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6 Rules, Relationships and Movements

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3.6 Rules, Relationships and Movements


Chinese did not go less far than the Greeks, they went somewhere else.”134 Now we

have shown that also for the sciences.

3.6.1 Characters and Literary Discourse

I am convinced that a language that is not linear, but pictorial and ideogrammic,

like Chinese, had its weight in favouring representations that were different from

those of Greek and Latin, where alphabetical languages are used. In the text of

the Zhoubi, numbers referred to figures, and figures to numbers. The former made

it possible to understand the latter, and the latter were a help to understand the

properties of the former. The argument was developed around a circle, and as this

moved, it became possible to use it in 10,000 different cases. The Zhoubi appears to

us as a page written in the same characters as other literary texts. The passage from

the jing [straight line] character to the xian character for the hypotenuse probably

only indicated the evolution of the language, and did not represent the search for a

special technical term. Actually, xian also means the chord of the arc and the string

of musical instruments.135

With their choice of characters, Chinese scholars appear not to desire to

distinguish their possible different uses when they discussed of mathematics or other

subjects. In general, they did not manifest any particular interest in the invention

of a symbolism that would allow them a certain detachment from current literary

discourse. The famous zheng ming of Confucius: “It is necessary to rectify the

names” was an invitation to make the names agree with the sense, so that the

sense could successfully guide behaviour.136 The only ones who had tried (with

what results?) to coin new technical terms for the sciences would seem to be the

followers of Master Mo.137 But for the most part, the invention of new terminology

was condemned.138

When Westerners had already come on to the scene, a mathematician of

success like Mei Wending (1633–1721), rectified some terms of mathematics in

order to avoid confusion, using the same characters of the language. He, too,


Vernant 1974, p. 92.

“Their beginning and their end are like a circle, whose order has no end”; Zhuangzi XXVII,

1982, p. 256. Above, Sect. 3.3. Archery was not only one of the arts that a gentleman had to learn,

together with music. It also had to serve as an example to follow in order to educate. Mencius

wrote: “The virtuous man draws [the bowstring], but without darting it”. That is to say, the pupil

should be encouraged, but left to follow his own way spontaneously. “How similar the Tao of

heaven is to the act of drawing a bow!”; Daodejing LXXVII; 1973, p. 165. Jullien 2004, pp. 309ff.


Confucius XIII, 3; 2000, pp. 104–105. Cf. Hansen 1956, pp. 72–82. Jullien 2004, pp. 225–235

and 264.


Hansen 1983, p. 109. In order to achieve the maximum of clarity, the Mohists renounced the

elegance of literary style. Needham & Robinson 2004, pp. 101–103.


Graham 1999, p. 359.



3 In Chinese Characters

followed the tradition of designating some mathematical objects by means of terms

indicating concrete things. For example, he wrote “canine teeth” for the angles of

an icosahedron.139

As well as facilitating open circular arguments, and helping scientific discourses

to keep both feet on the ground, and to be comprehensible for all educated people,

some Sinologists have underlined a third important characteristic of the Chinese

language which is pertinent here: the lack of a verb “to be”, that is to say, of a

character that can express a suitable equivalent. The character you [there is, exists,

not distinguished from the verb ‘to have’] expresses possession, and refers above all

to wu [material things]. Surrogates, recent among other things, such as shi [right,

yes, this] are weak, compared with the peremptory “is/are” of old Europe, rich in

cultural harmonics. Instead, in the Country at the centre, discourses abound in wei

[to do, to act, to become], a character also used in the place of what would be

expressed in Europe by the verb to be.140

Franỗois Jullien has underlined the event that the inclination of Chinese culture

to prefer organic correlations has remained impressed in the language. For example,

these can be seen in the terms dongxi [east-west] to indicate a generic “thing”,

or shanshui [mountains-waters] for “charming panoramas”; we have already met

another case, which will immediately be found again: yuzhou [space-time] for

“universe”. They also say:

huwen jianyi

[the ones with the others the writings, [and] you will see [their] correctness.]

