THE STORY

A gaol is a goal, a goal is a gaol. The reader can digest this clever pun in his own manner.What I like in it is the smart manner to show, with a slight exchange of two letters, the beauty of an eternal dual transformation between two opposite but complementary things, a duality dynamics, an eternal recurrence, illustrating well a characteristic of the metamorphosis of the world. Indeed, many scientists especially philosophers believe in the ubiquity of the duality description of the world. Many believe that the interplay of pairs of key opposite elements is just the origin of the diverse dynamics and transformations of the world, and numerous tasks, if not all, attributed once to God can be just the product of this dual interplay. However, this picture is to date only a conceptual understanding of the world. A great step will be to formulate it into exact science with mathematics. To me this is the only way to distinguish this extraordinary conception from other conceptual interpretation of the world, religious or metaphysical, and to fashion it into useful tools to give quantitative prediction but not merely qualitative and behindhand understanding. This fractal picture we created from the ancient figure of Yin-Yang duality was inspired by this reflection. It shapes an eternal dynamics with the opposite-complementary mechanism of duality at every scale of the world. We thank Dr. OU Congjie (欧聪杰) from Huajiao University for his help in the mathematical computations for a set ofthese fractal structures in our laboratory at ISMANS in 2008, one of them is shown here.

For understanding the normalization formula with a power in the figure, please see the incomplete statistics and its multifractal application.

此段英语还算简练清楚，留在这里，算正文，正经文字。下文也不是不正经。待慢慢道来。

上边英语那两个词的概念既不同，又统一。妙在不细看还以为是一个词。牢笼（gaol）会是目标（goal），比如身处牢狱者要打破它。目标（goal）也会变成牢笼（gaol）。比如目标达到了，此目标及其理念常演入极端，乐极生悲，变成另一个牢笼。道理既明，例子俯拾皆是。常给人祸福相随之感（鄙人得福就哆嗦有祸就乐!）。这个道理浅显。上面短文意不在此。想说明的是那个阴阳一体的分形图的用意。觉得那个图有一定的姿色。其艳丽藏有几何及数学上的严谨。以不同尺寸而结合，对应不同分形维度，等于图面上那个求和公式（参见非完全统计及其分形应用）里的指数。不细说了。感谢华侨大学欧聪杰博士做博后其间对此图几何及数学计算上的协助。

此图美则美矣，最多做个唯像模型的机制，模拟什么现象。与铺天盖地的数字模型们无本质差别。也不错。如年轻的江健及王茹博士的有待进一步发展的合久必分分久必合模型（参见文章）。这也算是那个图的一个初衷。但放在这里饶舌的意愿，则不止于此。自然界的辩证机制及二项性，已是老生常谈。两千年来不知谈掉了多少门牙大牙。褒贬不一。不用管它。其最得意的时日，也不过宣讲大道理，放马后屁。如祸福相随一句，没人知道，福到了是应该哆嗦还是喝酒，什么时候哆嗦什么时候喝酒，还是哆嗦着喝酒。等你祸来了，老子便说：我说了不是？活该!

没有数学演算，没个祸福几率分布函数，空口无凭，只好听老子高调。没有数学参与，任何高论都不是精确科学（exact science）。既然此辩证哲学原理放之四海而皆准（如老子黑格尔马克思所说），不变成精确科学，甚为可惜。能否从它导出个量化的原理。拉它从天上下凡，作精确科学的一个基本原理。此乃一梦想。七月四日的博文，既与此意相关。是第一步尝试，从经典物理入手。欢迎批评讨论。

感谢【科学通报】编辑及技术人员们精巧的颜色设计，使其成为通报2011年56期的封面。