This is one of those blog posts where I take two seemingly very different topics and connect them to China or Chinese. This time it’s about Pascal’s Triangle, one of my favorite mathematical concepts. In case you’re unfamiliar with Pascal’s Triangle, here are some images from Wikimedia Commons that nicely illustrate the principle:
Here’s the China connection (via Wikipedia):
> The set of numbers that form Pascal’s triangle were known before Pascal. However, Pascal developed many uses of it and was the first one to organize all the information together in his treatise, Traité du triangle arithmétique (1653). The numbers originally arose from Hindu studies of combinatorics and binomial numbers and the Greeks’ study of figurate numbers.
> In 13th century, Yang Hui [杨辉] (1238–1298) presented the arithmetic triangle that is the same as Pascal’s triangle. Pascal’s triangle is called Yang Hui’s triangle in China. The “Yang Hui’s triangle” was known in China in the early 11th century by the Chinese mathematician Jia Xian [贾宪] (1010–1070).
Yang Hui’s diagram contains some interesting-looking numbers. Check it out:
Compare that to Pascal’s triangle above. What’s up with these Chinese numbers? You can follow the upper-right to lower-left diagonal (one row in) to follow the numbers 1-8. You get this:
5. [no Unicode symbol for this one; it’s just 亖 + 一 (vertical)]
8. [no Unicode symbol for this one; it’s just ᅵ + 三 (horizontal)]
You can gather that 10 is 으 [a symbol I borrowed from Korean Hangul for the purposes of this post], which also looks like “10” turned sideways. 20, though, is 〇二 [except with the 〇 sitting on top of the 二], and so on.
I’ve written before on Chinese number character variants, but these are different from those. The numbers look similar to Suzhou numerals and Shang oracle numerals, but are still a bit different from both. I’m curious if anyone out there know more about these numbers? The diagram supposedly dates to 1303 (more info on Wikimedia Commons).
There’s another personal connection between me and Pascal’s Triangle. As part of my research for AllSet Learning, I make use of basic set theory and higher-level Venn diagrams. Considering that in a Venn diagram, by definition, all possible logical relations between sets must be represented, it can get quite tricky to draw these things when you delve into Venn diagrams with higher numbers of sets (more than 3). But how do you know how many overlapping regions there are in the Venn diagrams as the numbers of sets increase? Pascal’s triangle.
(BTW, some of the research we’re doing now at AllSet Learning could make use of interns with a foundation in statistics, mathematics, or computer science. If that’s you, get in touch! More on AllSet Learning’s interns here.)
It’s hard to believe I’ve been working on this project for a whole year, and also thinking about it, in some form or another, ever since founding AllSet Learning. Today, I’m quite happy to finally release the AllSet Learning Grammar Wiki.
What is it? Well, in a nutshell, it’s a mini-Wikipedia devoted entirely to Chinese grammar. Think comprehensive, think interlinked, think referenced. I’ve felt for a while that Chinese grammar has needed its own champion online, and since forming AllSet Learning, I’ve finally got both the need and the means to make it happen and keep it going.
I won’t say too much here; there’s a blog post on the AllSet Learning blog introducing the features and concepts behind the Grammar Wiki. Obviously, you can also just go straight to the wiki and check it out.
There’s not yet any public forum on the AllSet Learning websites, so if you’ve got feedback, feel free to leave it in the comments here. Please do read the AllSet Learning blog post first, though, as it may answer some of your questions. I’d also like to reiterate that the Grammar Wiki is not finished, and I’m not sure it ever will be, but with 500 articles and a good juicy set of grammar points it’s now at a point where it’s clearly useful to learners, so it’s time for it to emerge from its cave and be exposed to the rest of the world.
Finally, I’d like to thank the AllSet Learning interns who, over the past year, have helped make the Chinese Grammar Wiki a reality: Lucas, Greg, Hugh, and Jonathan. You guys were an immense help. Thank you also to all bloggers and friends who help spread the word by linking to the Chinese Grammar Wiki. Please help spread the word!
That’s all for now… Happy Chinese New Year!
Most Americans are familiar with the “base system” baseball metaphor for physical intimacy. If you’re not familiar with it, you might check out this XKCD comic for the complicated version, or this excerpt from baseball metaphors for sex from Wikipedia:
> 1. First base is commonly understood to be any form of mouth to mouth kissing, especially open lip (“French”) kissing.
