Stroke order of Chinese characters

Here on Language Log, we have often encountered the problem of stroke order and total number of strokes used in writing Sinographs (see the section on "Readings" below).  In this post, I would like to approach this problem from a discussion of how to write two seemingly simple characters:

tū 凸 ("convex; protude; bulge out")

āo 凹 ("concave; hollow; sunken")

Although I don't like to use the expression "ideograph" or "ideogram" for Chinese characters in general, since only a tiny proportion of them are actually ideographic in nature, these two really are ideographs.  I find these two characters cute, and actually have long harbored a secret affection for 凸 and 凹.  They are amusing and attractive — until you try to write them according to the rules of Chinese brush strokes and stroke order.  Then all hell breaks loose.

Current protocol seems to dictate that both 凸 and 凹 have five strokes, but when you set about writing them according to the rules for calligraphic strokes, they defy all your best efforts to reduce them to five strokes.

The radical ("semantic classifier") of both 凸 and 凹 is said to be Kangxi 17, 凵, which is pronounced qiǎn or kǎn and, in its oldest form, depicts "the appearance of an open aperture", hence "receptacle".  There's little doubt that Kangxi radical 17 has two strokes.  That means we somehow have to produce the rest of these two characters with three standard strokes.  People have been arguing for centuries about how to do that:

Tse Chun Yip 謝雋曄, "Qiǎn tán 'āo', 'tú' èr zì bǐshùn jiàoxué wèntí 淺談'凹','凸'二字筆順教學問題" ("A Brief discussion of questions on how to teach the stroke order of  '凹' and '凸'"), Yǔwén jiànshè tōngxùn 語文建設通訊 (Chinese Language Review [Hong Kong]), 116 (June, 2018), 37-40.

Your can watch 凸 being written here and 凹 being written here, sure enough with five strokes each, but breaking the rules as they go (the radical is not written as a unit, one stroke is made to undergo two or even three sharp turns, etc.).  Meanwhile, the stroke order in Japanese is radically different; see here and here.

Although these deceptively simple appearing characters pose rather extreme challenges to consensus according to the rules for brush stroke order and number, many other common characters present stroke order and / or number difficulties of their own (e.g., xué 學 ["study; learn"]).

This all makes a difference for looking up or inputting characters by their shape.  This morning in class, one of my M.A. students was trying to write "chá 茶" ("tea") on her phone with her finger as a stylus, but she just couldn't get it to come up.  I've seen this happen time and time again when people were looking for characters by diverse means.

1. Bathrobe said,

September 4, 2018 @ 7:16 pm

The Japanese order seems more within the rules, except maybe for the starting sequence.

2. AG said,

September 4, 2018 @ 8:34 pm

I used to pass this store in Yokohama's Chinatown and had no idea the first two things on the sign were Kanji – I thought they were some kind of cute Ghibli-style animal head or stylized mascot emoji.

http://www.tanzawa-net.co.jp/shop/06.html

(side note: there also seems to be a bar in Yokohama with a similar name wherein the "convex" and "concave" are what I must assume constitute an allusion to gendered body parts, so my innocent search for that store just brought me close to some NSFW content at work!)

3. Victor Mair said,

September 4, 2018 @ 9:04 pm

I was intrigued by the Romaji under the name of the shop: DEKOBOKODOU. The dekoboko goes with our two cute characters, 凸凹, and has the meaning "unevenness; roughness; ruggedness​". That sounds like a Japanese expression to me, for which the Chinese characters were borrowed to write it. Japanese specialists will be able to explain more precisely what the relationship between dekoboko and 凸凹 is, but there must be a more Sinitic sounding way of reading 凸凹.

4. Michael Watts said,

September 4, 2018 @ 9:04 pm

Is a stroke with two right angles supposed to be illegal? I thought that was normal based on 龍. How many "sharp turns" does the more complex stroke in 九 have? 几?

5. Victor Mair said,

September 4, 2018 @ 9:43 pm

Those hooks at the end of 九 and 几 do not count as sharp turns of a continuing stroke.

