-0

[28] Y. S. Zhang, L. Duan, Y. Q. Lu and Z. G. Zheng, “Construction of Generalized Hadamard Matrices ,” Journal of Statistical Planning, Vol. 104, 2002, pp. 239-258. doi:10.1016/S0378-3758(01)00249-X

[29] Y. S. Zhang, “Data Analysis and Construction of Orthogonal Arrays,” East China Normal University, Shanghai, 2006.

[30] Y. S. Zhang, “Orthogonal Arrays Obtained by RepeatingColumn Difference Matrices,” Discrete Mathematics, Vol. 307, No. 2, 2007, pp. 246-261. doi:10.1016/j.disc.2006.06.029

[31] X. D. Wang, Y. C. Tang, X. P. Chen and Y. S. Zhang, “Design of Experiment in Global Sensitivity Analysis Based on ANOVA High-Dimensional Model Representation,” Communications in Statistics—Simulation and Computation, Vol. 39, No. 6, 2010, pp. 1183-1195. doi:10.1080/03610918.2010.484122

[32] X. D. Wang, Y. C. Tang and Y. S. Zhang, “Orthogonal Arrays for the Estimation of Global Sensitivity Indices Based on ANOVA High-Dimensional Model Representation,” Communications in Statistics—Simulation and Computation, Vol. 40, No. 9, 2011, pp. 1324-1341. doi:10.1080/03610918.2011.575500

[33] J. T. Tian, Y. S. Zhang, Z. Q. Zhang, C. Y. Pan and Y. Y. Gan, “The Comparison and Application of Balanced Block Orthogonal Arrays and Orthogonal Arrays,” Journal of Mathematics in Practice and Theory, Vol. 39, No. 22, 2009, pp. 59-67.

[34] C. Luo and C. Y. Pan, “Method of Exhaustion to Search Orthogonal Balanced Block Designs,” Chinese Journal of Applied Probability and Statistics, Vol. 27, No. 1, 2011, pp. 1-13.

[35] Y. S. Zhang, W. G. Li, S. S. Mao and Z. G. Zheng, “Orthogonal Arrays Obtained by Generalized Difference Matrices with g Levels,” Science China Mathematics, Vol. 54, No. 1, 2011, pp. 133-143. doi:10.1007/s11425-010-4144-y

[36] Lao-tzu, “Tao Te Ching,” In: S. Mitchel, Transl., 2010. http://acc6.its.brooklyn.cuny.edu

[37] M.-J. Cheng, “Lao-Tzu, My Words Are Very Easy to Understand: Lectures on the Tao Teh Ching,” North Atlantic Books, Richmond, 1981.

[38] Research Center for Chinese and Foreign Celebrities and Developing Center of Chinese Culture Resources, “Chinese Philosophy Encyclopedia,” Shanghai People Press, Shanghai, 1994.

[1] Y. S. Zhang, “Theory of Multilateral Matrices,” Chinese Stat. Press, Beijing, 1993.

[2] Y. S. Zhang, “Theory of Multilateral Systems,” 2007. http://www.mlmatrix.com

[3] Y. S. Zhang, “Mathematical Reasoning of Treatment Principle Based on ‘Yin Yang Wu Xing’ Theory in Traditional Chinese Medicine,” Chinese Medicine, Vol. 2, No. 1, 2011, pp. 6-15. doi:10.4236/cm.2011.21002

[4] Y. S. Zhang, “Mathematical Reasoning of Treatment Principle Based on ‘Yin Yang Wu Xing’ Theory in Traditional Chinese Medicine(II),” Chinese Medicine, Vol. 2, No. 4, 2011, pp. 158-170. doi:10.4236/cm.2011.24026

[5] Y. S. Zhang, “Mathematical Reasoning of Treatment Principle Based on the Stable Logic Analysis Model of Complex Systems,” Intelligent Control and Automation, Vol. 3, No. 1, 2012, pp. 6-15. doi:10.4236/ica.2012.31001

[6] Y. S. Zhang, “Mathematical Reasoning of Economic Intevening Principle Based on ‘Yin Yang Wu Xing’ Theory in Traditional Chinese Economic(I),” Modern Economics, Vol. 3, No. 2, 2012, pp.

