0.999… = 1?

Such an innocent question. So much controversy around it.

No doubt, you have heard of the usual explanations:

1/3 = 0.333…, therefore 1 = 0.999…
Let x = 0.999…, then 10x – x = 9. Therefore x = 1.
You can’t find a number between 0.999… and 1.
The = sign here merely means “approaches”.
… and many more.

Some of these explanations are valid; some are not. But, even as the rational part of your brain accepts that 0.999… = 1, the intuitive part of your brain might still be complaining “but it doesn’t feel right”. You know why? Because it isn’t right. It isn’t complete. The full statement should be:

If 0.999… is a real number, then it must be equal to 1.

The part of your brain that thinks “but it doesn’t feel right”? It’s trying to say, hey, this doesn’t look like a real number.

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Lyrics to Finnemore’s Woof Woof Woof

Well, since you asked me for the lyrics to Finnemore’s Woof Woof Woof, Goes The Wolfhound…

Three major variants appear in the series. Here they are:

Pier Pressure version (Episode 1)

(Two, three, four!)
“Woof woof woof,” woofs the wolfhound
“Arf arf arf,” barks the chow
The bloodhound howls “ow ow ow ow”
The dogs of war sing sweetly now

Truly, wonders never cease
The dogs of war sing songs of peace
The nightingale informs us so from the tree

Dogs may snarl and dogs may slather
The nightingale prefers to have her songs set in a more melodious key
So she sings:

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Yin and Yang

Yin and yang are no strangers to English speakers. The dark and the bright. The cold and the warm. The chaos and the order.

Let’s get one thing out of the way: yang sounds like “young”. An a in pinyin always sounds like aah. Pinyin wasn’t designed with English in mind.

The concepts of 阴yīn and 阳yáng come from Taoism, a philosophy that has tremendous influence on the Chinese languages and cultures, but that few today actually understand. A typical Chinese person might not know much more about yin and yang than a typical Westerner, but they will know these words that involve this dual concept:

太阳tài yang

太阳 is the sun. 阳 is usually reduced to a natural tone, but when enunciating or in a theatrical setting, it might still be read in the second tone.

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Bilingual chain: a game | 双语链条：游戏开始

Here’s how this game works. I start with a word in Chinese, and I translate it into English. The English word will have multiple meanings, so I’ll translate it into a different Chinese word. The Chinese word will have multiple meanings, so I’ll translate it into a different English word, and so on and so forth, until we reach a word so specific that it can’t be translated in two different ways.

游戏规则：从一个汉语词开始，地二把它翻译成英文。这个英文词有多个含义，地二取其中一个译回汉语。这个汉语词又有多个含义，地二取其中一个译回英语，如此往复，直到找不出多义词为止。听上去有些困难，但是汉语和英语多义词都很多，而不同语种的两个语言，每个词的外延经常不完整覆盖，所以形成一个长链条其实很容易。

This may sound a bit difficult, but both Chinese and English have lots of homonyms, and their definitions rarely overlap exactly, so it’s not entirely challenging to form a reasonably long chain. What better word to start with than game:

游戏yóu xì

游戏 is the most straightforward translation of game. It goes with 玩wán; to play a game is 玩游戏. A word game is 文字wén zì游戏, which, without context, typically refers to the dishonest practice rather than the innocent fun. Board games are often abbreviated to 桌游zhuō yóu, and video games are called 电脑diàn nǎo游戏 if played on a computer, or 街机jiē jī游戏 (lit. street machine games) if played on an arcade machine.

既然是做游戏，那就从“游戏”这个词开始。游戏一般翻译成 game。桌游叫做 board games，文字游戏可以翻译成 word games。汉语里提到文字游戏，一般是指咬字眼纠细节那种不诚实行为，但是诸如成语接龙等文字类的游戏也可以称作 word games。电脑游戏，一般叫做 video games（很少叫 △ computer games），但 video games 也指在游戏厅玩的那种街机游戏。

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Italics in Chinese

Western languages often make use of italics to convey certain intonations. If you haven’t noticed before, italics is a separate font, and not just a mechanical tilting of the upright letters. (Mechanical tilting does exist, and it’s called oblique.) Compare:

The quick brown fox jumped over the lazy dog.

The quick brown fox jumped over the lazy dog.

