@Zhangyun Lei: "怎样用这个方程来解释 ?
無極而太極, 太極生兩儀, 兩儀生四像, 四像生八卦 ...
还有,这个方程里,是不是有一些常数呢 ?"
Good, good, very good. Now, we are talking.
Let me start with a personal story. My father was a professor at Taiwan university for 40 years, and some of his works can be viewed at
http://readopac1.ncl.edu.tw/nclserialFr ... 2%E7%BE%A4 . And, he was a Yijing expert. That is, I was able to recite ‘無極而太極, …, 四像生八卦’ before age 10 and was often showing off that great knowledge at that young age to many his colleagues. Yet, after I became a physicist, those sayings are no longer meeting the standard of scientific epistemology. I showed a very simple example, as below.
Statement A: Father and mother ‘而’ baby.
The ‘而’ of this statement is clearly understood and defined. At one happy occasion, one sperm and one egg fused into one (fertilized egg), then in mother’s body, it goes through the morphogenesis ‘process’ which transformed that fused item into an embryo, then fetus, and finally a baby. On the left side of 而 is {happy occasion, sperm, egg, morphogenesis process}, while the right side is {baby}. Yet, how about the statement below,
Statement B: 無 極 ‘而’ 太 極. What is this ‘而’ all about? What is 無 極? How can this ‘而’ transform 無 極 into 太 極? What is 太 極?
If we don’t know what the ‘essence’ of 無 極 is, what are its ‘attributes’? How can we ‘observe’ and measure those attributes? In order to answering those simple questions, we must first introduce two very important modern physics concepts, the symmetry and the ‘spontaneous symmetry breaking’.
What is symmetry? If the {East, West, North, South} cannot be distinguished, there is a ‘4-direction’ symmetry. Can you tell that this special symmetry will give you some problems? That is, you no longer are able to know the ‘direction’. So, symmetry means less ‘order’ and more ‘chaos’. Then, there is Noether's theorem (
http://en.wikipedia.org/wiki/Noether's_theorem ) which says that every symmetry produces a conservation law.
Time symmetry produces ‘energy conservation law’.
Left-right space symmetry produces ‘linear momentum conservation law’.
Yet, conservation means, not change. Thus, now we know that,
Symmetry = less ‘order’ and more ‘chaos’ = conservation = not change
For a perfect round ball (a perfect symmetry) was rotated by a kid when we were not looking, there is no way for us to find out whether he did it or not. But, if we mark a white dot on its surface, then we will know whether it has been moved or not. This one marked dot breaks ball’s perfect symmetry. This is called symmetry breaking (
http://en.wikipedia.org/wiki/Spontaneou ... y_breaking ) which gives rise to ‘order’ as we can tell whether that ball have been moved or not.
After knowing these two most important concepts of the modern physics, we can now define what 無 極 is. In dictionary, 無 means ‘nothing’, but we don’t real know its ‘attributes’. Now, is there any difference between the 無 in your hand and the 無 in my hand? If we cannot find any difference between the two, then they are symmetric, that is, indistinguishable, less order, more chaos, and is conserved, not changing. When all, all, all 無 in this universe are indistinguishable, it is 無 極, the totally chaotic and not changing.
Now, we know why 易 有 三 易 (Yi has three essences), 不 易 (not changing), 變 易 (changing), and 簡 易 (simplicity). The 無 極 is the conservative (immutable) and not changing, thus 不 易. In 「道 德 經」 (Tao Te Ching), it says, “有 物 混 成 , 先 天 地 生 。 寂 兮 寥 兮 , 獨 立 而 不 改 , (Chapter 25)”. The 混 and 不 改 are about the indistinguishable (chaotic) and immutable (not changing). That is, both the Taoism and Confucianism (Yijing) have the same idea, 無 極 is 混 and 不 改.
With the above understanding, we might still not know what the ‘essence’ of 無 is, but we do know its attributes now.
無 is a symmetry (formless and directionless, 混, orderless) = immutable (conservative, 不 改, not change, 不 易)
Thus, we can now guess what the ‘而 ’and ‘太 極’ are. ‘而’ must be a symmetry breaking process, and ‘太 極’ must be an ‘ordered’ system which comes out from a total chaotic system of 無 極.
Only after we know what ‘而 ’, ‘太 極’ and ‘無 極’ are all about, the statement “無 極 ‘而’ 太 極” can have meaning. The entire Chinese culture was hinged on one single word (而), a symmetry breaking process.
