Wednesday, May 20, 2009

Peace: Enjoy the Zen


One of the words that gets bandied about a lot these days, to my chagrin, is Zen. People talk about 'zen gardens' (no such thing), zen toaster ovens and toilet roll holders, and often it is remarked that some stripped down and bare, even austere environment is 'zen'. People talk about 'Zen architecture' - but what is it really? The answer may surprise you, for true Japanese 'Zen architecture', a specialized style of temple construction and termed Zen-shūyō (禅宗様), is anything but pared down and stark.

Zen style was brought into Japan via a number of routes, and is not limited to architectural characteristics one can observe at extant Zen Sect buildings, but is in fact quite diverse and more widely spread. As with other imported architectural tastes, soon enough the Japanese set to work selecting, assimilating, and adapting what they liked, discarding the rest, and thus a distinctive style ultimately emerged in Japan.

What does the character 'Zen' , '', actually mean? It stems from an earlier character which looks a bit similar: '' The radical on the left side of the character, '', stems from a pictograph of an altar with a square/rectangular surface. Thus it connotes altar, the gods, the supernatural, and also the sense of show, indicate, display, express, given that things are often displayed upon an altar. The piece on the right side of the character '', namely '', comes also from a pictograph:


This picture represents a flat rattan weapon used to trap and beat small game. Somehow this character came over time to have the meanings of simple and single (perhaps because the weapon was simple in form and was a single tool that did more than one function - this is however a supposition on my part). Thus, the character 'Zen', '' (the modern simplification of which is ''), means simple religion, more or less a reference to the directness and simplicity of meditation as a vehicle into higher spiritual levels. The Sanskrit word for this form of religious practice is dhyana, a word meaning concentration, meditation, and meditative stability. When this form of Buddhist practice spread from India to China, it was termed chánnà, '禅那' in Mandarin, which eventually became shortened to just 'chán'. The word chán, borrowed by the Japanese and transformed as a result of their different phonetic language base, becomes 'Zen'.

So, what characterizes Zen-Style architecture in Japan? First of all, the roofs are of the more sophisticated hidden rafter-decorative rafter system. This system was no doubt a Japanese development, since no such roof structural system was ever employed in China. Probably the first temples in the Zen-shūyō manner had the simpler single roof, but this didn't last long and no examples of single roof Zen style buildings remain today in Japan. Most characteristic of the Zen-shūyō roof is that is has a strong amount of curvature at the eave corners - with the way many in the west are using the word 'Zen' these days, one might have expected Zen style buildings to have subdued, mild roof lines, 'hints' of curvature, and so forth, but such is not the case. In the Zen style building roof, typically the roof surface is steeply inclined, and supporting bracket complexes become smaller in scale but more numerous. Further, many of the structural elements are exposed on the interior of the building, creating a real sense of dynamism. In short, this style is a richly ornamented one.

I titled this post 'Peace: Enjoy the Zen' because I wanted to talk about a particular Zen style pagoda called Anraku-ji (安楽寺). The character for 'temple' is , while 'Anraku', '安楽' is the combination of characters meaning tranquil '' and enjoy '', which taken together mean ease, comfort. Anraku-ji is located in Nagano Prefecture, near Ueda City. So, please get comfortable, and have a look-see at this fine example of a Zen-Style Pagoda.

First of all, this pagoda is absolutely unique because it is octagonal:


The temple grounds of Anraku-ji were consecrated in 1288. The pagoda itself is a somewhat rare entity in a Zen sect compound, and this one happens to be the only building remaining in this compound today. Though it looks 4-storied, this is deceptive - the lower most roof is simply a mokoshi, or wrap-around perimeter roof. The purpose of this roof relates to the interior space and it's high interior to the paneled ceiling - this makes for longer columns, and thus the mokoshi gives a massing down low and precludes a visual effect of instability. A partial cross-section view of the elevation makes it clear that this pagoda has but three floors:


Here's the drawn elevation view:


The height of this pagoda is 18.75m.

A look at the first floor reveals some classic Zen-shūyō design details:


A view of the column and bracket complex:


The details I refer to are:

- the fan-raftering (rare in Japanese style, or 'Wa-yō' Architecture)
- the use of an upper penetrating tie beam with the nose, or end of the beam highly molded
- the top of the pillar being rounded (termed chi-maki)
- the vertically-set wavy grill bars, 'u-ne-gumi' (畝組), also called yumi-ranma (弓欄間)
- small scale of the bracket complexes in relation to the diameter of the pillars


In 'Wa-yō' Architecture the bracket complexes pile up, and each set carried its own continuous tie beam, and the brackets themselves do not extend out much to the sides. In Zen-shūyō architecture, the bracket complexes pile up one atop another without using continuous tie beams, the bracket arms are extended sidewards to a greater extent. Also, unlike 'Wa-yō', the bracket complexes can be found not only on top of the columns, but are also placed in the bays between them. In some cases, these inter-columnar bracket complexes give the feeling of being very tightly packed - take a look at the third story space between roofs and you'll see what I mean:


The windows and doors in the upper floors are purely decorative.

