Chinese vs. Western Thought

5 posts


* Ancient Chinese mathematics was completely sterile, and never really got anywhere. Even if they had disconnected mathematical "proofs", they never realized proof as a general principle (to handle the more intricate notions - more and more intricate logical relations and functions), and so instead the mathematics just remained as astronomy or surveying. The myth that they had a general "proof" of the Pythagorean theorem is completely exploded in Cullen (2007) - the claim originates in a faulty translation by Needham. Of course, the Greeks never quite realized the full power that proof might have, but they nevertheless applied this principle in geometry, whereas the Chinese avoided geometry.

* Chinese "philosophy" seems to be mostly some sort of elaborate but feeble baby-talk. They did not have any general conception of the syllogism, nor the formal analogy between inference and algebra (Boole), nor quantification (or even the implicit idea that a "general" concept - every time an algebraist writes down a symbol or diagram - consists of varying every possible particular case, of changing one part of the diagram while another part is unchanged). Their neo-Confucian "synthesis" (Zhou Dunyi, Shao Yong, the Chengs, Zhu Xi [Chu Hsi], even the polymathic Wang Fuzhi [Fu-chih]) was wholly "metaphorical" instead of logical: see this and this , this and especially this . Very early on, the Chinese had a brief period of military engineers (the Mohists ) who were engaged in dialectical analysis, but that still remained trivial since it was unfertilized by (sufficiently formal) mathematics - the entire point of mathematics was the perfect generality of its concepts, that one does not refer to any particular thing (e.g. particular triangle) but every possible object with a certain property. And of course the puzzle of how purely "deductive" inference can be non-trivial is a starting point for much of meaningful "philosophy" (Leibnitz, Kant, Peirce, Frege, Husserl, Wittgenstein, Ramsey etc. all started from the philosophy of mathematics).

Zhou Dunyi's chart of the "supreme ultimate"

The other branch of Chinese "philosophy" is really just Buddhism - an interesting recent attempt to synthesize Whitehead with the Hua-yen Buddhists can be found here . Both formal philosophy and Husserlian phenomenology seems to have caught on in China. Chen Qiwei wrote an interesting article on C. S. Peirce.

* The Chinese discovered the magnetic compass by pure trial-and-error. Nevertheless it was not the compass itself, but the combination of it and sufficiently accurate clocks (the most difficult feat of engineering before the industrial age) that enabled the accurate determination of longitude (that only European countries were able to do). This is common knowledge among specialists in the history of technology (though apparently not among "general historians").

* Chinese "martial arts" is of very dubious value, except maybe as eye candy in martial arts movies.

* Positive aspects are: the calligraphy , classical gardens , the very long novels, elaborate food , ceramics , jade , ink painting, furniture (they have these special wooden construction techniques) and cinema (movies like "Crouching Tiger" etc. are interesting) - of which they are completely unmatched in terms of the absolute quantity of high-quality work, requiring the finest technique. Calligraphy is their unique, "abstract" art form, just as classical (instrumental, tonal and atonal) music is for Western Europe.

CIA Documentary on China (more relevant today than ever):

Niccolo and Donkey

To sum up: the Chinese did not even understand what a "general" concept was (like the concept of a function), or what quantification was. They had no muscular thought whatsoever, of the type that requires the greatest effort to keep in track of many things at once, of combinatorial or geometric intuition - and one way to characterize the preceding is: that one does not play around with words or fancies or pure "analogies" but rather, with complicated physical arrangements (in the laboratory), and with diagrams that are always slightly more complicated than one can immediately keep in track of.

I distinctly remember, when I was an undergraduate in [deleted for reasons of privacy], how many of the top "Chinese" students who came directly from Chinese high schools almost all flunked out of the first "advanced" math course (in which one has to construct proofs), after getting A+s in "calculus" (itself very superficially taught) etc.

I think the reason why people like Leibnitz and Babbage valued "notation", was exactly because a succession of symbols forces us to remember that concepts, such as (to take a really elementary example that just anybody would know) the "integral" of something


are the composition of different concepts that having nothing necessary to do with each other, as distinct from simply some "holistic", mysterious entity in itself (like all of the Chinese concepts, like "qi"), perhaps accompanied by verbal commentary or the sound of words.

