Showing posts with label geometry. Show all posts
Showing posts with label geometry. Show all posts

Tuesday, 26 April 2016

Square Seal Calligraphy - Chinese and Kufic


A Chinese calligraphy in the block square seal style

Several posts ago we noted the central place of the octagon in Chinese design. (See here.) It was mentioned there, but only in passing, that the same geometrical figure occurs throughout Islamic designs. This current post explores the matter of common elements in Chinese/Islamic design more thoroughly based, once again, upon observations made during travels through the Sino-Asiatic world. The consonances, similarities and parallels between these two very different traditions only become obvious when you see them first-hand. 


* * *  

We tend to experience the world nowadays through abstract media – web logs included - rather than through concrete realities. A key component in this is the so-called ‘research’ undertaken by teams of academics in universities. The world has never been so ‘researched’ and the ‘research’ has never been so tainted by the zeitgeist of the era. The truth is that the world is being ‘researched’ to death. The stream of ‘research’ papers and books is unending, along with theories and counter-theories, and then documentaries and videos and conferences and lecture tours. Very little of it amounts to very much of substance. Most of it concerns ‘deconstructing’ a supposedly evil past. The present author grew weary of all of that and has set out instead upon a journey through two continents and a dozen countries, travelling cheap, leaving theories and conferences behind and observing, as they say, the ‘facts on the ground’, the smells and tastes and textures of the world. The abstractions of the academic life are nebulous and neurotic; there comes a time when it is necessary to put some concrete foundations under the castles in the air.

Certain things become plain when you see them in reality rather than through the medium of books or academic studies. Among the neo-orientalist preoccupations of the author is the historical and on-going encounter between the Mohammadans and the Chinese. This is one of the key themes of the second leg of his sojourn in Asia and accounts for his current trajectory – albeit gradual - overland towards the old silk road. First, though, he has spent time in the Prince of Wales Island, or Pe Nang, where the Malay Muslims live side by side with a very old and illustrious colony of Han Chinese. The two cultures overlap and sometimes clash, but generally they yield to a constructive co-existence. You can read about these Islamic/Chinese encounters, but to witness them first-hand brings an entirely different sense to them. Academic studies pose as objective, but it is an objectivity in service to certain agenda. It is good to put that aside and to see the realities from the street-level.

In this context, the author was able to see numerous examples of two calligraphic traditions – one Islamic and the other Chinese – that, very obviously, and regardless of what academic obfuscators might say, are related. He had read of such before in erudite studies, but encountering it first hand rendered the parallels plain and palpable. Academics quibble over the historical connections, and there is always some deconstructionist professor out to deny the obvious, but there can be little question that the two traditions have, at some point, cross-fertilized. On the one hand we have the so-called ‘Kufic’ style of Arabic calligraphy, named after the city of Kufa, a city at the far end of the silk road. And on the other we have Chinese calligraphies which have developed from the very ancient tradition of block seals by which the Chinese have long signed documents and other official accounts. Related to this, we can also observe the tradition of Islamic geometrical patterning on the one hand, and the tradition of Chinese geometrical screen patterns and latticework on the other. The same or a similar genius seems to work in each of these traditions, regardless of how remote they might be in time and space. They are related, and point to the common ground where the Mohammadan tradition and the Chinese tradition meet.

Some examples:


Here is a typical Kufic Arabic design:


The cursive exuberance of the Arabic script has been tamed and confined into geometrical shapes used to fill the rectilinear space. The very same design strategy is used in certain Chinese calligraphies, such as these which the author photographed at the Western & Oriental Hotel in George Town:





Here the Chinese characters for wisdom and wealth are stylized into a rectilinear geometry. The similarities with the Kufic style known to the Mohammadans should be plain. Some other examples from an old temple gate in George Town:







It is not until seeing these two traditions side by side in situ that their common foundations can be fully appreciated. The Mohammadan and Chinese universes are assuredly very different - the Malays and the Chinese are assuredly very different peoples with starkly different sociologies - and yet there is a deep substrata of common foundations. The present author knows of no academic studies that penetrate that substrata in any meaningful way. 