Kenneth Robinson and Joseph Needham have interpreted the same characteristics, e.g. shensuo [lengthen-shorten], as a different way of abstract terms, in this case

“elasticity”, which are created in great quantities in the Indo-European languages.

However, it seems to me, rather, a way of avoiding abstractions, and remaining

anchored to the sensible aspects of things. The two authors bring arguments to show,

to anybody who needs them, that Chinese was capable of expressing anything that it

wanted to express, including numbers, technical details or scientific reasoning. But,

surprisingly, we also read today that for the Zhuobi men of letters would be satisfied

with presenting a simple “example”, in order not to destroy the Tao by proofs,

passage after passage. “There was, therefore, in China a considerable barrier to the


Martzloff 1981b, pp. 173–178 and pp. 301–302. Needham & Robinson 2004, pp. 172–175. Even

Harbsmeier – in Needham and Harbsmeier VII 1998, p. 234 – had to recognize “. . . a natural and

strong gravitational force towards the non-abstract down-to-earth use of words.” The insistence of

Karine Chemla on assigning a technical meaning to characters in classical Chinese mathematical

texts sounds anachronistic, because it derives from modern symbolic habits; cfr. Neuf Chapitres,

pp. 99ff.


Hansen 1983. Graham 1990. In Part II, Sect. 8.2, we shall recall the problems of the most famous

translation from Latin into Chinese, that of Euclid’s Elements. Tonietti 2006a, Chap. 4.

3.6 Rules, Relationships and Movements


formulation of mathematical proofs, due to the social attitude of the educated.”141

On the contrary, we have seen that Chinese books offered different proofs from those

of Euclid, which were not, are not, and will not be the only ones possible, even in

Europe. Whether it depended on the Tao, on language or on culture in general, the

reader will be able to make his own opinion through the following pages.

Chinese words, which do not distinguish in general between verbs, nouns and

adjectives, express better a reality in movement. In order to render a Chinese text

more faithfully, then, we need to abound with the verbs, and limit the number of

nouns, especially if abstract. I prefer to leave to the following Sect. 3.6.4, dedicated

to the continuum, a discussion of the characteristic presence in the Chinese language

of classifiers, because it will become clearer and more meaningful there.

Two philosophers were arguing and one said to the other:

“There are two types of people, those who like dichotomies

and those who don’t”. The other replied:

“That’s nonsense!”

Evelyn Fox Keller.

3.6.2 A Living Organism on Earth

In China, the world was not divided between heaven and earth, because they were

both part of the same unitary cosmos. Both shared the same fa [rules] and the same

li [reasons]. In the Zhoubi,we read that the former appeared to be round, and the

latter square. But the two forms were considered as welded together, like the gou

and the gu with the xian, like 3, 4, and 5, like the flat bottom and the curved shell of a

tortoise. Joseph Needham started out on his long study of Chinese sciences with the

idea that in them, the world was represented as a living organism.142 The Chinese

scholar did not forget that we live on the earth, and we observe the sky from here.

Therefore, in order to study it, it needs to be brought back to earth.143


Jullien 2004, p. 429. Needham & Robinson 2004, pp.108–110, 141 and passim. Joseph

Needham (at the age of 93) even affirmed “. . . certain disadvantages of the Chinese script . . . ”.

Compared with the advantages of printing with the alphabet, the Chinese “were hamstrung by the

complexities of Chinese characters.” Needham and Robinson 2004, pp. 210, 227 and 230. In this

aspect, Needham ended up by becoming too similar (was it his Christian attitude?) to the Jesuit

Matteo Ricci; see Part II, Sect. 8.2. The serious Eurocentric stereotype, about the lack of proofs

among the Chinese, is discussed and criticised also by Marc Elvin. But even he does not succeed

in doing so in a satisfactory manner, with his contaminated style typical of one who presumes

to decide who was “superior” or “inferior”, “ahead” or “behind” in the supposed race towards a

“progress” which is as imaginary as it is senseless; Needham and Robinson 2004, pp. xxxi–xxxii.

Chinese poets’ anchoring their verses to space-time was stressed by Turner 1986. Cf. Fenollosa

and Pound 1919.


Needham & Wang II, 1956.