In case you see something different in your browser, this is how it appears to me:

Notice the “a” and the “g” which are now completely different, and the rounded “v” and “w”. Other letters are subtly different too (do you see how the middle of the “e” is now curved?).

Now, here’s something that lots of foreign companies don’t pay attention to in their translated user manuals and web pages: italics doesn’t exist in Chinese. The “italics” button usually just turns Chinese characters into oblique (mechanical tilt); it looks ugly, and it’s the sign of a poorly typeset piece of text.

What does Chinese use instead? It depends on what you are using italics for.

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Jianpu (simplified staff)

It’s one of those things that weren’t invented in China but took off in China: 简谱jiǎn pǔ is a way of writing down music using numbers and dots and dashes. It was invented because the standard notation can be difficult to read, especially to beginners:

But this is (arguably) more accessible:

For one thing, there’s no need for “every good boy deserves fun” anymore.

Wikipedia (en, zh) says this notation was invented in France in the 1700s and came to China by way of Germany and Japan in the early 1900s. I haven’t seen it used anywhere outside of China, though — which is a shame, because it’s such a handy tool.

The Notes

简谱 uses the numbers 1 through 7 to denote the seven notes on a major scale — that is, do, re, mi, fa, so, la, si (ti) — and uses a 0 to denote a pause. Very often, this translates to 1 = C, 2 = D, …, 6 = A, 7 = B.

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When is the Chinese New Year?

At this point, most of the English-speaking world has an awareness that the Chinese New Year happens somewhere around January or February. Some might even know that it moves around relative to the western calendar because the Chinese calendar is lunar. But did you know that the Chinese calendar is actually half-lunar, half-solar? It even relies on the same solstices and equinoxes that we know and love in the west.

Through the thousands of years in China’s ancient history, the Chinese calendar has been revised multiple times, so the rules we describe below will not perfectly backdate to ye olden days. The basic principles have always been the same, but the details (leap years and such) haven’t been consistent throughout.

The Chinese calendar currently follows the Chinese national standard GB/T 33661-2017, which was last revised in 2017 (as the name suggests). For some reason, you can purchase the full text through the (American) ANSI webstore for the low, low price of $180 (lol).

Following the GB/T, we’ll reach this conclusion: the Chinese New Year happens on the second, occasionally the third, new moon following the winter solstice.

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Reading Math Out Loud | 数学公式的英语读法

This will be a bilingual post. 本文双语。

When multiple readings are possible, the most commonly used ones are listed on top. 有多种读法时，最常用的读法排在前面。

For Chinese learners
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英文读法在这里
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Basic arithmetic | 四则zé运yùn算suàn

1 + 2

一加jiā二

一加上shàng二

one plus two

add two to one

1 – 2

一减jiǎn二

一减去qù二

one minus two

subtract two from one

one takeaway two*

* takeaway 稍不正式，一般是教小孩子做减法时这么说。

1 × 2

一乘chéng以yǐ二

二乘一

one multiplied by two

one times two

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过去、条件与虚拟

英语中每个动词最多只有五种形式（唯一的特例是 be）。在西方语言中，英语是个特例——学过法语、德语、西班牙语等的同学们都知道，一个动词能有多少种变化：

法语动词 offrir (to offer, to provide) 的一部分变形
图片来源：*https://conjugator.reverso.net/conjugation-french-verb-offrir.html*

英语中一个显著的区别，就是没有单独的虚拟形式。

过去形式

英文中的所有动词，全部都有现在和过去形式。在《动词的五种形式》里，地二把这两种形式称作一形和二形。

描述过去的动作，英文中有两种结构。

一形变二形

能从一形变二形的，就从一形变二形。

(1a) I know. / 我知道。→ I knew. / 我早就知道。
(1b) I have three apples. / 我有三个苹果。→ I had three apples. / 我曾有三个苹果。
(1c) I need to leave. / 我得走了。→ I needed to leave. / 我当时得走了。

这种变形语法上不复杂，重点在于对过去时态的掌握。汉语中没有明确的过去时态，有些时候可能会忘记变形。

(2a) James died on Sunday. He was 59. / James 周日过世了，享年59岁。
(2b) I told him I didn’t want to go. / 我跟他说了我不想去。
(2c) It’s your birthday today? I didn’t know. / 你今天生日？我才知道。

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