PREFACE
This book deals with evolutive theory in hexagram and ensemble theory in physics because the fundamental principles of the “Yijing” infer the complementarity, integrity, complexity and correlativity of many branches of learning.
Firstly, the research area of Santa Fe Institute, U.S.A. is focused on ecology, origin of life, evolution of human societies and the theoretical immunology. The mutuality between these four areas and Yijing-diagram-hexagram is explained as follows:
The eight natural states (8 trigrams) on the earth are the source of matter-energy of ecological system.
(2) 64 gene codes of life are represented by the superposition of 3 palar molecules according to 3 levels of trigram. 4 biochemical palar molecules A.C.G.U. constitute 64 gene codes.
(3) 64 hexagrams straightforwardly indicate the fundamental model for the evolution of human societies.
(4) The theory of Yin-Yang and five elements in the “Yijing” directly indicate that the normal operation of Qi-blood of the five internal organs is the necessary condition of the theoretical immunology. Qi means vital energy belonging to Yang, and blood signifies matter relating toYin.
Secondly, the time and complexity in physical sciences involve the fundamental principle of the Yijing. For example, famous scientist Ilya Prigogine's “From Being to Becoming” refers to the following correlativity:
(1) In ensemble Hamiltonian mechanics of this book Part II, the state of a system of particles is described by the coordinates “q” and momenta ”p” of 2n-dimensions phase space. “q” means resting state represented by Yin (broken line - -); ”p” - active state denoted by Yang (continuous line ─). Generally speaking, in science, Yin symbolizes square, real axis, negatron, negative pole, matter, and so forth; Yang characterizes cycle, imaginary axis, positron, positive pole, energy, and so forth.
In physics, matter can transform into energy or energy level, so the positions of Yin and Yang in the “Yijing” are represented by level.
On the other hand, the ensemble of particle system can be described by a “cloud” of points in the phase space. This “cloud” may be represented as a continuous fluid with a density ρ(q.p.t.). It’s normalization corresponds to “Taiji”; that is ∫ ρ (q.p.t.) dq dp = 1
(2) In ensemble quantum mechanics, the analogous normalization of ρ(q.p.t.) is replaced by “trace operator” as follows
tr ρ =<ψ|ψ>= 1
In which tr ρ represents “trace operation” of ρ, and ψ is named “amplitude” of a particle.
(3) In the section on correlativity and complementarity of this book Part II, introducing the “adjoint” quantity ρ+ of ρ, we have the following complementary trace operation
For the time irrepressible processes, introducing “microscopic entropy operator” M, a more general form is such as
M is the time operator representing a fluctuating time and refers to “entropy production”. Therefore, the average of microscopic time corresponds to macro scope time.
(4) In the section on entropy operator and collision operator, introducing orthogonal projection operator “P” and “Q”, according to the four symbols of the Yijing, we have 4 operators:
PP, QQ, PQ, QP
From these 4 operators, we may deduce “collision operator”, “solitary wave”, “dispersion equation”, and “correlation out of the vacuum”. This then involves “Wuji” (vacuum energy or energy of absolute zero) creating “Taiji” (unity).
All above-mentioned contents indicate that there exist many internal relations between physical development toward ensemble direction and the systematic standpoint of the Yijing. Although the “Yijing” is not science, in fact, the ancients either explained the “Yijing” learning with science or leaded the “Yijing” learning into science. Ilya Prigogine’s ”The End of Certainty” indicates that the outcome illustrated in this book sets modern science pulling close to Chinese philosophy. “The Book of Change” implicates many important problems having relevance to scientific concepts; this then demands us to explore. The main aim of this book is to reveal the new colours of ensemble science.
~ September 2004 ~
Shi-Wei Niu (Professor of Mathematics)
Graduate School
Academia Sinica
P.O. Box 3908, Beijing 100039