The concepts of ‘symmetry and symmetry breaking’ were fully understood in physics (mainly by the Westerners) only 80 years ago, but they were the backbone in Chinese thoughts 3,000 years ago. Not only is this a thing of great pride for Chinese people but it will be the center point for understanding both Yijing and 道 德 經. But, it was viewed as ‘stupidity’ by the May 4th movement scholars. Are you able to guess what this ‘而 ’ is all about. I will discuss this symmetry breaking process (而) tomorrow.
@Yvan Razafindratandra: "Does "nothing" mean "void", or "emptiness", or "zero" in maths? … "Do you mean the general theory of relativity or anything else?"
Excellent questions!
For man, he is a two-leg animal, but not all two-leg animals are man. Thus, ‘nothing’ is void, emptiness and zero, but not the other way around. ‘Void’ and emptiness are often defined with an envelope, that is, it is not truly a total ‘nothingness’. There is a special ‘attribute’ about ‘zero’, that is, 1/0 = infinity. So, zero has a relationship with infinity. In physics, there is a space-time ‘vacuum’ which means that no ‘particle’ in a given space, but there is still ‘energy’ in that vacuum. This is why I was reluctant to define the ‘essence’ of nothingness in my previous posts but discussed its attributes only. But, I will discuss the essence of ‘nothingness’ soon.
Yes, General Relativity (developed in 1915) had good symmetry in it. Noether's theorem (discovered that symmetry equals to conservation) was published around 1950. The true understanding of ‘symmetry breaking’ was achieved around 1970s when the Standard Model of particle physics was developed.
Furthermore, the ‘nothingness’ was an untouchable issue in physics until a decade ago. In 1948, the Big Bang cosmology was developed, but by all means that the Big Bang itself is not ‘nothing’. In 1970s, physicists wanted to push this known universe beyond the Big bang, and there was the ‘Inflation cosmology’ which speculated that the universe started from a size much small than an atom (again, not nothingness). You might all hear about the news two weeks ago that BICEP2 announced that they detected the primordial gravitational waves which is the relic right after the creation of this universe from … (perhaps, nothing). By all means, the modern cosmology can still not be able to push our understanding all the way back to the ‘nothingness’.
On the other hand, the 八卦 (trigrams, 無極而太極, 太極生兩儀, 兩儀生四像, 四像生八卦 ...) was developed more than 5,000 years ago (by 伏 犧, about 2,000 years before 文 王). So, if we say that 八 卦 is the result of ‘symmetry and symmetry breaking’ and is the result of ‘nothing’ to something transformation, we are either talking about a joke or …. In fact, this ‘無極而太極’ saying was viewed as the stupidest and the greatest shame in the Chinese history by the May 4th movement scholars in the 1930s, all the way to 1980s. Today, most of Chinese scholars do not see it as a shame anymore but are definitely do not understand the seriousness of this issue.
Is Yijing only an ancient ‘story’ (no better than the Odyssey and Iliad by Homer) or a genuine cosmology? Well, let’s see what the Yijing’s own ‘claim’ was. In 系 辭 上 (Commentary One), it said, 乾 坤 定 矣 (points to that Yijing is about the laws of the nature universe), 貴 賤 位 矣 (points to that Yijing is about the laws of the moral universe), 剛 柔 斷 矣...,吉 凶 生 矣 (points to that Yijing can predict all the outcomes between the interactions (among the nature universe and the moral universe)). That is, by all means, Yijing did not see itself to be the same level as Homer’s stories. It is a cosmology and theology. Then, is it correct, especially in comparison to the modern cosmology? So, let’s see how did it transform the 無 極 into something (太 極 or else).
.
In Yijing, 無 極 (WUji,
http://en.wikipedia.org/wiki/Wuji_%28philosophy%29 ) is the state before the creation of the universe, being completely formless with the total homogeneousness and the total symmetry. Then, there is 一 劃 開 天 (one stroke created the universe). This one stroke created the 太 極 (Tai Chi,
http://en.wikipedia.org/wiki/Taiji ). In fact, this one stroke creates “three”, the ying, the yang and the dividing stroke. So, in Chinese theology, the concept of ying /yang and the number of 1/3 became the central pillars. As the number ‘1’ is the creating power, all odd numbers are assigned to be yang power. And, the even numbers are assigned as ying.
