The hidden secrets of the Yin-Yang symbol

Li, Xin Working Paper The hidden secrets of the Yin-Yang symbol Copenhagen Discussion Papers, No. 2014-46 Provided in Cooperation with: Asia Research Community (ARC), Copenhagen Business School (CBS) Suggested Citation: Li, Xin (2014) : The hidden secrets of the Yin-Yang symbol, Copenhagen Discussion Papers, No. 2014-46, Copenhagen Business School (CBS), Asia Research Centre (ARC), Frederiksberg, https://hdl.handle.net/10398/8891 This Version is available at: https://hdl.handle.net/10419/208645 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Copenhagen Discussion Papers cannot be republished, reprinted, or reproduced in any format without the permission of the paper's author or authors. Note: The views expressed in each paper are those of the author or authors of the paper. They do not represent the views of the Asia Research Centre or Copenhagen Business School. Editor of the Copenhagen Discussion Papers: Associate Professor Michael Jacobsen Asia Research Centre Copenhagen Business School Porcelænshaven 24 DK-2000 Frederiksberg Denmark Tel.: (+45) 3815 3396 Email: [email protected] www.cbs.dk/arc 1 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 The hidden secrets of the Yin-Yang symbol 阴阳图的隐藏秘密 Xin Li 李鑫 Asia Research Centre 亚洲研究中心 Copenhagen Business School, Denmark 丹麦哥本哈根商学院 [email protected] 1. My understanding of Yin-Yang 我对阴阳的理解 (1) The essence of Yin-Yang is that yin and yang are contrary yet complementary. 阴阳的本质是阴阳是相生相克的关系。 (2) This contrary yet complementary relationship can be described by three characteristics of Yin-Yang: nonexclusivability, transformability, and coopetitionability. Nonexclusivability means that anything contains yin and yang elements and neither yin nor yang elements can be excluded because within both elements there is a seed of the opposite element. Due to the existence of a seed of the opposite element, the yin and yang elements can be mutually transformed when the opposite seed grow to a certain size. Due to this possible growth of the inside opposite element, the relationship between yin and yang and their inside opposite element is one of competition and cooperation, i.e. coopetition. When the configuration ratio of an element’s opposite seed is within the range of 1% to 25%1, their relationship is more co-operative than competitive, and  1 For simplicity, I use 1% as the smallest dividable ratio. When we say an element is a yin element, it is actually because it consists of more yin element than yang element. The yang element is the opposite element or seed. Therefore, in an overall yin element, its inside opposite seed can have a ratio of any value between 1% and 49%. 2 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 therefore there is more synergy than tradeoff between them. The closer the ratio is to 25%, the stronger the synergy. When the ratio is within the range of 25% to 49%, their relationship is more competitive than cooperative, and therefore there is more tradeoff than synergy between them. The closer the ratio is to 49%, the stronger the tradeoff. 阴阳的相生相克关系可以描述为三个特性：不可排除性、相互转化性、竞 争合作性。不可排除性是指任何事物都包含阴阳两个对立元素，二者之任 何一个均不可能被排除在我，这是因为在阴或阳元素内部天然的包含着对 立元素的种子。正是因为这个种子的天然存在，阴和阳元素可以互相转 化，这种转化发生在对立元素种子成长到一定程度的时候。正是由于这种 对立元素的成长可能性，阴或阳元素和它内部的对立元素之间的关系是既 竞争又合作的。当内部的对立元素占总体元素的力量比例在 1%到25%之 间时，两者的关系是合作多于竞争，越靠近 25%这个点，这种合作的协同 效果也强烈。当这个搭配比例处于 25%到49%之间时，它们的关系将是 竞争多于合作，也就是他们更多互相排斥而非互相促进。当这个比例越靠 近49%，这种排斥效应越强烈。 (3) There are three levels of contrary yet complementary relationships: the individual level, the dyadic level, and the collective level. 这种阴阳相生相克关系可以发生在三个不同的层次：个体层次、两者之 间，集体层次。 (a) At the individual level, the excess and deficiency of an individual item are the yang and the yin respectively, and they are contradictory yet complementary and therefore need to be balanced. This is because everything (i.e. each individual item) has its pros and cons, and therefore, everything must be subject to the law that excess is just as bad as deficiency. For example, for the individual item of temperature,  为了简单起见，这里我使用 1%代表最小的可分比例。因此当我们说一个元素是阴元素的时候， 其实是指它在总体上表现为阴的成分多余阳的成分。这个阳的成分就是总体为阴的这个元素的内 部的对立元素或种子。所以，一个总体为阴的元素，它的内部对立元素可能占的比例是总体的 1%到49%这个区间中任意数值。 3 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 its excess (yang) state is too high a temperature while its deficiency state is too low a temperature. Both too low and too high temperatures are uncomfortable. To feel comfortable, the temperature should be set to a moderate or appropriate level. 在个体层次，任何一个事物自身的过度和不及状态可以分别看成是阳 和阴的状态，它们是相生相克的关系，所以需要平衡。这是因为任何 一个事物都有它的优劣之处，所以任何事物都是过犹不及的。比如， 就温度而言，它的过就是温度过高，它的不及就是温度过低。温度过 高过低都不好。只有适度的温度才会让人感到舒适。 (b) At the dyadic level, a contrary pair, such as the two concepts of cold and warm, can be seen as the yin and the yang respectively, and they are contradictory yet complementary and therefore need to be balanced. When it is not too cold and not too warm, it is the most comfortable state. The same can be said about the contrary pairs change and stability, centralized and decentralized, etc. 在两者之间这个层次，一对矛盾事物，比如冷和热两个概念，可以分 别看成是阴和阳，他们是相生相克的关系，所以需要平衡。当不是太 冷也不是太热的时候，才是最舒适的状态。类似地，比如变化和稳 定，集中和放权，等等，亦都同理。 (c) At the collective level, which means among multiple objects or concepts, one and the other might be contradictory yet complementary and therefore need to be balanced. This collective complementary yet contradictory relationship is not obvious from the Yin-Yang Theory, but it is explicated by the Chinese Five-Element Theory. Each of the five elements is complementary to the adjacent others but contradictory to the remote others. This Five-Element Theory is used in Chinese medical studies in which five organs/systems are linked to the five elements and said to have the same collective complementary yet contradictory relationship. 4 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 Therefore, the Yin-Yang Theory and the Five Element Theory are often integrated as the Yin-Yang Five Element Theory (see figure 1). 在集体层次，也就是在多个事物之间，某个元素和别的元素可能是相 生相克的关系，所以需要平衡。这个集体层次的相生相克关系在阴阳 理论中并不显明，但在中国的五行理论中却体现的很充分，即，五行 中的任一元素和它相邻的两个元素是相生的，而和它不相邻的两个元 素是相克的。五行理论被用于中医学，这五中元素和人体内五种主要 器官对应起来，所以这五种器官之间也有五行所规定的相生相克关 系。所以阴阳理论和五行理论常常被整合在一起成为阴阳五行学说 （如图 1所示）。 Figure 1. Chinese Medicine Yin-Yang Five Element Symbol 图1. 中医阴阳五行图 2. My understanding of Zhong-Yong 我对中庸的理解 (1) Mathematically, we can divide a number axis, starting from 0% and ending at 100%, into 3 zones, the first from 0% to 25%, the middle from 25% to 75%, and the last from 75% to 100%. We can treat these 3 zones as the deficiency zone, the Zhong-Yong zone, and the excess zone. Of course, there should not be fixed boundaries between these 3 zones, however, we can, for simplicity, roughly treat them in this way for now. 5 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 从数学度量的角度来讲，我们可以把一个从 0%到100%的数轴分成 3个 区域，第一个区域从 0%到25%，中间区域从 25%到75%，最后一个区 域从 75%到100%。我们可以把这 3个区域分别看成是不足区域，中庸区 域，和过度区域。当然，这 3个区域之间的边界不是固定的，不过，为了 简单起见，我们暂时可以这样划分。 (2) That excess is just as bad as deficiency implies that one should not fall into the two end zones. The principle of Zhong-Yong prescribes attitudes and behaviors to be accord with the requirements of the middle zone. However, Zhong-Yong does not request a fix position (say 50%) in the middle zone. Any position in the middle zone (recall Simon’s zone of acceptance) is of Zhong-Yong nature and may be appropriate or excellent under specific circumstances. 过犹不及意味着一个人应该避免落入两个边缘区域。中庸原则要求人的态 度和行为要符合中间这个区域的要求。但是，中庸并不要求一个固定的正 中间的位置（比如数轴的 50%这个点）。在这个中庸区域中的任何一个位 置都是中庸的，在不同的情况下都可能是最合适的或最好的。我们可以联 想西蒙教授的可接受区这个概念。 (3) This conceptualization of the Zhong-Yong principle allows the possibility of 50% being zhong-yong or excellent, and therefore, accepts asymmetric balance as well as symmetric balance. This, I argue, is one of the hidden secrets of the Yin-Yang symbol (which I will elaborate on later), namely, the equal sized white half and black half indicate symmetric balance while the small black pie in the white half and the small white pie in the black half indicate asymmetric balance. In a sense, the asymmetric balance and symmetric balance can be seen as a pair of yin and yang as they are nonexclusive, mutual transformable, and coopetitive. 这样理解中庸就使 50%的正中间状态也可以是中庸的成为可能，于是中庸 原则就可以包含非对称平衡和对称平衡，我认为这其实是阴阳图的一个隐 藏的秘密，我在后文会解释，即，阴阳图中黑白鱼尺寸均等暗示对称平 6 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 衡，而黑白鱼与它们各自腹中的白黑小饼尺寸的不均等暗示非对称平衡。 从某种意义上讲，非对称平衡和对称平衡可以被视为一对阴阳，它们互相 不可排除，互相可以转化，互相竞争合作。 (4) The link between Yin-Yang and Zhong-Yong is that due to this contrary yet complementary relationship between yin and yang, one need to dynamically balance between the two. Dynamic balancing is the essence of the behavioral principle aspect of Zhong-Yong (note: Zhong-Yong also has other philosophical meanings). 阴阳和中庸的联系是，正是由于阴阳的这种相生相克关系，我们需要在这 两者之间动态地平衡。动态平衡是中庸哲学的行为原则方面的核心（注 意，中庸还有别的哲学内涵）。 (5) I operationalize the behavioral principle of dynamic balancing by a 4 stage process model, namely, inclusion-selection-promotion-transition. By inclusion 包容, I mean that one should always include at least two contrary elements (input as well as output or objective) and should not exclude any of the contrary elements due to the complementarities among them. By selection, I mean, while one should not exclude any complementary element, s/he should also select one or some of them as a priority(ies) due to the contradictions between them. The selection of objective(s) to be prioritized should depend on the specific circumstances one is under. The selected objective will in turn determine which input(s) should be given relatively more emphasis. By promotion, I mean, while one should prioritize one or some elements (inputs as well as objectives), s/he should also promote the other un-prioritized elements to prevent the potential crowding out of the un-prioritized by the prioritized (inputs as well as objectives). By transition, I mean, as time passes, the external environment may change and the prioritization of an objective(s) should also be changed and therefore one should deliberately transit from previous prioritization to a new prioritization. 13 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 度，在这个满足区域内的任何位置（即比例额搭配）都可以被看成是中庸 适度的。 3.4 The third secret 第三个隐藏秘密 (1) If the two pies in the Yin-Yang symbol are continuously enlarged, the yin part and the yang part will eventually completely reverse their order, e.g. transiting from the left side to the right side (see Figure 6). This is what I call the third hidden secret of the Yin-Yang symbol which was first discovered by Jean Marolleau (1975)i. 如果我们把这两个小圆饼持续放大，到一定的时候阴阳图中原来的阴的那 一半就会完全变成阳的，而原来的阳的那一半就会完全变成阴的，如图 6 所示。我称这为阴阳图的第三个隐藏秘密。这个秘密最先是被法国人 Jean Marolleau 在他 1975 年的书中提出来的。 (2) One may wonder, in Figure 6, why two small dots suddenly appear because the natural consequence of enlarging the initial two dots should be a fully white half without a black dot inside and a fully black half without a white dot inside. This is indeed a problem embedded in Marolleau’s original figure. 人们可能会问，在图 6中，在顺时针方向的最后一个阴阳图中，为什么两 个小圆饼会突然出现，因为在它前边一个图中持续扩大原有的两个小圆饼 的结果应该是原来含有阴的种子的阳的一半会变成完全的阴而没有阳的种 子，而原来含有阳的种子的阴的一半会变成完全的阳而没有阴的种子。这 确实是 Jean Marolleau 的原图中一个令人疑惑的问题。 