6. Victor Mair said,

September 4, 2018 @ 11:33 pm

From Nathan Hopson:

First, I agree that these are great ideographs.

More animated GIFs of Japanese stroke order, FWIW:

凸　https://kakijun.jp/gif/0519200.gif
凹　https://kakijun.jp/gif/0517200.gif

The Sinitic reading (at least I assume that's what it is) for these characters is for 凹凸, not 凸凹. The former is おうとつ, the latter でこぼこ. They're synonymous, but as you'd expect the Sinitic is formal and the Yamato (?) is more casual.

Also FWIW, Japan teaches numerals and the alphabet with stroke order, too. And yes, you can lose points for writing an "a" with the wrong order, I hear (from my kids).

Finally, Wikipedia's 筆順 (JP) article helpfully shows and explains some differences b/t Japan and its neighbors. I found this rather enlightening.

7. Mark S. said,

September 4, 2018 @ 11:56 pm

Taiwan's Ministry of Education gives the same strokes and order for both tū (凸) and āo (凹), although Taiwan and China often differ in stroke counts.

8. unekdoud said,

September 5, 2018 @ 12:02 am

If we're using Wiktionary as a reference…

乃 (related to Zhuyin ㄋ and hiragana の) has a zigzag shape + hook without right angles, and it has two different stroke orders depending on language. 及 is "4 strokes in traditional Chinese and Korean", the zigzag being two strokes in order to form the 又 radical, while it's "3 strokes in mainland China and Japanese" with a proper zigzag-shaped stroke. The stroke orders of these two characters also differ in terms of which side goes first.

In Japanese only, 凸 as でこ is also "forehead", and 凹 comes with many other readings in its compounds. Even though 凸凹 appears in the JLPT N2 wordlist as でこぼこ, some dictionaries mention an On reading: とつおう. The related 凹凸 only has the reading おうとつ. (Both 凸凹 and 凹凸 occur in Chinese with the usual pronunciations.)

September 5, 2018 @ 12:37 am

In response to Nathan Hopson's comment added by VHM: I don't think that some notion of "stroke order" in teaching roman-alphabet letters is as outlandish as your comment about your kids suggests. I remember at least some examples from when I was taught to write in various North American schools in the 1950s. For example, in writing "cursive", we were taught to dot lower-case I and cross lower-case T and X after completing the rest of the word. I'm also pretty sure I remember being taught to write 5 in much the same order as a similar character would be written in Chinese, i.e. starting at the upper left corner and moving down and around, then coming back for the horizontal stroke on top.

10. David Marjanović said,

September 5, 2018 @ 6:23 am

For example, in writing "cursive", we were taught to dot lower-case I and cross lower-case T and X after completing the rest of the word. I'm also pretty sure I remember being taught to write 5 in much the same order as a similar character would be written in Chinese, i.e. starting at the upper left corner and moving down and around, then coming back for the horizontal stroke on top.

I was taught some such things, too, but they were never enforced. For instance, I immediately decided that writing 5 in two strokes was stupid (I don't like having to lift my hand in handwriting), have written it in one stroke ever since (starting at the top right), and nobody has ever said anything, assuming anybody ever noticed.

But then, in the US, cursive is considered calligraphy, and for normal purposes most people draw printed letters instead. Over here, cursive is just handwriting, so less value is placed on following the norm precisely.

11. David Marjanović said,

September 5, 2018 @ 6:24 am

I should add that I'm right-handed, so the horizontal stroke of 5 goes backward for me. I just prefer that over lifting my hand.

12. David Littleboy said,

September 5, 2018 @ 6:42 am

Japanese also pronounces 凸凹 as totsu-ou.

The dictionary at hand (WWWJDIC) has
凸凹コンビ = Dekoboku konbi = Odd couple.
and,
凸凹紙 = Totsuoushi = Embossed paper.