The above is just a theoretical talk. How can it be shown with a visible process? It is described with 羅 盤 (Luopan, Chinese geomancy campus,
http://en.wikipedia.org/wiki/Luopan ) which detects the energy flows from all “directions”. The center of the 羅 盤 is a small water basin (called 天 池, symbolizing the無 極). Before a magnetic needle is dropped on the surface of the water in 無 極, the 羅 盤 does not give out a direction, that is, one is in a directionless state. When the needle (the one stroke) was dropped in the 無 極, the floating needle will point to North. With this one stroke (the needle), the direction (or universe) is created, homogenous no more, the total symmetry no more. The universe is now divided into directions, and this is called 一 劃 開 天. This entire ‘process’ encompasses 1) symmetry (the 無 極), 2) symmetry ‘breaking’, the one stroke, 3) the result, the 無 極 was divided into two parts (ying and yang), the 太 極. So, now we know what this ‘無極而太極’ means. The ‘而’ here is the 一 劃 which ‘broke’ the super symmetry (formless or orderless) of 無 極. 太 極 has a broken symmetry, that is with form and order. The further symmetry breaking (生 兩 儀, 生 四 像, 生 八 卦) creates even more forms and more orders. More details on this, please see
post223.html#p223 .
Using 天 池 to symbolize 無 極 is indeed a great metaphor. But, by all means, it does not give the exact definition for 無 極. In 「道 德 經」 (Tao Te Ching), 無 does not totally mean as ‘nothing’, as it said, “故 常 ‘無’ , 欲 以 觀 其 妙 ﹔ 常 ‘有’ , 欲 以 觀 其 徼 。 此 兩 者 , 同 出 而 異 名 , 同 謂 之 玄 。 (Chapter 1)” and “有 無 相 生 (Chapter 2)”. That is, 無 is tightly bound with 有, the same as the 無 極 is tied together with the 太 極. 無 is the ‘key’ concept in Chinese culture. But, what is the ‘essence’ of 無 in Chinese culture, I will discuss it more in the future. 無 is very much different from 空 (emptiness).
Today, physics can still not discuss the ‘nothing’ to something transformation. The issue of ‘Why is there something rather than nothing?’ was discussed only 10 years ago. That is, ‘conceptually’, the Yijing (a book of 3,500 years ago from China) is more advanced than the current cosmology. But, in reality, Yijing does not explain the formation of stars and galaxies, that is, there are two different kinds of cosmology. I will discuss this soon.
After knowing how ‘無 極 而 太 極’ means and does, we now are able to discuss what the heck the Yijing is. Of course, the 重 卦 (64 hexagrams) is a further symmetry breaking, thus more orders (more structures for the universe). But, why stop at one 重 (stacking only once)? Why not 重 (stacking) one more time (to 512 nonograms)? I will discuss these issues too.
Now, we understand one sentence, ‘無 極 而 太 極’. From here, we get 八 卦 simply by the ‘permutation’ of two lines (ying and yang), the 生 兩 儀, 生 四 像, 生 八 卦. Why should this simple permutation carry any significant meaning (laws or principles) of this universe? If it does, then show me. So, what is the big deal about this permutation?
Confucius himself did claim that it is a big deal. In 系 辭 上 (Commentary One), he said, 乾 坤 ‘定’ 矣 (cosmology), 貴 賤 ‘位’ 矣 (morality), 剛 柔 ‘斷’ 矣 (dynamics)...,吉 凶 ‘生’ 矣 (??? Oracle?). Today, almost every statement in the ‘physics’ of Aristotle is not correct in terms of the modern physics, but the greatness of Aristotle is still respected for his ‘historical’ contribution. Thus, if Confucius was totally wrong on the above statements, his greatness will not be challenged. But, we should still investigate whether his above statement is right or wrong. I am going to discuss the first issue today. Is the 八 卦 a meaningful ‘cosmology’?
First, we should talk about the ‘modern cosmology’ which consists of the following parts,
One, inflation: starting from a ‘matter’ (something) small than an electron to a size of a ‘pea’ in one trillionth, trillionth a second.
Two, the Big Bang: that ‘pea’ universe exploded into an inferno, then it began to cool off after 300,000 years. The lights at that point cooled to about 2.7 degree of Kelvin ‘today’. This relic of that primordial lights is called the CMB (Cosmic microwave background,
http://en.wikipedia.org/wiki/Cosmic_mic ... background ) which is the top, top topic of the modern cosmology today.
Three, the expansion universe: after 300,000 years from the big bang, the stars and galaxies formed. The size of the current universe is about 15 billion light years across. The 99.99% of matter in the stars are hydrogen or helium, no heavy atoms at the beginning. Those hydrogen and helium are ‘fuel’ to power the burning stars. In the burning processes, the heavier atoms (such as, oxygen, carbon, iron, etc.) were produced as the ‘ashes’ of the ‘nuclear’ burning process.