[ Edit: a clearer discussion is the following.] Of course, it goes deeper than that. The Leibnizian notation reflects that observation made by Lagrange and then quoted by Charles Babbage (in his essay on the visual power of notation , which I might upload here) -- that the power of analysis lies in the fact that the level of abstraction (hence the objects that one can distinguish) varies *continuously*. The notation makes it clear that an abstract object decomposes into component objects -- but also that it decomposes into "levels" of structure, organized by how large they are. But they also illustrate how you can shift *continuously* between different levels. One trivial example is the following quick observation: there is an obvious isomorphism between V* ⊗ W and Hom (V, W), here both V and W being finite-dimensional (making the question trivial), V* the dual space of V, which is simply the natural map that takes pure tensors of the form (λ(v) ⊗ w) to λ(v) w , the λ(v) being a constant in the field [we are assuming is algebraically complete, such as the complex numbers]. And this "map" is itself only slightly -- i.e., continuously -- more complicated than the idea direct evaluation, from the dual V* to the double dual V**, and this feature of it is reflected in the notation -- i.e., the notation for the function is just a slight bit more complicated.

Now in order to "prove" this, perhaps the first move would a false step of considering, e.g., any *single* object v inside V, the vector space. But in fact seeing that this is not going anywhere, you continuously shift yourself to larger components of the structure -- instead of fixing any single element in V, you consider any possible "basis" for the entire space V and W (and a basis is not "any" single element, but a set of such elements). If that somehow did not work, then you would think of other forms of decomposition of such a space -- again, the notation draws attention to the fact that you can *continuously* move upwards into slightly more complicated objects. For example, the tensor product itself of two vector spaces can decompose by means of a direct sum, and so on.) (By the way, the above train of thought should take no more than 3 or 4 second, given the ability to visualize rows of symbols inside the head on one side, and algebraic calculations on the second side.)

Another form of "continuous" shifting around which is facilitated by the notation is the following: that a proposition can be *continuously* weakened, which is primarily the point of abstraction (assertions about abstract objects are weaker). A quick example is: the construction of an isomorphism is a quite "strong" assertion, so you talk about some other object built on top of the entire map -- say the character of a representation from a group G to a vector space. Then if you don't go that high, you can still stick to other indirect structures -- such as the inner product in a vector space (and this even works in a Hilbert space, without any finite-dimensional basis).

So to sum up: one does not analyze merely "objects" which are abstract, but more specific levels (which have a visual "essence" or main point that summarize them), and on top of levels and their structure (and different modes of decomposition), one has properties. In fact it is usually properties that have more of a spatial or tactile content (hence that comment by V.I. Arnold, that the *properties* are more worth analyzing).

Anyway, back to the topic: They [the Chinese] did not have thinkers who were particularly powerful, either in mathematical thought (as above - simplifying more and more intricate notions), or else those like Faraday who may not have used mathematical analysis, but who (1) thought in a geometric and very very intricate language (lines of force), and (2) an incomparable "sense" of what parameters to keep in track of and what to ignore (physicists know what to ignore).

Real Chinese "mathematicians" only began to appear in the 20th century - the only three of any prominence are Chern, S.-T. Yau and Terence Tao, and they don't cut it. Terence Tao and Yau together are not quite on the same level as Connes (France), or Gromov (Russia). The former created noncommutative geometry while the second is the main creator of modern symplectic geometry, both of which is far from reaching its height even now.


There is the following very useful passage from Studies in Chinese Thought ed. by Arthur F. Wright, the article by Derk Bodde ("Harmony and Conflict in Chinese Philosophy"):


Of course, this echoes what has been well said (was it by Otto Neurath?) that atheism tends to breed among those who work the land, and whose livihood completely depends on their own labor, rather than the hunter-gatherers who depend a great deal on luck and chance.