Both of 凸凹 are standard-use characters (amongst the 2000 or so characters one is supposed to limit oneself to) and quite common, both alone and together.

13. Ursa Major said,

September 5, 2018 @ 7:20 am

@David Marjanović

If I write 5 in your way it comes out exactly like S – I start in the top left, go horizontally to the right, then back over the line I just drew, then down and around. 4 is the only numeral I normally write with two strokes (my short vertical stroke doesn't connect at the top), although I sometimes dot the middle of my 0 if there is potential for it to be confused with O/o. I also use the retracing technique in letters like d (anti-clockwise loop, vertically up, vertically down, hook at bottom right) and p (vertically down, vertically up, clockwise loop). I have 6 letters with two strokes (f, t, i, j, x, and I cross my z horizontally so it doesn't look like 2).

14. Andreas Johansson said,

September 5, 2018 @ 7:24 am

I was taught, in Sweden in the 1990s, exactly the same things Bob Ladd mentions re I's, Ts, X', and 5's.

There was, however, no points that could be deducted for doing it the "wrong" way, and in later years of education nobody much cared how you wrote as long as it was legible.

In the event, I do most of those particular things "right", when I actually do write cursive these days, but I do some other things "wrong"*, and as I discovered when we moved, what was "right" and "wrong" could vary from school to school.

* I've developed an idiosyncratic way of writing lowercase t in cursive: I do the horizontal crossline when writing the rest of the word, and then go back and add the vertical line along with dotting i's and the like.

15. Nick Kaldis said,

September 5, 2018 @ 8:43 am

亞 is a favorite of mine, and in my eye belongs with 凸 and 凹. The identical 4th and 5th solo/single brush-movement strokes are each comprised of 3 alternate vertical-horizontal-vertical, two-angled forms that make up the bottom left and top right halves of the character, as I recall, but I couldn't get the Baidu site to show the 亞 stroke order.

As for the Baidu stroke order of 凸 -could it be wrong? It shows the 4th stroke as a solo/single brush-movement comprised of 4 alternate horizontal-vertical-horizontal-vertical, three-angled form th. I thought the top horizontal stroke came first, then the lower left half, then the top right half, and finally the bottom horizontal stroke?

September 5, 2018 @ 12:06 pm

Very often, whatever is designated as a character's Kangxi heading (so-called "radical") is not a component at all. A good example is simplified 爱, whose heading is 爪, whereas it's glaringly obvious from the character's evolution that 爪 is not a component at all. The entire top part, what together looks like 爪 + 冖, is really a corruption of 旡, which was historically the sound component.

In other, equally frequent cases, a genuine component's stroke sequence is interrupted by the strokes of a different component. Anything that has 囗 around it, e.g., 國, is like that.

With all of this I just mean to say that a character's stroke order is a completely different matter from the meaningful graphical components making up the character. In that sense, the fact that 凸 and 凹 are filed under the 凵 Kangxi heading, basically for want of a better option, doesn't say anything about their "proper" stroke order.

17. ~flow said,

September 5, 2018 @ 5:04 pm

18. Victor Mair said,

September 5, 2018 @ 11:12 pm

"proper" indeed!

19. ~flow said,

September 6, 2018 @ 2:51 am

While characters like 凸 and 凹 (and 非 and lots of others) are rather difficult to write 'correctly', that is, in the strokeorder that a given standard stipulates as 'the correct one', it is perhaps worthwhile, especially for the foreign learner, to keep in mind that native users of the script often find it difficult, too, and do differ in their opinions and practice; it is quite instructive to go and look up how famous calligraphers have written a common character like 馬 over the centuries (i.e. in quite a few different ways where the modern school system would have you believe there's one true way).

As for a practical answer on how to get to grips with characters like 凸, 凹 and 非, I think it's important to remember that in symmetric shapes, you normally want to start at the top, then finish the left half, then the right half, then the bottom. In 非, this means you start with left vertical stroke, then attach the three horizontal ones to it, then go back to the top and draw the right vertical, and finally the three horizontals attached to it.—The alternative would be to first draw the two verticals (to get the backbone right, as it were) and then write all the six horizontals. I used to write 非 like this for years, but looking at the samples at http://shufa.guoxuedashi.com/975E/, I'm maybe the only human to have done so. Happens.