Here's a look at the first floor, showing the front door:


The small fence in the foreground should not be confused with an actual railing on the veranda, which this pagoda does not have. The doors are of the sangarado type, meaning they are paneled doors of the 'Chinese' style, and feature pole hinges attached to protruding wall sockets top and bottom. The walls are wood paneled.

One of the most interesting aspects of this pagoda to this writer, however, relates to the design principle upon which it is founded. Readers who have been coming a while to this blog may recall a series of posts I did in February 2009, especially one called "Are We Golden? V", in which I introduced the vesica piscis as a design tool. This pagoda was designed upon a close relation to the 'fish bladder' as well:


I find this astonishing and can't help but wonder if this design principle was imported from China (via the Silk road?) or whether it is of independent invention on the part of the master carpenter, or?? Anyway, it goes to show that much can be accomplished with a deep knowledge and exploration of but a few basics.

Here's one last photo to show the beautiful and powerful sweep of the eave to each hip:


The roof is hiwada-buki, bark shingles.

Zen Style is indeed powerful, dynamic, and richly decorative, not at all what most connote with the word Zen in the modern west. I hope you enjoyed this look at an intriguing pagoda, the only 8-sided one that remains in Japan. There was apparently a 9-story octagonal pagoda built in the 11th century in Japan, but it burnt down soon after completion, in 1058. Too bad - that would have been something to see!

In contrast to the calm restraint and harmony of 'Wa-yō' Architecture, the Zen Style is exotic and exuberant. One might wonder why the Japanese, often conservative otherwise, would preserve such a style over time and not mold it into something more like their usual 'Wa-yō' taste? As Mary Neighbour Parent pointed out, the flamboyancy of the architecture itself surely was a counterbalancing influence to the Zen sects themselves and the austerity of the sect practices in general - an antipode if you like that created harmony between opposites. Unlike the low ceiling of the 'Wa-yō' spaces, these Zen structures had soaring vibrant space, with tall ceilings (the ceilings themselves flat and smooth in contrast to the variegation of the exposed raftering and bracketry). Finally, the morés of Zen suited the Warrior class in Japan, and thus support (patronage) for the architectural scheme was there at high levels of the society. I'll be showing other Zen-shūyō buildings in later posts, so I hope to give the reader more examples of this style to give a clear picture as to its depth and richness.



Tuesday, May 19, 2009

Pagoda Primer

One of the words relating to Japanese or Asian architecture in general that gets misused a lot is pagoda. A lot of people seem to term any roof with upturned corners at the hips a 'pagoda roof', when in fact this form of roof is hardly exclusive to pagodas at all.

The word in Japanese for pagoda is : '塔' This is a character worth taking a closer look at, so please enjoy the excursion...

'塔' comprises earth on the left, '土', a character we looked at in an earlier post, and the following element on the right: '荅'. That element, a kanji all by itself (albeit not commonly used) means the azuki bean plant, and breaks further down into '合' on the bottom and an abbreviated rendering of '艸' on the top. Let's take those pieces one at a time:

'合' is comprised of hole '口', with a cover on top. The core meaning of this element, a character in its own right, is "press/fit a cover upon and object so that it covers precisely", which has led by extension to modern meaning like fit, join, put together, meet. Here are a few kanji compounds taking that character:

合一 unification, union

合力 cooperation, resultant force, assistance

連合 league, federation, alliance

'艸' is comprised of a pictograph of a grass shoot (屮) doubled up, and means grass. The character '艸' is a very common radical element, always found on top of a character, and whenever you see it you can assume the character means something to do with small plants and grasses. Here are a few examples of what I mean:

葉 leaf

菜 vegetables

菊 Chrysanthemum

花 flower

Okay, so '艸' + '合' gives '荅', that is, press/fit together grass plants, which is a reference to the azuki bean plant. Let's take a look at a picture of an azuki bean plant to see how it compares to the etymological meaning of it's character:


Well, jury is out on that one for the time being I guess....