> 2. Second base refers to tactile stimulation of the genitals over clothes, or of the female breasts.
> 3. Third base refers to groping naked genitals (handjob or fingering), or oral sex.
> 4. Home run (or rounding the bases, scoring a run, hitting a home run, scoring, going all the way, coming home, etc.) is the act of penetrative intercourse.
For the visual-oriented among us, here’s a graphic (adapted from XKCD’s complex version):
I can understand that a country little love for baseball might be confused by this metaphor system. Apparently even Europeans are confused by it. However, some people in China have picked it up, but in the process changed the system:
> 1. “一垒”代表拉手，
> 2. “二垒”代表拥抱，
> 3. “三垒”代表亲亲，
> 4. “本垒”代表XX
> 1. “First base” represents holding hands,
> 2. “Second base” represents hugging,
> 3. “Third base” represents kissing,
> 4. “Home” represents _____
Clearly, this is a whole ‘nother ballgame the Chinese are playing, and their playing field looks like this when superimposed onto the American field:
So much for “rounding the bases!”
The idea of the “linguistic power struggle” is one I’ve been dealing with and thinking about for a long time. I’ve made some attempts to find scholarly research on the subject, looking into discourse analysis (which is often concerned with power), expectancy violations theory, and communication accommodation theory, but so far I’ve turned up very little (even outside of Wikipedia!). Thus the discussion which follows will be mostly descriptive and anecdotal, but will raise more questions than it answers.
First, a typical example of the language power struggle. The dialog below is taken from a ChinesePod lesson aptly titled Language Power Struggle. I directed the creation of this fictional dialog two years ago, drawing on my own real experiences and those of other friends in China. The content in square brackets [like this] is a translation of the original Chinese. Note that the Chinese person speaks mostly English, while the American speaks only Chinese.
> American: [Hello, can I sit here?]
> Chinese: Sure, nice to meet you.
> American: [I’m also really glad to meet you.]
> Chinese: Your Chinese is very good.
> American: [Not at all!]
> Chinese: How long have you been to China?
> American: [I’ve been in China for more than two years. I’m studying Chinese.]
> Chinese: Oh, you are learning Chinese?
> American: [I want to work in China, so I need to learn Chinese.]
> Chinese: Oh. I think Chinese is very difficult for you. How do you feel this bar?
> American: [It’s not bad. It’s just that nobody will speak Chinese with me, so I’m a little disappointed.]
> Chinese: Ha ha! You are very serious!
> American: [Because I want to practice more, so that I can learn Chinese more quickly.]
> Chinese: I want to practice English. In Chinese, we say “[learn from each other]”, you know?
> American: [I know. But in China we should be speaking Chinese.]
> Chinese: I like talking English with you.
> American: [Heh heh, then you should go to America. I came to China just to learn Chinese.]
> Chinese: I want to go to America. Let’s be friends. Can you give me your mobile number?
> American: [Sorry, I’ve got to go.]
The root of the conflict is quite clear: the American guy wants to speak Chinese, while the Chinese guy wants to speak English. There are quite a few issues contained within this small dialog, though. Below I’ll get into more details.
While reading up on one of my favorite topics, the technological singularity, I recently came across this interesting passage in an article by renowned futurist Ray Kurzweil entitled The Law of Accelerating Returns:
> To appreciate the nature and significance of the coming “singularity,” it is important to ponder the nature of exponential growth. Toward this end, I am fond of telling the tale of the inventor of chess and his patron, the emperor of China. In response to the emperor’s offer of a reward for his new beloved game, the inventor asked for a single grain of rice on the first square, two on the second square, four on the third, and so on. The Emperor quickly granted this seemingly benign and humble request. One version of the story has the emperor going bankrupt as the 63 doublings ultimately totaled 18 million trillion grains of rice. At ten grains of rice per square inch, this requires rice fields covering twice the surface area of the Earth, oceans included. Another version of the story has the inventor losing his head.
> It should be pointed out that as the emperor and the inventor went through the first half of the chess board, things were fairly uneventful. The inventor was given spoonfuls of rice, then bowls of rice, then barrels. By the end of the first half of the chess board, the inventor had accumulated one large field’s worth (4 billion grains), and the emperor did start to take notice. It was as they progressed through the second half of the chessboard that the situation quickly deteriorated. Incidentally, with regard to the doublings of computation, that’s about where we stand now–there have been slightly more than 32 doublings of performance since the first programmable computers were invented during World War II.