"Chinese thought" undoubtedly took a fundamentally unique direction of its own and the fundamental sign of this is exactly how they lacked any concepts that passed beyond a certain degree of complexity in the sense explained in the previous posts. That is, they scorned any attempt to break anything down or to simplify anything by a first approximation rather than trying to comprehend various things "as a whole", or getting at it by indirect metaphors. The secret to formal mathematics lies exactly in how every complicated problem has to break into parts, but it is a matter of how to break it up that is the problem. It can be illustrated in the following "dialogue" between Descartes and Leibnitz (quoted in Polya):

The Chinese (after the Mohists[*]) also scorned geometry as well as (and this is interesting) the ability of language to express anything adequately. So they saw the use of metaphors, but they lacked (due to the deficiency in geometry and any complicated mathematical machinery) visual metaphors. But they actually developed a very elaborate system of their own to talk about various metaphysical forms of "Being", "non-Being" without directly speaking of categories - "form", "matter", etc. - they spoke rather in very elusive and elaborate metaphors to describe various processes of changing. This is probably the point of the visual "Yijing" - that it serves as some kind of metaphorical language for their ontology. This entire distinctive "Chinese" mode of thought (completely different from that of the Greeks or Indians) was probably solidified somewhere after the Han dynasty, definitely by the time of Wang Pi, the commentator of Lao-Tse and founder of "dark learning" (xuanxue). The two most reliable sources in English are Confucian Thought by Tu Weiming and Metaphorical Metaphysics by Chen Derong, and maybe also the study by Wagner.

Anyway, I'm not sure if there is anything to all this (I voiced my doubts in the first post), but the point is that the Chinese "thought" is the only kind of thing that is fundamentally different from the thought of the West, and not influenced or absorbed by it in any way. In the entire history of thought, the fundamental contrast is exactly between the Greeks (who founded Western thought) and the Chinese (after the Han Dynasty and the disappearance of the Mohists) who followed fundamentally different paths - not between the Greeks and the Indians.

And contrary to what might be concluded by extreme "racialist" theories of history (that seem to exist only on the "internets" - and so, hardly seem to merit any kind of proper response as opposed to diagnosis), the Chinese inability to do various things (and the particular path they actually took) had nothing whatsoever to do with lacking a few exceptional "savants" of super-intelligence, like Newton, Euler, Gauss, etc. This was exactly because those "savants" even in the West were not actually the most "influential" figures, they simply combine the achievements of maybe a fifty or a hundred top-quality individuals in a single person. Rather, the truly "influential" ones were others - those who fully worked out a certain path by the guide of extra-rational belief (like Kepler, Tycho Brahe). Kepler depended on Apollonius' mathematical machinery of conics, which was absolutely necessary for his formulation of the laws, just as Newton and others generalized Kepler's laws, from astronomy to all mechanics (so no Kepler[**], Brahe and Apollonius = no nothing). The uniquely successful, Greek development of "formal mathematics" (based on formal proofs) depended heavily on the fact that it was in geometry that the Ancient Greeks focused on (in which logical relations between constructions were more transparent), and that the Greeks were compelled to construct formal proofs for mystical reasons that were mostly extra-rational. It was not, therefore, due to superintelligence or over-awing technique, or even clarity of apprehension, but simply blind luck and favorable circumstances (political disunity). Without Newton on the other hand, mechanics would have developed somewhat more slowly, but only by a few decades as there were plenty of other scientists of almost-equal capacity in the same period.

[*] Edit: I have to say that the what survives of the Mohist "logic" (e.g., Hui Shih) strikes me as an unimpressive, intellectually weak, very very nominalistic "logic" reminiscent of the Stoics and Chrysippus or even Diodorus, the worst part of Ancient Greek thought on our side. But then, 90% of the written material of that period was supposed to have disappeared after the consolidation of the Han totalitarian rule.

[**] A slightly technical point not usually noticed about the discovery of Kepler's laws (and in consequence, all of mechanics and classical physics): virtually all problems of mechanics are described by nonintegrable equations. Only a few (like the classical two body problem) are actually integrable. Now, it was also again by "luck" that the human race developed in a planetary system (in contrast to so many others in the galaxy) that had only one star - and also, where the planets lie at large distances from one another with masses each much smaller than that of the Sun. Only under these circumstances can you actually work with the equations that are actually integrable, and also such that planetary motion (revealed by integration) is very simple. That is, it is the particular structure of the solar system that was crucial (that fact that the motion of our planets is relatively simple, and can be described by integrable differential equations). This was definitely a necessary condition for the human race to discover (relatively quickly) the laws governing the motions of the planets and then generalize them to all mechanical motion (Newton).