Lloyd 1994, 160; Tonietti 2003b, p. 233.


3 In Chinese Characters

Fig. 3.7 How Yang and Yin penetrate each other in the “Extreme limit” (Needham 1956, vol. II,

plate 21)

The figure of the string, as an argument for the fundamental property of the

gougu, did effectively remain on earth. In the Chinese culture, they trusted the eyes

that observe and the hands that shift and move the pieces of the figure. The sky could

be seen and measured with the gnomon. Indeed, it could be understood by watching

a shadow on the ground. The Chinese scholar remained down here, because he put

his trust principally in the earth. Only the school of the Mohists criticised knowledge

by means of the senses, and in particular by sight.144

Chinese scholars tried to arrive at knowledge by studying the links between

things. They believed that the world was not white on one side and black on the

other. A characteristic figure is the one called taiji. This can be literally translated

as “the greatest limit”, “the extreme limit” (Fig. 3.7).

This represented the interplay of the two principles that generate the world, Yin

and Yang. It is clear that these were inseparable, and that their mixture, taking the

process beyond all limits, became a sort of emulsion like a fractal. It is well known

that Yin represents female, cold, damp, shadow, the moon . . . whereas Yang refers to

male, hot, dry, the Sun . . . Another more popular modern figure is circular in shape,

and is reproduced almost everywhere, as in the editions of the Yijing. Also in these,

it is important to note the presence of the small black circle in the white area, and


Graham 1999, pp. 188–189; Needham & Harbsmeier VII 1998, p. 254.

3.6 Rules, Relationships and Movements


vice versa, a white circle in the black part; these reproduce on a small scale the

initial circle. And so on, beyond all limits.145

Unfortunately, dualism is so deeply rooted in the way of thinking of Westerners,

that even Yin and Yang are often considered in this light. The most famous precedent

of this serious misunderstanding of Chinese culture (and of the dao) is the one

found in Leibniz.146 As regards numbers, a similar mistake was made by our valiant

Needham, who was misled by the myth of a single universal science, even though

the Taoist philosophies, which he knew very well and appreciated, should have led

him elsewhere.147

The character xin means both heart and mind. In this case, the search for the link

is no longer necessary, because the language has made them identical. In the Chinese

culture, the zhen [the true] is not separated from the real, and so it remains on the

earth. To arrive at the veritas of the Greek and Latin world, it would be necessary

to write zhenli, but the li [reasons] would still maintain with the zhen reality as the

authentic place that decides it. In the same way, cuowu [the false] is not opposed to

the true, but would be more suitable to render the idea of a wrong or bad action. I

becomes a moral judgement on the actions of human beings, an expression regarding

the quality of things like food: cuowu is its harmful result.

In commenting on the Jiuzhang [Nine chapters], Liu Hui criticised the

astronomer and mathematician, Zhang Heng (first century).

Suiyou wenci, si luandao poyi.

[Although he writes in a classical style, [Zhang Heng] confuses the Dao [the way, the

procedure] and damages what is right.]

How is it possible not to perceive, even here, for a mathematical calculation, the

echo of a judgement that is more moral than technical?148

The absence of veritas in Chinese culture has already been effectively explained

by Jacques Gernet: “The concept of a transcendent, unchangeable truth is foreign


Yijing 1950 [I King], p. 39; 1995 [I Ching], pp. 67–72. Needham & Robinson 2004, p. 90.

Part II, Sect. 10.1.


Needham & Wang III 1959, pp. 139–141; II 1956, pp. 339–345. Joseph Needham knew very

well that Chinese culture had generally (not only with Taoism) remained distant from the dualistic

transcendence typical of the West, at least until recent times. We can read of several cases in his

books, which we, too, have appreciated. And yet he would have liked, thanks to his ecumenical

idea of science, to succeed in finding a compatibility (in a Confucian or Taoist style?) between

Christianity, Marxism and Taoism. The modern reader may judge by himself to what extent this

was only the personal experience, and wishful thinking, of the professor educated at Cambridge in

the Thirties, or, on the contrary, what an ironic twist of history was to concede in the China of the

twenty-first century. But that conviction was so strong and deeply rooted in him that, unfortunately,

it closed his eyes sometimes in front of St. John the Evangelist, Plato, the Legalists, Francis Bacon,

or the quantum mechanics of Bohr and Heisenberg, with all its defects of nuclear war technology.