Four, super novae: when the ‘fuel’ of a star burned out, it collapses into a neutron star while a big chunk of that dying star was thrown out into the ‘space’. Only the super nova chunk contains the heavy atoms (oxygen, carbon) which are the vital parts for building ‘life’. When such a chunk was caught by a young star (such as our Sun), that chunk had the chance for ‘life’ to arise. Note: the oxygen and carbon in our bodies (mine and yours) are not coming from our Sun, as its heavy atoms are not yet released. That is, both you and I were once a part (at least in the form as heavy atoms) of a star lived billions years ago.
Of course, all the processes above are governed by ‘quantum mechanics’ and ‘general relativity’ while both of them are deeply tied to the ‘symmetry and symmetry-breaking’. But, there are two important points in the above story.
First, it does not address the issue of where that ‘seed’ of inflation came from? No ‘nothing’ to something transformation.
Second, the story does allow ‘life’ to arise but no connection to life directly, let alone about the connection to humanity.
That is, the modern cosmology is purely about the ‘physical’ universe, having nothing to do with the ‘humanity’ universe.
Now, let’s see the Yijing cosmology.
One, ‘無 極 而 太 極’: 生 兩 儀 (ying and yang)
Two, 生 四 像: this corresponds to ‘four sides (四 面)’ of the universe.
Three, 生 八 卦: this corresponds to ‘eight directions (八 方)’ of the universe.
This cosmology is obviously not giving any explanation for the formation of stars and galaxies. Is this Yijing cosmology much inferior to the modern one? This can be answered by investigating what relevant issues each cosmology have addressed.
a. The modern cosmology (MC) does not address the issue of ‘creation’, from nothing to something but Yijing did.
b. The MC does not show the concepts of ‘symmetry and symmetry-breaking’ directly although its underlying laws (quantum mechanics and General Relativity) are the products of those two concepts. But, these two concepts are directly revealed by Yijing.
c. Today, all of us taking the ‘direction (right vs left)’ for granted. Yet, it was the most difficult issue in physics 70 years ago. In physics, there is CPT symmetry (
http://en.wikipedia.org/wiki/CPT_symmetry ). C is electric charge conjugation, P the parity and T is the ‘time’. Under this symmetry, there was no way to distinguish the left from the right by physics laws. Fortunately, in 1950s, two Chinese physicists (T. D. Lee 李 振 道 and C. N. Yang 楊 震 寧,
http://www.bnl.gov/bnlweb/history/nobel/nobel_57.asp ) discovered the p (parity) symmetry-breaking (
http://en.wikipedia.org/wiki/Parity_(physics) ). They two won the Nobel physics prize on this. Only with this discovery, the left-right can be distinguished by physics law. However, the MC does not show this parity issue ‘directly’ while it is the center issue in Yijing.
d. Most importantly, MC has no ‘direct’ connection to humanity. On the other hand, humans play a ‘central’ role in this Yijing cosmology.
Confucius said in 系辭下 (Commentary Two, on Yijing), "易之為書也,…﹕有天道焉,有人道焉,有地道焉。兼三材而兩之,故六。" Again, he said in 說卦 (Explanations about Yijing), "昔者聖人之作易也,… 是以立天之道,… 立地之道,… 立人之道。兼三才而兩之,… 故易六 ‘位’ 而成章”。 This same issue, he said twice, that is, this is the key point of why 重 卦 (stacking).
Most people views the ying-yang (the 兩 儀 or 太 極) as the backbone of Yijing. They are not wrong but not exactly right neither. Without the concept of ‘三 才’, the 八 卦 Yijing will not have much ‘value’. The ‘三 才’ is the ‘soul’ of Yijing. ‘三 才’ consists of three entities (天, Heaven; 地, Earth; and 人, human). In addition to the nature and spiritual world (Heaven and Earth), man plays a major part in this ‘three part’ universe. After the formal participation of human in the nature and the spiritual world, Yijing was transformed into a book of ‘theology’ from the simple original cosmology.
In Christian theory, the key word is 信 (faith in Jesus as savior). In Buddhism, the key word is 悟 (enlightenment). In Confucianism, the key word is 參 (participation) in the ‘union’ of Heaven and Earth. Now, Christian also practice the petitionary Prayer, but it is in principle different from the 參 in Yijing. In Christianity, the petitionary prayers are begging for mercy, as the Heaven and the man are separated by the original sin regardless of the prayers or not. In Yijing, it is all about the 天 人 合 一 (the union of Heaven, Earth and man).