Now, as for 凸, you want to start again at the top. The question is whether or not to complete the 冂 part first before going down the left hand side. The answer is typical for the kind of reasoning you often have to apply for finding good strokeorders: When you peruse the renderings at http://shufa.guoxuedashi.com/51F8/, you can see that where the overall style of the writing allows it, the writers did choose to draw the entire right hand of 凸 in a single stroke ㇎ (which may be surprising). Therefore, if you wanted to finish 冂 before going down on the left side, you cannot do so before finishing the right side, because after 丨 comes all of ㇎ . So you have to write 丨一丨 first (in model script 楷書 at least you can not write a horizontal right-to-left, so there's no mirror image to ㇎). In all, this leaves you with 丨一丨 for the left, ㇎ for the top and right, and finally 一 for the bottom part of 凸.

I realize that not only one can argue differently (using other rules or changing their relative order) and come up with different answers how to write a given character, and that e.g. in Japan, even the strokeorder of a simple and basic character like 田 is presented differently. I also realize its not everybody's cup of tea to agonize over and deeply contemplate CJK strokeorders.

OTOH given that many many millions of people have to / ought to / are being forced to learn how to write characters in a decent manner, it's perhaps a good idea to see whether we can make sense of all those nitty gritty rules. The only book that I'm aware of to talk about strokeorders in depth is by one Yu Pei-Lin (俞佩琳《中文字序學》, 啓業書局, Taipei 1990). In most cases, only the most basic rules—start at the top, proceed from left to right, outside to inside, bottom last—are mentioned, even by strokeorder dictionaries (yes, there are strokeorder dictionaries).

I'd love to get any pointers on CJK strokeorder literature. Reading 《中文字序學》
convinced me that there is some reasoning behind strokeorders, that there may be
sets of rules; at any rate, having delved into this topic, I'm convinced that we
can at least do better than just hand out prescriptive strokeorder diagrams for
the most important 2000 characters, which is what is seemingly happening in
education.

20. Luke said,

September 8, 2018 @ 8:09 am

These characters (凸 and 凹), which I successfully input with only 4 strokes each on my iPhone, amused me when I first started learning Mandarin. My teacher said they were sometimes used with erotic overtones by young people today.

The strokes in question,㇅ 横折折 (HZZ) and ㇎ 横折折折 (HZZZ), don’t seem to be problematic in China today. I asked several friends and colleagues, and all say they were taught them in school. They are 派生笔画 (“derived” strokes), 复合笔画 (compound strokes) or 即折笔 (“multi-Z” strokes; my translation). The 百度百科 page says traditional texts cite 8 basic strokes but the language reforms in 1965 and 1983 included only 5 basic strokes. And yet other strokes and characters have always existed. 25 compound strokes were made official in 2001, including HZZ and HZZZ, but these were already widely accepted even in Chinese academic circles—they wouldn’t have made it into the standard if they weren’t.

https://baike.baidu.com/item/笔画

21. Philip Taylor said,

September 16, 2018 @ 7:57 am

I clearly remember that when I studied technical drawing after leaving school, we were taught the correct stroke order for the digits zero to nine, and to this day I still form my eights as two distinct circles, one sitting on the other (and I remove my pen from the paper before drawing the second circle); I am less sure whether we were taught the correct stroke order for the letters "a" to "z". What I do know, however, is that in prestigious drawing offices such as that of Rolls-Royce (of luxury car and Merlin jet engine fame), stroke order for all letters and digits is prescribed and mandated (I have a friend who started his career in the RR drawing office). As regards 凸 & 凹, although I thought that I knew the correct stroke order (and for each character would have drawn exactly five strokes), on looking at the animations I see that I was completely and utterly mistaken in my beliefs.