Needham and Robinson 2004, pp. 84–94 e 232.


On the contrary, with her different translation and interpretation, Karine Chemla blots out the

moral judgement, and reduces it, anachronistically, to a criticism of errors of calculation; cf. Neuf

Chapitres, pp. 62 and 382–383. Lloyd & Sivin 2002, p. 52.



3 In Chinese Characters

to Chinese thought”. “. . . Chinese thought has never separated the sensible from

the rational, . . . nor has it ever admitted the existence of a world of eternal truth

separate from that of appearances and transitory realities”.149 Thus, in the Country

in the centre, even judgements which would be taken (or rather, misinterpreted) as

technical and factual judgements in the West, were inevitably linked with morals,

and with the good or bad result of human behaviour.

Among the “one hundred schools”, one could surely be found which sustained

a different position: that of Master Mo. There, on the contrary, the desire was to

distinguish, to make a clear-cut separation, instead of connecting.

buke liang buke ye.

[It is not possible that both [are] impossible.]150

In the evolution of Western sciences, the principle was indicated by the Latin

name of “tertium non datur”. In other words, there is no way out of the straightforward alternative between true and false. But the rival schools of the Confucians and

the Taoists criticised this, and succeeded in overcoming it.

The Zhuangzi sustained: “How could the Tao be obscured to the point that there

should be a distinction between the true and the false? How could the word be

blurred to the point that there should be a distinction between affirmation and

negation? . . . That which is possible is also impossible and the impossible is also

possible. Adopting the affirmation is adopting the negation. [. . . ] The appearance

of good and evil alters the notion of the Tao. [. . . ] The word is not sure. It is

from the word that all the distinctions established by man come. [. . . ] The word

that distinguishes does not arrive at the truth. . . . Knowing that there are things that

cannot be known, that is the supreme knowledge.”151

Discriminatory distinctions are to be found only in one passage with a Legalistic

tone, quoted by Lüshi Chunqiu [Springs and autumns of Master Lü], a text

considered syncretic.152 Among Mohists, Confucians and Taoists, disputes took

place about the possibility, or otherwise, of discriminating between ‘right’ and

‘wrong’.153 It is interesting, however, that even the Mohists used the character

bian with the meaning “to reason, to dispute, to debate”, and not the similar, more

stringent homophone, bian (drawn differently) “to differentiate, to distinguish, to

discriminate”. Thus, even those who were the fiercest supporters of the possibility


Gernet 1984, p. 72 and passim; pp. 219ff. Hansen 1983, p. 124. Graham 1999, pp. 24–27, 31–32,

227, above all 264–271. Cf. Needham & Harbsmeier VII 1998, pp. 193–196. Jullien 2004, pp. 157

and 229.


Graham 1990, p. 335. Hansen 1983, p. 121. Graham 1999, p. 226.


Zhuangzi II, 1982, pp. 23–28. See also in VII the apologue on Indistinctness.


Needham & Harbsmeier VII 1998, pp. 226 and 234.


Needham & Wang II 1956, p. 180 and passim; Graham 1999, p. 43 and passim.

3.6 Rules, Relationships and Movements


of “debating” what was ‘right’ and what was ‘wrong’, left the subjects of the dispute

present in the term used.154

In the Daodejing, the exaltation of “non-discrimination” went so far as to connect

“nothing” with “something”.

youwu xiangsheng

[nothing and existence are born from one another,]

“difficult and easy complete each other, long and short make up for each

other, high and low are determined by one another, sounds and voices are in

harmony with each other, former and latter form the series with each other.”155 The

famous wuwei [non-doing] represented another expression of the youwu. Is it really

necessary to underline again that the conception was facilitated by the characters wu

[nothing] and you [something], which referred to real things on the earth, subject to


All the living creatures on the earth were a part of the same world-organism,

including human beings, guided by their moral values. And this was the reason

why the Chinese scholar could not have imagined any of his activities, including

mathematical sciences, as independent of ethical behaviour. In this, with their

behaviour, people, starting above all with the emperor, became jointly responsible

for cosmic harmony.157 The Confucian ren [benevolence, pietas], continued to guide

the good scholar, also in the mathematical, astronomical and musical disciplines.