The history that shaped this common foundation is uncertain, although it seems likely that the Chinese tradition was primary and the Arabic tradition derivative. The roots of Chinese block calligraphy are very ancient. The geometrical style developed from the need to adapt Chinese characters to block seals and stamps for official purposes:





It seems likely that this geometrical style of script then travelled the silk routes from the Far East into Mesopotamia where, for whatever reason, it found a home in the calligraphic schools of Kufa. That is, the Arabs learnt this style from the Chinese, just as they did such technologies as silk-making, with the silk road through Central Asia the connecting historical link. The extent of this debt to the Chinese, which is to say the extent to which Islam absorbed Chinese influences, is rarely appreciated. Academics in an age of deconstruction dwell on differences and downplay similarities. Yet the similarities are what are of interest here: not merely the fact of similar artistic conventions but, more importantly, similar mentalities and mind-sets. In both the Chinese and the Muslims we find a certain sense of the geometric, a Platonic sense of the geometric underpinnings of the dynamic cosmos. In both cases this is expressed via a sacred calligraphy in which world-as-text is implicit. 

Below are some photographs of Chinese geometric seals from a temple in George Town:









Anyone familiar with classical Mohammadan design will see the similarity between these Chinese seals and corresponding designs found throughout the Middle East. But it is not just a matter of historical appropriation and 'influence' - quantifiable 'influences' are a matter of academic 'research'; it is more a matter of a common intellectual core, remarkable because to every outward appearance the Chinese and Mohammadan temperaments and world-views seem so very different or even at odds. At a certain level, then - quite aside from historical encounters on the silk road - the Chinese and Mohammadan traditions meet. 

Regarding the broader question of the sense of the geometric and a shared mentality, consider also the tradition of Chinese lattice designs. Here again we are clearly in a similar intellectual domain to that which created the great heritage of Islamic geometric patterns. 








Yours,

Harper McAlpine Black


Wednesday, 30 March 2016

On Octagons


As reported in a previous post – here – the moment one ventures from the Indian world into the Chinese world one is confronted by a wash of the lucky colour red. Red, or more correctly vermillion, or cinnabar, is the colour of the Chinese and Chinese-influenced traditions. It is very conspicuous. It is everywhere. And along with it, also conspicuous, is the profusion of eight-sided figures, octagons, within the Sino-Asiatic order. They are nowhere to be seen in Hindoo temples, nor in Boodhist temples even though Boodhism features an eightfold path – this takes the form of the eight-spoked Dharma Wheel in typical Boodhist iconography. The octagon, however – the eight-sided plain figure with or without an eight-pointed star – is conspicuously Chinese. 

The author of these pages is currently resident in the old city of George Town on the Prince of Wales Island, the only city in Malaysia that boasts a Chinese majority. A feature of the old city is the beautiful temples and clan houses, some of them very extensive and sumptuous, some very old. They are among the best Taoist and Confucian temples outside of China proper. Chinese from both Formosa and the mainland travel to George Town to visit them. It is a major temple city and a major centre of traditional Chinese religion.

An immediately obvious feature of such temples, and the attending buildings, and the Chinese domestic terrace houses too, is the proliferation of octagonal forms – tile designs, floor patterns, sacred insignia, altar iconography, and so on. The Chinese “lucky colour” is vermillion. The “lucky number”, as the Chinese will tell you, is eight. Sets of eight, preferably arranged in octagonal forms, are considered auspicious. It is by far the most common geometrical motif in traditional Chinese decoration.

Below are a few examples of octagonal forms to be seen around George Town. Some of the roads feature large octagonal designs and octagonal tile designs are everywhere to be seen. The geometrical tiles themselves were originally imported from Sheffield by the British, but the Chinese were so taken by them – such is their love of the octagonal pattern - that they adopted them as a standard feature of their homes, temples and pathways. The present author has noted the tile patterns of George Town - one of the most striking and beautiful features of the old city - in a previous post here.


 

Octagons feature as a design on several streets in George Town old city. 






Design on the wall of the Chinese clan association building in George Town



Octagonal tile patterns found throughout George Town


What, though, is the significance of the octagon, both in principle and specifically to the Chinese? It is, of course, not exclusive to the Chinese tradition; it does feature in the symbolism of other traditional orders as well, but nowhere so extensively. In the occidental order we find it the symbolic form of baptism. Several famous baptistries, such as that in Florence, are octagonal, and – a residual continuation of the same symbolism - baptistimal fonts in Catholic and some Anglican and Lutheran churches. Amongst Christians, though, it is a form more typical of the Eastern churches where it occurs naturally with a sacred architecture featuring a dome atop of rectilinear understorey. 