This confusion is caused by the simplification in the drawing of the initial Yin-Yang symbol. According to Yin-Yang philosophy, anything is a combination of yin and yang, including the yin element and the yang element per se, which means, the black and the white dots in the YinYang symbol should also be a combination of black and white parts rather than purely black and purely white parts. However, the designers of the initial Yin-Yang symbol simplified this ceaseless yin-yang 14 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 composition idea by depicting the black and white dots as purely black and white, without the intention to show that they are pure. Therefore, although the white part of the black dot and the black part of the white dot are not depicted in the Yin-Yang symbol (as they are indeed very small if depicted) we should imagine they are there. So, when we enlarge the black dot and the white dot, the un-depicted small white part and black part inside them are proportionately enlarged, which therefore result in the last symbol in Figure 6. 这个困惑的产生是由于阴阳图在最初的设计上采用了简化的处理所致。根 据阴阳哲学，任何事物都是阴阳的统一体，包括阴阳图中阴和阳本身。那 么阴阳图中两个阴阳小圆饼本身也应该是阴阳的统一体，也就是这两个小 饼内部也应该有他们各自对立面的种子，而种子内又有对立面的种子，这 样可以无限循环下去。但是为了简化，阴阳图的原始设计者并没有在两个 小圆饼内部画上可以无限一分为二的种子，而是把它们画成了两个纯色的 实心饼，但他们并不是要表示这两个实心并真的就是纯粹的阴饼或阳饼。 所以当我们在持续扩大两个阴阳小圆饼的时候，他们各自内部的对立面的 种子也应该持续扩大，所以我们才会看到图 6中最后一个阴阳图中依然有 两个小圆饼。 (3) This secret implies that one can make change happen by promoting the opposite force(s) (or the opposite seed). This hidden secret corresponds to the third and fourth stages of my aforementioned inclusion-selectionpromotion-transition process of dynamic balancing, which is the essence of the behavioral principle of Zhong-Yong. 这个隐藏秘密意味着，我们可以通过扶持对立面来实现我们希望的改变。 这个隐藏秘密对应这我对中庸的 4阶段模型中的第三和第四阶段。 15 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 Figure 6. The dynamic change of yin and yang 图6. 阴阳的动态变化 3.5 The fourth secret 第四个隐藏秘密 (1) If the bottom pair of the mirrored Yin-Yang symbols in Figure 6 is combined, then the two combined S curves look like Figure 7a. If a number of these pairs are connected in a circle, then the S curves will look like Figure 7b. 如果将图 6中最下端的两个镜像的阴阳图重叠起来，那么两个图中的倒 S 曲线组合在一起就如图 7a 所示。如果很多个图 7a 并排放置，就如图 7b 所示。 (2) Figure 7b can be seen as a combined series of Figure 7c (‘X’s) (see Figure 7d). ‘X’ can be viewed as two connected signs (‘>’ and ‘<’). The sign ‘>’ can be seen as a symbol of convergence or integration, while the sign ‘<’ can be seen as a symbol of divergence or separation, and therefore the symbol ‘X’ can imply a unity of convergence/integration and divergence/separation, which are the characteristics of Yin-Yang thinking, i.e. separating one into two and integrating two into one. I call this the fourth hidden secret of the Yin Yang symbol. 图7b 可以看成是多个图 7c（X字形）并列排列而成，如图 7d 所示。“X” 可以被视作‘>’ 和 ‘<’两个符号连接而成。符号‘>’可以被视作汇聚或整合的 象征，而符号‘<’可以被视作分流或分散的象征。从而，“X”象征整合与分散 16 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 的统一， 这也代表了阴阳思维的特征，即，一分为二，合二为一。我称这 为阴阳图的第四个隐藏的秘密。 Figure 7a Figure 7b Figure 7c Figure 7d 17 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 4. The inverted U curve and the Yin-Yang 倒U曲线和阴阳 (1) It is a fact that many Westerners are very used to the inverted U curve/relationship, but not many understand or accept Chinese Yin-Yang. Why? 事实上，很多西方人都非常熟悉倒 U曲线关系，但很多人却不懂中国的阴 阳。这是为什么呢？ (2) I argue that this is because the inverted U curve is concerned with oneto-one relationships such as learning-innovation relationships, while YinYang is about two-to-one (such as two types of learning and innovation relationship) or two-to-two relationships (such as two types of learning and two types of innovation relationships). So, Yin-Yang and ZhongYong are much more complex than the inverted U. 我认为，这是因为，倒 U曲线是关于一个自变量对一个因变量的关系，比 如学习与创新的关系，而阴阳则是关于两个自变量对一个因变量的关系 （比如探索式学习和利用式学习这两个自变量和创新这一个因变量之间的 关系）或两个自变量对两个因变量的关系（比如探索式学习和利用式学习 这两个自变量和点滴创新和重大创新这两个因变量之间的关系）。所以阴 阳和中庸要比一般的倒 U曲线复杂。 (3) The S curve in the Yin-Yang symbol should be viewed as a dynamic changing relationship between the two inputs and the two outputs with the horizontal axis showing the proportional combination of the two inputs, and the two vertical axes indicating the two contrary outcomes. For outcome 1, the ratio of input 1 to input 2 has an inverted U relationship with outcome 1. For outcome 2, the ratio of input 2 to input 1 has an inverted U relationship with outcome 2. 在图 8中，阴阳图中的倒 S曲线应该被视为是一种在横轴上的两个自变量 的比例搭配和左右上下两个纵轴所代表的两个因变量之间的动态变化关 系。对于结果变量 1，输入变量 1和输入变量 2的比例搭配与结果变量 1 之间有个倒 U关系。同样的，对结果变量 2，则是输入变量 2和输入变量 1的比例搭配与结果变量 2之间有个倒 U关系 18 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 Figure 8. The two-to-two relationships of Yin-Yang (4) If we use the above modern explanation of Yin-Yang, it may be easier for Westerners to understand what Yin-Yang means. 如果我们用图 8以及上述相应的数量倒 U关系来解释阴阳和中庸的话，西 方人也许能更容易理解阴阳和中庸。 5. Why is the 25:75 or 75:25 combination optimal? 为什么 25:75 或75:25 比例是最优的？ (1) For inputs as well as outcome objectives, yin and yang elements are two competing proportions making a whole, meaning, yin + yang = 100% 对于输入或结果变量作为一个整体来看，阴和阳两个元素在数量关系上是 此消彼长的，也就是两者相加是 100%。 (2) If yin and yang are equal, meaning50:50, they are mutually contrary yet complementary. 如果阴阳两个元素是势均力敌的，即 50:50 的比例，他们将是互相对立又 互相互补的。 (3) If yin and yang are not equal, there will be a dominant one and a subordinate one. Since the subordinate one must be within a 0%-50% range, then how big or how small should the subordinate one be in order to gain maximal complementary synergy between the dominant and the subordinate one? I argue that the answer is that the optimal proportion 19 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 the subordinate should take is 25%, which is the mean position of the 0%-50% range. 如果阴阳两个元素不是势均力敌的，那将是一个为主另一个为辅。因为为 辅的元素相对整体的比重必然是在 0%-50% 这个区间以内，那么这个辅助 元素究竟应该占到多大的比例才能在它与主导元素之间收获最大的互补性 呢？我认为答案是辅助元素应该占到整体的 25%的比重，也就是它所被允 许的 0%-50% 这个区间的中点。 (4) Why is this so? This is because if the subordinate one is too small and has little power, say in a combination like 10:90, then the dominant one may neglect or try to crowd out the subordinate one. In such a situation, there is little competition as well as complementarity. In contrast, if the subordinate one is substantially large, say in a combination like 40:60, then the subordinate one is sufficiently powerful and confident and may desire to catch up or even overtake the dominant one. In such a situation there is more contradiction than complementarity. Both situations are not optimal because excess is as bad as deficiency. Only when the subordinate one is not too small and not too big, i.e. 25%, there will be a healthy tension between the dominant and the subordinate one and therefore the gain of maximal synergy between the two. 为什么是 25%呢？这是因为，如果辅助元素占比太小的话，它相对与主导 元素来看它的力量太小，比如如果辅主元素比例为 10:90 的话，主导元素 可能会忽略或者排挤掉辅助元素。在那种情形下，主辅元素之间只有很小 程度的竞争和合作互补。相反地，如果辅助元素占比较大，比如辅主元素 按40:60 的比例搭配，那么辅助元素就足够强大或自信从而期望赶超主导 元素。在这种情况下，主辅元素之间将是竞争多余合作互补。这两种情形 都不是最佳的，因为过犹不及。只有当辅助元素不大不小比例适度中庸 时，即占比 25%时，在主辅元素之间才会有一个最为健康的竞争合作关 系，从而两种在一起才会产生最大的协同效应。 20 Asia Research Centre, CBS, Copenhagen Discussion Paper 2014-46 Reference Javary, C. (1997) Understanding the I ching. Boston and London: Shambhala Marolleau, J. (1975) La galaxie Yin-Yang: Ou, Le triomphe de la forme (French Edition). R. Dumas.  i The series of Yin-Yang symbols with changing sizes of the two pies of Jean Marolleau (1975) can be found at http://www.comecucinarelanostravita.it/il-trito-e-ritrito-simbolo-del-tao-e-lo-schema-chiamatotai-ji/. A revised version of the series of Yin-Yang symbols can be found in Javary (1997). COPENHAGEN DISCUSSION PAPERS 2005: 2005-1 May: Can–Seng Ooi - Orientalists Imaginations and Touristification of Museums: Experiences from Singapore 2005-2 June: Verner Worm, Xiaojun Xu, and Jai B. P. Sinha - Moderating Effects of Culture in Transfer of Knowledge: A Case of Danish Multinationals and their Subsidiaries in P. R. 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