Thus, the 八 卦 is more than the ‘eight direction’. It represents the 三 才, the union of Heaven, Earth and Man. Then, 兩 之 (the 重 卦) formally expresses the interaction of Ying-yang and 三 才 and thus complete the system of Yijing.
Now, we know what the 八 卦 cosmology is and why the reason for 兩 之.
One, it shows the transformation (symmetry-breaking) from ‘orderless’ to ‘order (directions)’. This is as good as MC if not better.
Two, it shows the ‘place’ for humanity in this newly created order (the union of Heaven and Earth, the physical universe).
So, does Yijing only make ‘historical’ contribution (similar to the physics of Aristotle) as a great heritage treasure but without any relevancy today? I have given the answer above. Yijing is not only still relevant today but in many senses are much better than the modern sciences. Now, we begin to see what the Yijing is all about. It is,
One, a genuine cosmology: by wholly understood the concepts of ‘symmetry and symmetry-breaking’.
Two, a genuine theology: it addressed the issue of creation (無 極 而 太 極), and it connected human to that creation (including this physical universe, described by the modern cosmology).
Anything more? Definitely. There are more about Yijing, and I will discuss some of them tomorrow.
I have compared Yijing to and with the most advanced modern concepts. One reason is to examine the ‘relevancy’ of Yijing to today’s knowledge. Yet, most importantly, we truly need those new concepts to understand fully what the Yijing is all about. Let me introduce two more modern concepts, and then we can move to part 2 after this.
First, the anthropic principle (
http://en.wikipedia.org/wiki/Anthropic_principle ) which was introduced in 1973 as a check pen in cosmology. If a cosmology does not allow the emerging of life, it must be wrong as we (lives) are here. Yet, there are two versions;
the weak anthropic principle (WAP): it merely allows the rising of lives but does not compel to it;
the strong anthropic principle (SAP): it demands that lives much emerge.
The current modern cosmology which I discussed in previous post follows the WAP, as the super nova does provide the life building material (oxygen, carbon, etc.) but there is no compelling force in the theory to demand the rising of lives. On the other hand, the 三 才 of Yijing is obviously taking the view of SAP as the human is playing a part in the union of this universe.
Second, the cellular automaton (
http://en.wikipedia.org/wiki/Cellular_automaton ) which was introduced by John von Neumann in 1940s when he was studying the issue of ‘self-replicating systems (the artificial life system)’. There was a story about von Neumann. At his death bed, three CIA and FBI agents were there, not for seeing his last step for his life but were trying to take the ‘note’ of what he would say about the top secret on the nuclear warhead design before his last breathe. In addition to the nuclear bombs, the most important contribution of von Neumann was the invention of a new discipline (science) of ‘artificial life, the alife (formally named by Christopher Langton in 1986), see
http://en.wikipedia.org/wiki/History_of_artificial_life .’
In 1970s, there is a very important development on alife. A great British mathematician John Conway invented the ‘game of Life (
http://en.wikipedia.org/wiki/Conway's_Game_of_Life )’ which plays on a ‘Go’ board (圍 棋 盤). One of the ‘species’ of the game is called glider (
http://en.wikipedia.org/wiki/Glider_(Conway's_Life) , an automaton) which has the ability of ‘Self-replication’, that is, it is alive, an alife. These developments shocked the entire world about the meaning for ‘life’.
Why am I talking about these? Because, both 八 卦 (trigrams) and 64 卦 (hexagrams) are ‘automatons’ (see
chinese-culture/about-yijing-the-general-discussions-t10.html#p395 ). That is, the 卦 體 (八 卦 (trigrams) and 64 卦 (hexagrams), the part 1) do carry those modern concepts.
But, one major question is whether those Yijing authors (伏 犧, 文 王, 周 公 and 孔 子) knew about these, as after all both 八 卦 and 64 卦 can be constructed simply with the permutations of two lines (ying and yang). That is, there was a big chance that those Yijing authors constructed them without knowing the true meanings of them, especially not knowing those modern concepts.
However, from the statement of ‘無 極 而 太 極’ and ‘兼 三 材 而 兩 之’, it is clear that they do have ‘some’ understanding about these modern concepts although might not be in these modern ‘forms’. Furthermore, Confucius claimed that Yijing is able to ‘通 神 明 之 德’ and ‘類 萬 物 之 情’, that is, his ‘claim’ clearly reached to the height of these modern concepts.
Of course, we can find out the answer very easy, simply by examining the texts (the part 2) which they wrote about them (八 卦 and 64 卦), especially from how they were constructed (演 卦), and this will be the part 2.
If they did understand those modern concepts somewhat, how can then anyone talk about Yijing if he does not know about these new concepts?