This is the form appropriated from the Byzantine Christians by the Mahometans when they built the Dome of the Rock in Jerusalem – perhaps the most impressive octagonal building in the world. It was possibly from this inspiration that Emperor Frederick – who had seen the Dome of the Rock during the Crusades - built his mysterious octagonal folly, the Castel de Monte, in southern Italy. All the same, these architectural examples are exceptions. The octagon is not as conspicuous as a symbol in the occidental world as it is in the orient. It occurs naturally in Mahometan geometrical patterns, but there it is not imbued with the same symbolic value – marked as “auspiciousness” – that we find among the Chinese. 


The Castel del Monte

Basically, the symbolism of the octagon is this: it is an intermediate form between the circle (of heaven) and the square (of earth). Its primary meaning therefore is: regeneration. It signals: the square that returns to the circle. That is, it consists of two superimposed squares which are in the process of returning into a circular form. Thus the association with baptism: the rite of regeneration. In the Chinese (which is to say Taoist) context, though – and this is quite apart from its correspondences with the eight trigrams of the I Ching and other symbolic parallels such as the eight directions – the signification of regeneration is overtly alchemical. 


As with the colour red, the meaning behind the “luck” the Chinese associate with the symbol is to be understood via the strongly alchemical nature of the Chinese order. Alchemy concerns exactly this: regeneration. The regeneration of matter into spirit (if we are to describe it dualistically). The regeneration of base metals into gold. In the octagon, the square (matter, earth) is regenerating into the circle (spirit, heaven). It is for this reason that it finds such a prominent place in the Chinese tradition – it is the pre-eminent (stable) expression of the doctrine of alchemical regeneration, which is the core theme of Chinese spirituality. 




Yours,

Harper McAlpine Black




Friday, 25 March 2016

The Nuptial Number Revisited


The so-called 'Nuptial Number' is by far Plato's most intractable mathematical problem. It is so dense and so obscure that many commentators, both ancient and modern, have decided that it has no rational solution but is instead an item of satire, not to be taken seriously. Others - including the present author (an admitted obscurantist) - see it as one of the great keys of the Platonic canon, if only it is understood correctly. Like the impossibly obscure formulae of the alchemists, it is the key to the Mysteries. 

It is not the purpose of this post to offer any sort of detailed solution to the 'problem' posed by this most difficult of passages from Plato's Republic; rather its limited purpose is simply to present the passage in question in a clear, accurate translation usefully divided into its component parts. The Greek text is impossibly convoluted and many of the words used are both rare and esoteric. No translation can save the passage from what seems to be deliberate obfuscation on the part of the author. But much of it can be disentangled and made clearer by some explanatory additions and a careful break down of its parts. 

What the infamous 'number' might be and what its significance might be is another matter, but the drift of the passage in itself  - leaving aside the formula of the number - can be straightened out into a largely lucid account. That is what is attempted below. The rendering is based upon those of Benjamin Jowett and James Adam (with copious references to the lexicon of Liddel & Scott. We begin at Republic 545D:




THE PROBLEM: WHAT CAUSES STATES TO DECLINE?

“Come, then,” I said, “and let us try to discern the way a timocracy will develop from of an aristocracy. Or is it the simple and unvarying law that in every form of government disturbance begins among the ruling class itself, when sedition arises among it, but as long as it is at one with itself, disturbance will not occur?”

“Yes, that is so.”

“How, then, Glaucon,” I said, “will disturbance arise in our ideal city, and how will our auxiliaries and rulers fall out and be at odds with one another and with themselves?

INVOCATION TO THE MUSES

Shall we invoke the Muses as Homer does in order to tell us “‘how faction first fell upon them,’” and shall we, like a tragic poet, picture the Muses speaking in an elevated style, as if they are speaking seriously when in fact they are playing with us and teasing us like one child teases another?

“How?”