Consequently, he did not conceive of any distinction between “man” and “nature”;

as a result, nature, too, was charged with the relative moral values.158 The dao, the

procedure for obtaining the result, also depended on the de [virtue], as in the title

of the Taoist classic, Daodejing. The fact that the links between sky, earth and man

were real and effective was guaranteed by the unique universal qi which pervaded

everything and made everything sympathetic.

3.6.3 Rules, Models in Movement and Values

Dao ke dao, fei chang dao; ming ke ming, fei chang ming.

Wu ming tian di zhi shi; you ming wan wu zhi mu.

[The way, the right way [is] not the unalterable way; the description, the right description

[is] not the unalterable description; the beginning of heaven and earth is undescribable; the

mother of the 10,000 things is describable.]


Hansen 1956, pp. 82–88 and Chap. 4. Apart from the inevitable shifts in the meaning of

characters, this subtlety escaped the attention of Graham 1990, pp. 335ff., who, however, corrected

himself in Graham 1999, p. 43. On the contrary, it is overlooked by Lloyd & Sivin 2002, pp. 61ff.


Daodejing II, Tao te ching 1973, pp. 31 and 178.


Graham 1990, pp. 345–346.


Graham 1999, p. 485. Lloyd & Sivin 2002, p. 78. Jullien 2004, pp. 172–173.


Sun 2005, pp. 53–55.


3 In Chinese Characters

The Chinese scholar who took his inspiration from the beginning of the

Daodejing, would believe that the most appropriate description for a changeable

world was a changeable description. He thought that studying the generation of

things had a sense, but not trying to find out the beginning of heaven and earth.159

In the Yijing [Classic for changes], the procedure does not finish in just one

hexagram, but this may be transformed into another one. The Yang associated with 9

is transformed into Yin, while the Yin of 6 becomes Yang. The result, as represented

by the two different hexagrams, appears to be unstable. Thus it is not fixed, but

rather a process, a tension between two different situations.160 What is to be done

in the uncertainty of the conduct to be followed? What decision should be taken?

The Yijing helps the enquirer to reflect, so that in the end, he or she can choose.

It is not expected to reveal a destiny already established and unchangeable, learnt

by means of a deterministic procedure. On the contrary, it is recognized that the

world where we live is unstable and in continual transformation: it appears to be

dominated by chance and by uncertainty. Why ever should we search for stable,

eternal elements in it, on whose rules it would depend? In the Yijing, Chinese culture

mimes its instability, rather, through a procedure that includes counts that depend

on chance. In counting the stems, numbers are created which are necessary to know

the uncertainty of the world.

In China, everything was represented as in movement and in transformation;

certainty was achieved with the ability to shift from one thing to another, depending

on the aims and convenience. The proof of the Zhoubi was obtained by moving

pieces of figures with simplicity and in reality.161 In a book of 1921, Liang Shuming

wrote: “The Chinese have never discussed questions that derive from a static,

unchanging reality. [Chinese] metaphysics has only dealt with change, and never

with static, unchangeable reality.”162 Referring to the seismograph, a scholar of the

eighteenth century had criticised it, affirming:

youding buneng ce wuding

[. . . [it] remains fixed, it cannot measure that which is not fixed.]163

Enough has already been written, from various points of view, on the difficulty of

finding a good equivalent of the European (also scientific) law in Chinese culture.164

The philosophers-cum-ministers who inspired the guiding principles followed by

the first Emperor, Qinshi, to subdue a large part of China, were called fajia. In the

West, this name has been commonly translated as Legalists, because they would

have liked to regulate everything with precision and intransigence, systematically


Daodejing I; 1973, p. 177; translation different from the one on p. 27. Zhuangzi XXVII; 1982,

p. 256. Cf. Hansen 1983, p. 71. Graham 1999, p. 299. Cf. Jullien 2004, pp. 320 and 376–380.