In the character for pagoda, '塔', the element for earth, '土' is added to the side of '荅', and becomes the principal radical suggestive of the character's meaning- this kanji '塔' has something to do with earth - in fact, the original meaning is something built with one layer of earth pressed upon the other. A 'tower of earth' in other words. That is a reference to the stupa. What is a stupa?

Stupa is a sanskrit word literally meaning 'heap', and is a mound-like structure which contains Buddhist relics, typically the remains of a Buddha or other saint. Originally it was a simple mound of mud or clay, but over time the stupa became more elaborated and developed in various ways, culminating in their modern classification into eight different types, each symbolic of a particular stage of Buddha's life. In terms of the elements that go to make up the classic Indian form of the stupa, there are five distinct parts:

1) a square base (representing earth)
2) a hemispherical dome (representing water)
3) a conical spire (represents fire)
4) a crescent moon or lotus parasol (represents air)
5) a circular disc (representing space, the void)

The stupa is an artifact that traveled along with the spread of Buddhism from India through to other parts of Asia. When Buddhism was introduced to Japan around the 6th century, the stupa came in too, however by this stage and through transmutation through cultures, the stupa came to have a different form. Actually, the stupa came to have two principal forms in Japan. One of these is the gorintō (五輪塔), "the five-ring-tower"; these are made of stone and look somewhat like this example (right side of photo):


Looking closely, one can observe the 5 elements present - here's a picture showing the breakdown a bit more clearly:

Moving from bottom to top, we have earth-water-fire-air-space.

The other form of stupa is called the sō-rin 相輪. It may, rarely, take the form of an independent structure, like this:

Or this:


But much more commonly, the sō-rin (相輪) is located on top of the pagoda itself, like this:


Sō-rin are made often from bronze, but also examples in iron exist. Unlike the classic 5 parts of the original stupa, the sō-rin is a more complex item, having 7 parts. Referring to the picture immediately above, and taken from the bottom, here are the seven parts:

1) Ro-ban (露盤), a box like structure covering the roof peak
2) Fuku-bachi (伏鉢), the small inverted bowl atop the ro-ban
3) Uke-bana (受花), an open upturned lotus flower, usually with eight petals
4) Ku-rin (九輪), nine metal rings attached to the tubular sheathing which covers the central pillar of the pagoda (there are examples with 7 or 8 rings, but 9 is standard)
5) Sui-en (水煙), combines characters for water (水) and fire (煙) and is often flame-shaped; this like the ku-rin, is attached to metal sheathing on the central pillar
6) Ryū-sha (竜車), lit. means 'dragon vehicle'
7) Hō-jū (宝珠), a sacred gem in the shape of a ball or tear drop, believed to have the power to cleanse corruption, fulfill wishes, and expel evil. Often these are decorated with flame designs.

A pagoda typically has an uneven number of floors, often three or five, though examples exist with nine and even thirteen floors. While the pagoda is essentially a highly decorated pole marking the grave of Buddha, it is not always the case that there are actual Buddhist relics buried below, as in an Indian stupa. In other words, they are more symbolic. The English word for a structure that contain sacred relics, is reliquary. Some pagodas are reliquary structures, and some are not. In fact, there is an entire class of pagodas in Japan that are associated to esoteric Shingon Buddhism and have no reliquary function whatsoever - these are called tahōtō (多宝塔). Tahōtō are a two story type of pagoda characterized by a square first story surrounded by a peripheral roof (mokoshi), and supplanted by a cylindrical form above which is covered by a pyramidal or hōgyō (方形) roof. There are many examples of tahōtō in Japan - here are a couple:


Now that we've looked over some of the basics about pagodas, in future postings I look forward to delving into some really neat examples that I have come across in my studies. I have been spending time over past months compiling a photo database of the more than 100 pagodas to be found today in Japan, and this has now amounted to over 1000 pictures, so I have lots of interesting stuff to share. I think pagodas are very intriguing structures, and a good place to study Japanese framing methods for supporting deep eave structures.

A final note: there used to be a theory that the central pillar in a pagoda served like a kind of spinal column or dampening rod and this is what helps pagodas withstand earthquakes so well. As it turns out, this theory is completely erroneous - I will explain why in a future posting.

Friday, May 15, 2009

Hopper

In the previous visit we took to the mysterious room we went around the side and up the stair to the top, where we took a look at one Japanese approach to the sine function of a right angled triangle.

Today we will head towards the other door to the mysterious room, the door that the carpenter might normally take. Again, we pass by a sign on the way:


Setting aside what the sign says for the moment, notice the interesting form this object takes: besides the lovely carving and lacquer work, it is in the form of a splayed box. It would appear that the box has a regular plan with 90˚ turns at the corners, and that the sides of the box slope an equal amount on all sides. Further, the sides connect to each other with butt joints, not miters.

