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6 Rules, Relationships and Movements
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
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
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
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:
[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,
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:
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,
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
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
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”.
[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 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.