[7] Y. S. Zhang, S. S. Mao, C. Z. Zhan and Z. G. Zheng, “Stable Structure of the Logic Model with Two Causal Effects,” Chinese Journal of Applied Probability and Statistics, Vol. 21, No. 4, 2005, pp. 366-374.

[8] C. Luo, X. D. Wang and Y. S. Zhang, “Orthogonality and Independence—New Thinking of Dealing with Complex Systems Series Three,” Journal of Shanghai Institute of Technology (Natural Science), Vol. 10 No. 4, 2010, pp. 271-277

[9] C. Luo, X. P. Chen and Y. S. Zhang, “The Turning Point Analysis of Finance Time Series,” Chinese Journal of Applied Probability and Statistics, Vol. 26, No. 4, 2010, pp. 437-442

[10] Y. S. Zhang, X. Q. Zhang and S. Y. Li, “SAS Language Guide and Application,” Shanxi People’s Press, Taiyuan, 2011.

[11] Y. S. Zhang and S. S. Mao, “The Origin and Development Philosophy Theory of Statistics,” Statistical Research, Vol. 12, 2004, pp. 52-59.

[12] N. Q. Feng, Y. H. Qiu, F. Wang, Y. S. Zhang and S. Q. Yin, “A Logic Analysis Model about Complex System’s Stability: Enlightenment from Nature,” Lecture Notes in Computer Science, Vol. 3644, 2005, pp. 828-838. doi:10.1007/11538059_86

[13] N. Q. Feng, Y. H. Qiu, Y. S. Zhang, F. Wang and Y. He, “A Intelligent Inference Model about Complex System’s Stability: Inspiration from Nature,” International Journal of Intelligent Technology, Vol. 1, 2005, pp. 1-6.

[14] N. Q. Feng, Y. H. Qiu, Y. S. Zhang, C. Z. Zhan and Z. G. Zheng, “A Logic Analysis Model of Stability of Complex System Based on Ecology,” Computer Science, Vol. 33, No. 7, 2006, pp. 213-216.

[15] C. Y. Pan, X. P. Chen, Y. S. Zhang and S. S. Mao, “Logical Model of Five-Element Theory in Chinese Traditional Medicine,” Journal of Chinese Modern Traditional Chinese Medicine, Vol. 4, No. 3, 2008, pp. 193-196.

[16] X. P. Chen, W. J. Zhu, C. Y. Pan and Y. S. Zhang, “Multilateral System,” Journal of Systems Science, Vol. 17, No. 1, 2009, pp. 55-57.

[17] C. Luo and Y. S. Zhang, “Framework Definition and Partition Theorems Dealing with Complex Systems: One of the Series of New Thinking,” Journal of Shanghai Institute of Technology (Natural Science), Vol. 10, No. 2, 2010, pp. 109-114.

[18] C. Luo and Y. S. Zhang, “Framework and Orthogonal Arrays: The New Thinking of Dealing with Complex Systems Series Two”, Journal of Shanghai Institute of Technology (Natural Science), Vol. 10, No. 3, 2010, pp. 159-163.

[19] J. Y. Liao, J. J. Zhang and Y. S. Zhang, “Robust Parameter Design on Launching an Object to Goal,” Mathematics in Practice and Theory, Vol. 40, No. 24, 2010, pp. 126-132.

[20] Y. S. Zhang, S. Q. Pang, Z. M. Jiao and W. Z. Zhao, “Group Partition and Systems of Orthogonal Idempotents,” Linear Algebra and Its Applications, Vol. 278, No. 1-3, 1998, pp. 249-262. doi:10.1016/S0024-3795(97)10095-7

[21] J. L. Zhao and Y. S. Zhang, “The Characteristic Description of Idempotent Orthogonal Class System,” Advances in Matrix Theory and Its Applications, Proceedings of the 8th International Conference on Matrix and its applications, Taiyuan, Vol. 1, No. 1, 16-18 July 2008, pp. 445-448.

[22] X. P. Chen, C. Y. Pan and Y. S. Zhang, “Partitioning the Multivariate Function Space into Symmetrical Classes,” Mathematics in Practice and Theory, Vol. 39, No. 2, 2009, pp. 167-173.