Further along our walk, we come to a small stand, and again notice a small splayed box on top:


These sort of splayed boxes are called by various names - battered boxes, hoppers, funnels, and so forth. In Japanese this form often goes by the name of asa-gao-gata, 朝顔形, or 'morning glory shape' boxes. In case the reader hasn't seen a Morning Glory flower before, here's a look at one variety:

Interesting that the Morning Glory has pentagonal symmetry, like a lot of flowers. The asa-gao-gata box can be any number of sides you like, however the most common and simplest to deal with has four sides, each side sloped the same amount. That's the kind of box I will be discussing here.

If you think about it, the hopper form is the same as that of a hipped roof, only upside down. In fact, if you made a lid for a box in the form of an inverted hopper, you may as well say you are making a lid in the form of a hipped roof shell. Thus, the geometry that applies to the angles in which the boards of the hopper connect at their corners will also have applications for parts in a hip roof that are oriented in a similar manner. Most obviously, boards which are employed to plank over the rafters, would share the geometry of the hopper boards where they meet atop the hip rafter, but there are many other possibilities, both in Western and Eastern carpentry.

A hopper is the foundation stone of studying compound joinery, and these are forms with a wide variety of applications. Here's a hopper I made for use as a water stone soaking pond and sharpening station:


Time is running short today, so I'll have to put off considering the geometry of the hopper box in further detail and how we might determine the cut angles.

There are two conditions only: butt joints and miter joints. Further, in sum total there are only three angles we need to figure out for most constructions:

1. The face cut angle
2. The edge cut angle for butt joint
3. The edge cut angle for miter joint

If the hopper is to have through-tenoned connections at the joins, there is an additional 4th special angle. Typically of course, the hopper would be joined with the same form of joint at all four corners, if only to be nailed together, and thus we would only need to figure out two angles (1 and 2, or 1 and 3) to make the piece.

In case it isn't clear: if the boards did not slope, there would be no compound joinery problem to deal with -- the face cut angle would be 90˚ and the edge cut angle would be either 45˚ (miter) or 90˚ (butt joint).

All the angles can be figured with simple drawings which I show in the essay The Art of Japanese Carpentry Drawing, Volume II (available for purchase via the link at the top right of the page). It helps to be methodical I find when entering into a topic - compound joinery - that can get somewhat complicated after a while, and thus I have written a very complete description for how to lay out and build hoppers.

Tuesday, May 12, 2009

The Mysterious Room

I would now like to walk over to a mysterious room, located up in a cloud-lapped mountain temple, with a sign at the main gate reading "Japanese Triangle World". There are two doors to this mysterious room, one reached after a fairly long climb and is associated to abstract heights of trigonometry. The other door is no sweat to get to at all - quite a practical proposition actually. This is the door taken by the Japanese carpenter. If you go in by the carpenter's door, everything will seem fairly simple. If you go in via the trigonometry door, you will need special glasses, and these glasses can make everything look quite complicated. Normally, I wouldn't bother at all with the trig door for this room, but since we have spent lots of time on these steps already in past posts in our look at tangent, sine and cosine, it makes sense to walk a couple more steps and go in through that trig. door, even if it is the harder route. Once we've had a brief look around, and felt the dizzying height, I'll take you down and in the carpentry door, and there the air will be easier to breathe by far.

With that analogy then, I'll begin our walk. In our preliminary look at the Japanese approach to the unit circle, I introduced the names for the three parts of a right-angled triangle, and explored their root meanings in detail. The Japanese carpentry drawing system uses the relationships between the parts of the unit triangle to determine the cut angles needed in regular non-orthogonal (that is, connections that are at compound angles) joinery work. That method is called -ko-gen-hō (勾殳玄法). Here is the summary of the triangle so far:

As far as the basic trigonometric functions are concerned, the first we considered in the previous discussion on the Indian/Arabic depiction of the unit circle, was tangent, which is given by the relationship of opposite to adjacent, or 勾/殳. In the Japanese unit circle, if the angle we were dealing with lay at the center of the circle, the opposite would be the rise, '勾' and the run would be '殳'. Like the unit circle from before, we know the radius, or run, to be 1.0 unit long, thus the tangent would be given by 勾/1.0. There is no difference here, other than the use of the kanji to define the parts, from the western method, so I feel no special need to elaborate further upon the tangent.