Yijing, any edition. Jullien 1998, p. 61.


See above, Sect. 3.3. Needham & Robinson 2004, pp. 182–183.


Gernet 1984, pp. 260, 263ff.


Needham & Wang III 1959, p. 634. Jullien 1998, pp. 66ff.


Needham & Wang II 1956, Chap. 18. Graham 1999, pp. 375–381 and 397.

3.6 Rules, Relationships and Movements


and rigidly excluding everything that did not conform. But they fell with the

first Emperor. The subsequent Han dynasty refused the methods of the Legalists,

preferring ren, the sympathetic pietas recommended by Confucians. Since then, a

dominant orthodoxy of this type has existed in Chinese culture.

In brief, people (in other words, unfortunately, men, in China,) were preferred

to laws, and were considered as more important than abstract general principles.

Consequently, the possibility was favoured of adjusting the rules to single cases,

considering them as easily adaptable depending on the circumstances. Responsibility remained with the people who decide or choose, and was not passed on to

(or rather, covered by) a superior, transcendent entity. The obvious limitation of

the Chinese judicial system lay in the greater possibility of corruption. If the judge

was good, and intelligent, the sentence would be more equitable, but if he was bad,

or bribable, the result would be particularly unfair. In any case, anybody in power

would have various means available to decide trials.

In the Chinese culture, the event that it was people who did things and therefore

they bore the responsibility, was clearly shown by the use of the term jia [family]

to indicate even schools of thought. The important person in these was the teacher,

to be followed also in his moral behaviour, from whom the adepts were almost

considered to be blood-descendants.165

For all these reasons, the Confucian man of letters could not believe that laws

with universal claims were the best instrument to understand the multiple forms and

continual transformations of the world in which we live. They would become too

tight an attire, a rigid suit of armour that would hamper necessary movements.

The character fa was not often included in the titles of ancient books on

mathematics or astronomy. On the basis of a rapid statistical review of the rich

sample of books contained in the bibliography of volumes III and IV compiled by

Needham, we find about 20 titles. Most of them refer to books that gave suanfa, that

is to say, “rules for calculations”, including the one from which we took the pages

explaining the lülü.

In the Jiuzhang suanshu [The art of calculating in nine chapters], there are very

few examples of fa. In chapter one, problem 32, we find:

ran shifu cifa

[However, for generations, this rule has been taught,]

which was used to calculate the ratio, 3 to 1, between circumference and



fangcheng fa

[. . . fangcheng rule . . . ]


Lloyd & Sivin 2002, pp. 52–55.


3 In Chinese Characters

to solve systems of equations by arranging the numbers of the coefficients in a

square. Only those heretics of the Mohists used to speak frequently about fa.166

In the title of the book, fa was not used, but shu, that is to say, the “art”, “craftwork”

or “ability” of calculating by hand, using rods arranged in a certain orderly sequence

on a table. The term shu was continually used in the text.167

Fa were also provided for the calendar, as well as for measuring fields, for waterclocks and for buildings. In any case, fa did not have a meaning similar to ‘law’,

because it referred rather to a ‘model’, a ‘way’, a procedure to obtain something.

It would thus appear to be a less rigid and absolute term, seeing that different

models can be invented. For this reason, I prefer to translate it as ‘rules for’. Fa,

we shall see,168 was to become the favourite term of the Jesuits for their books

on mathematics and astronomy, which were presented as full of xinfa [new rules],

though for them, these had now become laws.

Due to the use that the Legalists made of it, the character fa had not to be

always popular in China. Chinese scholars preferred to use the character li, which

means ‘texture, weave, reason’. For example, it forms the word wuli ‘the reasons

for material things’ that is to say, for us Westerners, ‘physics’. Can this discipline

be interpreted as ‘the laws of matter’? Also in this case, the translation would be

forced, because the idea of man following a spontaneous order would remain also

in the li: li dongxi means “putting things in order”. Li is always accompanied by the

spatial image of the frame on which carpets are woven.169

In a culture that took living bodies as its model, where numbers were represented

by wooden rods in movement on the table, also the mathematician Liu Hui took

his inspiration for the li (far more often present than fa) from the butcher of the

Zhuangzi.170 Here, the li meant the spatial organisation of the body to be cut up.