[23] C. Y. Pan, X. P. Chen and Y. S. Zhang, “Construct Systems of Orthogonal Idempotents,” Journal of East China University (Natural Science), Vol. 141, No. 5, 2008, pp. 51-58.

[24] C. Y. Pan, H. N. Ma, X. P. Chen and Y. S. Zhang, “Proof Procedure of Some Theories in Statistical Analysis of Global Symmetry,” Journal of East China Normal University (Natural Science), Vol. 142, No. 5, 2009, pp. 127-137.

[25] X. Q. Zhang, Y. S. Zhang and S. S. Mao, “Statistical Analysis of 2-Level Orthogonal Satursted Designs: The Procedure of Searching Zero Effects,” Journal of East China Normal University (Natural Science), Vol. 24, No. 1, 2007, pp. 51-59.

[26] Y. S. Zhang, Y. Q. Lu and S. Q. Pang, “Orthogonal Arrays Obtained by Orthogonal Decomposition of Projection Matrices,” Statistica Sinica, Vol. 9, No. 2, 1999, pp. 595-604.

[27] Y. S. Zhang, S. Q. Pang and Y. P. Wang, “Orthogonal Arrays Obtained by Generalized Hadamard Product,” Discrete Mathematics, Vol. 238, No. 1-3, 2001, pp. 151-170. doi:10.1016/S0012-365X(00)00421-0

[28] Y. S. Zhang, L. Duan, Y. Q. Lu and Z. G. Zheng, “Construction of Generalized Hadamard Matrices ,” Journal of Statistical Planning, Vol. 104, 2002, pp. 239-258. doi:10.1016/S0378-3758(01)00249-X

[29] Y. S. Zhang, “Data Analysis and Construction of Orthogonal Arrays,” East China Normal University, Shanghai, 2006.

[30] Y. S. Zhang, “Orthogonal Arrays Obtained by RepeatingColumn Difference Matrices,” Discrete Mathematics, Vol. 307, No. 2, 2007, pp. 246-261. doi:10.1016/j.disc.2006.06.029

[31] X. D. Wang, Y. C. Tang, X. P. Chen and Y. S. Zhang, “Design of Experiment in Global Sensitivity Analysis Based on ANOVA High-Dimensional Model Representation,” Communications in Statistics—Simulation and Computation, Vol. 39, No. 6, 2010, pp. 1183-1195. doi:10.1080/03610918.2010.484122

[32] X. D. Wang, Y. C. Tang and Y. S. Zhang, “Orthogonal Arrays for the Estimation of Global Sensitivity Indices Based on ANOVA High-Dimensional Model Representation,” Communications in Statistics—Simulation and Computation, Vol. 40, No. 9, 2011, pp. 1324-1341. doi:10.1080/03610918.2011.575500

[33] J. T. Tian, Y. S. Zhang, Z. Q. Zhang, C. Y. Pan and Y. Y. Gan, “The Comparison and Application of Balanced Block Orthogonal Arrays and Orthogonal Arrays,” Journal of Mathematics in Practice and Theory, Vol. 39, No. 22, 2009, pp. 59-67.

[34] C. Luo and C. Y. Pan, “Method of Exhaustion to Search Orthogonal Balanced Block Designs,” Chinese Journal of Applied Probability and Statistics, Vol. 27, No. 1, 2011, pp. 1-13.

[35] Y. S. Zhang, W. G. Li, S. S. Mao and Z. G. Zheng, “Orthogonal Arrays Obtained by Generalized Difference Matrices with g Levels,” Science China Mathematics, Vol. 54, No. 1, 2011, pp. 133-143. doi:10.1007/s11425-010-4144-y

[36] Lao-tzu, “Tao Te Ching,” In: S. Mitchel, Transl., 2010. http://acc6.its.brooklyn.cuny.edu

[37] M.-J. Cheng, “Lao-Tzu, My Words Are Very Easy to Understand: Lectures on the Tao Teh Ching,” North Atlantic Books, Richmond, 1981.

[38] Research Center for Chinese and Foreign Celebrities and Developing Center of Chinese Culture Resources, “Chinese Philosophy Encyclopedia,” Shanghai People Press, Shanghai, 1994.