One comment can be made though about how the Japanese describe slopes: it is based on the number of units rise 勾 in sun (寸) in ratio to the run 殳. One sun measures 3.03 cm., and 10 sun comprise 1 shaku (尺). A shaku is therefore equal to 30.3 cm., or 11.93" in the Imperial system. Curiously then, a shaku is very close in size to an English foot, except it is divided into 10 units instead of 12. The character for sun, 寸, was originally described by the following pictograph in ancient China:



This pictograph shows a hand with a tick mark or line, '-' , below, and originally referred to the pulse, which is a point indicated by the '-' mark. That is, the pulse point is found at a distance of approximately 3 cm from the base of the palm.

The word for 'slope' in Japanese is kōbai (勾配), a compound of two characters which literally means the apportionment/distribution (配) of rise (勾). Slopes are described upon the basis of how many sun comprise the rise, the run always taken as 10 sun, 1 shaku. Thus the following illustrates a 4 sun kōbai (勾配):


Calculating the tangent to obtain the angle measure in degrees is just as simple as before - this is simply a 4/10 slope after all. Tangent is opposite/adjacent, therefore:

4/10 = 0.4

Use your calculator to find TAN 0.4 = 21.8014˚

The handy thing about having a run of 10 is that it is but one decimal shifted over from 1.0, which is the basic unit upon which the calculator operates for trigonometric functions.

Okay, that was a bit of an aside. Let's take a look now at the sine, and we'll swing the trig. door to the mysterious room open a bit. Take a deep breath....

Recall the two ways that sine can be depicted in the previously-described unit circle:


The Japanese method is quite simple too:
In -ko-gen-hō, the first step, which happens to obtain the sine value, is to take the unit triangle and divide it into the next two largest triangles possible - by running a line (illustrated in red in the above drawing) from the hypotenuse into the 90˚ corner. Since this line comes perpendicularly off of the hypotenuse, '玄', the two smaller triangles thus formed within the unit triangle also have one 90˚ interior angle, and therefore these two triangles are similar to the unit triangle. By similar, I mean they have the same geometry in terms of the three angles which compose them, though the lengths of their sides are different than those in the unit triangle.

The red line dividing the unit triangle into two is given a special name: chū-, written in kanji as '中勾'. You can see that the second kanji, '' is the same as the one already described for the rise of the triangle. The first character, read 'chū' (long 'u' sound), is written as ''. This character, a very common one in Chinese and Japanese, derives from a originally from pictograph of a flag pole with fluttering banners:



The pole pierces the center or middle of the frame, 'o', therefore the character's meaning: center, middle. Thus, the chū-kō, '中勾', is the center/middle rise of the unit triangle. It should be obvious why they called it that, since the chū-is the primary dividing operation of the unit triangle and, in the case of an angle like 45˚, would divide the triangle exactly in half.

The term chū- is, in Japanese carpenter-speak, is a word to describe that particular division of the unit triangle, and it's length. In Western carpenter-speak, as you may recall, we had the terms rise, run, and length, but that was it. There are no western carpenter-speak expressions for the sine length, or any other trig function length, other than the specific terms of trigonometry, which I set apart earlier as trig-speak. People who are unfamiliar with the unit circle depiction will likely not be thinking of sine and cosine as being line lengths anyhow, but rather parts of formulae they have learned (SOH CAH TOA) to calculate angles.

The line length of chū-is also the sine. Just as we have different triangle terms in use depending upon whether we are using carpenter-speak, trig-speak, or Swahili, the Japanese, naturally, have their own trig-speak term for the sine: sei-gen (正弦, or 正玄). The second kanji, 弦/, we are already familiar with - it's the term for hypotenuse. The first character, '正' means 'correct, right, just, straight' - which leads to abstract applications such as uprightness, straightness. So, in a loose translation, the Japanese call the sine the 'upright hypotenuse', and since it stands 90˚to the unit triangle's hypotenuse, that makes good sense.

So to recap before we get utterly lost, what I have just shown is that the terms chū-and sei-gen describe the same thing, the first in carpenter-speak, and the second in trig-speak.

And that is about all the look I want to take at the moment from the Japanese trigonometric door to the mysterious room. I fear that some readers may be getting that moist sheen on their foreheads that comes from utter confusion (if so, my apologies), so let's leave off for the moment, and shuffle down to the carpentry entrance to the room where the living gets easier. Next post I'll go in the carpentry entrance to the mysterious room, and we'll see what sense can be made of this whole insane chū-thing. As you'll see, when we come down from the clouds of abstraction, you'll find that the chū- is a pretty simple and very useful thing. Stay tuned.