Thus, in order to render it better outside classical Chinese, we should avoid “laws”,

“principles” or “structures”, and be content with “organs” and “organisations”.171

For the geometry of the Zhoubi as for the pipes of music, for the calendar of

astronomy as for the cycles of time and the seasons, Chinese scholars searched,

not for laws, but for models. For them to be convincing, they had to be manifested

in ways that were clearly visible and sensible. Preference was attributed to xiang

[image] models, linked with phenomena.172 They trusted appearances because

they thought that behind the mask, they would find exactly what they saw. They


Neuf Chapitres 2004, pp. 179–180, 635–636 and 918–919. But here fa has been translated by

the overly Cartesian term of méthode. Graham 1999, pp. 199–200.


Neuf Chapitres 2004, passim and 986–987. Now Karine Chemla’s translation of procédure

renders the idea appropriately.


Part II, Sect. 8.2. Cf. Jullien 2004, pp. 273–276, 383ff.


Gernet 1984, pp. 219–226. Graham 1990, pp. 420–435. Graham 1999, 391–394. Cf. Needham

& Harbsmeier VII 1998, pp. 238–240. Also Jullien 2004, pp. 192 and 261.


See above, Sect. 3.4.


Neuf Chapitres 2004, pp. 950–951.


Graham has quoted the “Great comment” of the Yijing; Graham 1999, pp. 497 and 499.

3.6 Rules, Relationships and Movements


even related it in an apologue.173 The world appears to us to change continually

because it is really continually transformed. It would be vain to search for another

representation of it. Where could it be hidden? What advantages would we obtain

from inventing universal, absolute fa and li? It is useless to study the sky as

independent from the earth, or the earth as governed by fa and li different from

those of man. Man remained at the centre of things, and related to them.

For all these reasons, in Chinese scientific culture, nobody in general would have

tried to detach fa and li from the literary language, maybe in an impossible search

for absolute symbologies. The literal meaning of a term remained pregnant with

other possible senses, through which the ambiguity maintained by the text would

succeed in expressing the richness of its links with the other aspects of a world in

continual evolution. And in the end, it would be the environment constructed by

people that would give the text a comprehensible meaning, precisely because it is

changeable like them in history. In the Country at the centre, there was to the letter

the cult of history: history was consigned to two classic works, the Shujing [Classic

for [historical] books] and the Chunqiu [Springs and autumns], a history which

necessarily (or rather, following the Dao) continually had to be rewritten.

Hence, we are forced to conclude that in general, we would not find any attempts

to render the facts independent of the values, to put it briefly, in accordance with

the current habits of certain Western philosophies. Here, in Chinese culture, the

values that guided the behaviour of scholars, as they investigated the figures of

geometry, the sounds of the pipes, that calculations of roots, the winds or the qi,

were not hidden, but were rather presented as an integral part of the explanations.

Even when commenting on poems, the Chinese man of letters avoided interpreting

them in a symbolic, transcendent sense; he preferred to find in them, among the

various figurative meanings hidden between the lines, the historical, political and

moral values congenial to him. And he was so reluctant to lose himself in abstract

symbols that he used the term qixiang [image of the qi, atmosphere] for the scene

portrayed in the poems.174

3.6.4 The Geometry of the Continuum in Language

The harmony of music has guided us from the beginning to recognize the background against which Chinese scholars have generally set their affairs, including

the naturalistic and mathematical ones. It was made up of the material continuum

of the qi, impalpable and at the same time fraught with consequences. The event

that we have dedicated our attention, and a whole section to it, should save us from

misunderstanding Chinese scientific culture, as reduced to numbers. We may thus

re-establish the balance with an equally important and interesting geometry, starting



Tonietti 2006a, p. 239.

Sivin 1986. Graham 1999, pp. 444, 480 and 485–486. Jullien 2004, pp. 193ff., 204, 216–217.

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