“In some such fashion as follows:

THE WORDS OF THE MUSES

[Having been invoked in the Homeric manner - albeit ambiguously - the Muse now speaks, and it is through this quasi-Homeric Muse that we are given the Nuptial Number. It is an open question as to how seriously we should take this entire construction, although let us note that Plato uses this "Muse" in other contexts in other dialogues. Many of the 'Platonic myths' are introduced in this way.]

ALL THINGS PASS

It is indeed difficult for a state ideally constituted as we have described to be shaken and disturbed; but since for everything that is born there is also a time of destruction, even a constitution such as ours will not last forever, but it shall surely be dissolved eventually.

This is the manner of its dissolution:

THINGS MOVE IN CYCLES

Not only for plants that grow from the earth but also for animals that live upon it there is a cycle of fertility and barrenness of soul and body as often as the revolutions of their orbs come full circle, in short cycles for the short-lived things and long cycles for long-lived things.

BEGETTING CHILDREN OUT OF SEASON

Concerning human beings, there are also laws of fecund birth and of infertility, and there will come a time when these laws will escape the men you have bred to be the rulers of your city. For all their wisdom, and combining calculation with observation, they will beget children out of season.

A PERIOD COMPREHENDED BY A NUMBER

Now for divine creatures there is a period comprehended by a number that is final and perfect, but for a mortal the number is the first in which multiplications of root by square - when they have attained three distances, with four limits, of that which makes like and unlike and waxes and wanes - have rendered all things commensurable with one another.

THE BASE PRODUCES TWO HARMONIES

The base of this, containing the ratio of four to three, yoked with five, produces two harmonies when increased three times.

1. One of them is equal an equal number of times, so many times a hundred.

2. The other is equal length one way but oblong

- one dimension of a hundred numbers determined by the rational diameters of five diminished by one in each case, or of the irrational by two; the other dimension of a hundred cubes of three.

LORD OF BETTER AND WORSE BIRTHS

The sum of these - this entire geometrical number, a number measuring the earth - is lord of better and worse births.

THE NEGLECTFUL GUARDIANS

When the guardians of your ideal state neglect this and marry brides to bridegrooms out of season children of ill-nature and ill-fortune will be born.

NEGLECT OF THE MUSES

The best of their predecessors will indeed make rulers but these offspring, being unworthy, when they have succeeded to their fathers' offices of power, will begin to neglect us muses, though they are our guardians, and will pay too little heed to music, and then to gymnastics, so that the children will deteriorate and grow up without us.

THE METALLIC RACES

And the rulers who come after them will have little of the guardian in them for testing Hesiod's races and your own - races of gold and silver and copper and iron. And iron will be mixed with silver, and copper will be mixed with gold, and this will engender unlikeness within them, and an unevenness which is disharmonious, which things always create war and enmity wherever they are found. This surely is the pedigree of sedition, wherever it arises. As Homer says, "Of this lineage, look you!" (Iliad 6:211)

CONCLUSION

[Here the Muses finish and we return to the conversation between the interlocutors of the dialogue, namely Socrates and Glaucon.]

"And quite right too," said Glaucon. "We affirm what the Muses say as correct."

"Indeed," I said, "because they are Muses."

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Yours,

Harper McAlpine Black

Saturday, 19 March 2016

The Tile Patterns of George Town


George Town, on the Prince of Wales Island - or Pe Nang as the Malays call it (which means Land of the Betel Nut) - is possibly the best preserved of any colonial city. A defined area, extending outwards from the Chinese jetties, is a listed heritage zone and consists of superb colonial administrative buildings and extensive rows of terrace houses or what the locals call 'link' houses. Some are very old and many are very well preserved. In amongst them, in addition to these architectural riches, are many splendid Chinese clan temples some of which go back many centuries. As elsewhere, the Chinese and numerous other trading communities prospered here under the comparatively benevelent, tolerant and civilly constructive rule of the British. 



A terrace or 'link' house in the back streets of George Town. 

A striking feature of George Town architecture is the tiled floors, walls and pathways found throughout. This current post is a photographic essay illustrating samples of these distinctive tiles. In many instances, the floors have been redone in the 1920s, and it is largely from that era that these designs come, although some are considerably older. As readers can see, the designs are typically geometrical with those based upon the octagon predominating. Other patterns, less common, are floral. Please click on any image to see a large version. 




























































Yours,

Harper McAlpine Black