> This is the nature of exponential growth. Although technology grows in the exponential domain, we humans live in a linear world. So technological trends are not noticed as small levels of technological power are doubled. Then seemingly out of nowhere, a technology explodes into view. For example, when the Internet went from 20,000 to 80,000 nodes over a two year period during the 1980s, this progress remained hidden from the general public. A decade later, when it went from 20 million to 80 million nodes in the same amount of time, the impact was rather conspicuous.
I’d never heard the claim that the Chinese invented chess; I’ve always heard that the game was invented by the Indians or Persians and then later iterated by the Chinese. Kurzweil’s story also seems a bit suspect to me because of its reference to “squares,” which does not match the forms of Chinese chess I’m familiar with, but then again I’m no expert on any kind of chess. Wikipedia has this information on the history of chess in China:
> Joseph Needham posits that “image-chess,” a recreational game associated with divination, was developed in China and transmitted to India, where it evolved into the form of modern military chess. Needham notes that dice were transmitted to China from India, and were used in the game of “image-chess.”
> Another alternative theory contends that chess arose from Xiangqi or a predecessor thereof, existing in China since the 2nd century BC. David H. Li, a retired accountant, professor of accounting and translator of ancient Chinese texts, hypothesizes that general Han Xin drew on the earlier game of Liubo to develop an early form of Chinese chess in the winter of 204–203 BC. The German chess historian Peter Banaschak, however, points out that Li’s main hypothesis “is based on virtually nothing”. He notes that the “Xuanguai lu,” authored by the Tang Dynasty minister Niu Sengru (779–847), remains the first real source on the Chinese chess variant xiangqi.
In my half-assed 5-minute Wikipedia/Baidu Zhidao research, I don’t see reference to the emperor of China sponsoring the invention of any form of chess. Could this be an inaccurate reference to Han Xin (韩信), who is connected to the history of Chinese chess (象棋)? If anyone has more info, I’d love to hear it. Is Kurzweil’s story about Chinese chess, rice grains, and exponential growth just another fake Chinese anecdote, or is there anything to back it up?
If you’ve checked out many online Chinese dictionaries or websites on learning Chinese, you’ve seen a variety of ways to present characters’ proper stroke order. Animated GIFs are a favorite, but they often fall flat in one important respect: they display each stroke in a single frame, often leaving the direction of the stroke somewhat unclear.
This is where the Wikimedia Commons Stroke Order Project impresses me: not only are the animated GIFs large and attractive, but they fluidly demonstrate the direction of each stroke. A nice example:
More info from the site:
> Hello, and welcome to the Commons Stroke Order Project. This project aims to create a complete set of high quality and free illustrations to clearly show the stroke order of East Asian characters (hanzi, kanji, kana, hantu, and hanja). The project was started as there was none like it in terms of quality and it seems that it is the only one working on all three schools of Han character stroke order; simplified and traditional Chinese, and Japanese.
> You are free to use the graphics we’ve made and welcomed to join us and contribute to our progress. It’s easy, you just have to follow the simple steps stated in our graphics guidelines.
At 378 total characters, the project is still far from a complete set, but it’s off to a nice start!
I do, wonder, though, what kind of stroke order information is freely available out there that could speed the process along. I’ve seen enough separate sets of animated characters to make me suspect many have been automatically generated. (Anyone have info on this?) I’m also curious how the project is going to deal with the annoying issue of variable stroke orders.
Note that there is also an Ancient Chinese Characters sister project.
The Chinese internet has been all kinds of slow lately. Foreign sites load extremely sluggishly, and I can’t upload to Flickr at all.
Enter Firefox 3! The Chinese internet is still damn slow, but at least the browser is faster! Gmail works dramatically faster.
The one problem with upgrading immediately is that many Firefox addons might not be up to date and no longer work. Actually, though, most of these plugins can be forced to work by editing the compatible version range in the XPI file. Since I’ve started using Gladder as my proxy tool of choice, I can’t live without it. I figure some of you may be in the same boat, so I’m sharing my unofficial, hacked Gladder XPI file:
Gladder 184.108.40.206: unofficial hack for Firefox 3.0
I imagine this is not really a good thing to do, so use only at your own risk. (I just want Wikipedia back.)