Short divisions, etc.

Starbucks has got to have the most annoying drink sizes of all coffee shops. Instead of small, medium, and large, they offer “tall”, “grande”, and “venti”. It’s sometimes English and sometimes Italian, the small size is called “tall” and the medium size means “big”, and the large size forgoes adjectives altogether and just calls itself “twenty”. Twenty what? Twenty fluid ounces, of course, which, as we all know, is the standard unit for measuring coffee drinks worldwide and especially in Italy (yeah, right).

I can’t do anything about the fluid ounces, but the “tall” name actually has an explanation: Starbucks offers five drink sizes, not three:

Size Name	Fluid Ounces
Short	8 fl oz
Tall	12 fl oz
Grande	16 fl oz
Venti	20 fl oz for cold drinks, 24 hot
Trenta	31 fl oz

As of October 2021

It certainly looks like they planned to offer the first three sizes — short, tall, and grande — as the standard sizes, and venti and trenta were meant to be “super sized” drinks. Who knows, maybe the short cup is too short, maybe they underestimated the American appetite, it came to be that the middle three sizes became the standard. You can still ask for a short at Starbucks; they just don’t list that size on the menu anymore.

This venti-sized intro leads us to today’s main topic: we all know long division from school. Is there a short division?

Yes. Yes there is.

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Mortgage math

What’s the monthly payment on a $360,000 mortgage, at an interest rate of 3%, to be repaid over 30 years?

Just let me quickly have a Google…

No! What’s the fun in that? Let’s re-derive the formulas from scratch. We will, in the end, reach this conclusion:

$p = \frac{L\cdot r}{1-\frac{1}{(1+r)^n}}$

Although this post talks about a mortgage, this formula applies to any fixed-rate installment loans, such as a car loan or a purchase through Affirm.

Note: This is not a money blog. None of this is financial advice. This post will touch on a few minor financial topics, but only to clarify the math.

Principal and Interest

For most mortgages, interest does not compound. Let me say that again: mortgage interest does not compound. Unless your mortgage has a “negative amortization feature” (which, in the US, would be clearly indicated on page 4 of your Closing Disclosure), your monthly payment will cover the entirety of interest accrued in that month.

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Math with units

What’s the average fuel economy of two cars, one with 40 mpg, and the other with 10 mpg? It all depends on what you mean by “average”. (That’s 6 and 24 liters per 100 km.)

Mathematicians often deal with pure math — that is, numbers without units. (40 + 10) / 2 = 25 might be a correct equation, but it might not be the appropriate one for our problem. In real life, most numbers have a unit: 3 days, 5 cars, 8 people, 11 dollars. When numbers come with units, there are additional rules for doing math.

Addition and Subtraction

Adding is counting. Subtracting is counting backwards. When counting, one must stay with the same unit. “1 apple, 2 apples, 3 apples” is counting. “1 apple, 2 oranges, 3 pears” is a shopping list.

1 apple + 2 apples = 3 apples
5 hours – 3 hours = 2 hours
1 apple + 1 hour = ??? (doesn’t make sense)

You are, of course, allowed to convert units, if they’re convertible:

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动词的五种形式

英文中每个动词有五种形式：一形、二形、三形、四形、他她它形。

变形举例

这五种形式，大家都是很熟悉的，甚至能叫得出语法上的正式名称。各种形式的作用，地二等下再谈，这里先用一些常见动词举例：

一形	二形	三形	四形	他她它形
do	did	done	doing	does
have	had	had	having	has
play	played	played	playing	plays
come	came	come	coming	comes
give	gave	given	giving	gives
feel	felt	felt	geeling	feels
go	went	gone	going	goes
look	looked	looked	looking	looks

唯有 be 一个动词有多于五种形式：

一形	二形	三形	四形	你我他她它形
be	was, were	been	being	am, are, is

情态动词没有三形和四形，他她它形退化成一形：

一形	二形	三形	四形	他她它形
can	could	–	–	can
shall	should	–	–	shall
may	might	–	–	may
will	would	–	–	will

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Hindsight is 5.0

As the saying goes, “hindsight is 20/20”, meaning “things are clearer in retrospect”. 20/20 is a measure of a person’s visual acuity: you can see from 20 feet away what a “normal” person can also see from 20 feet away. In other words, your eyesight is normal (but you can still be colorblind, etc).

20/20 isn’t perfect vision; people with good eyesights often measure 20/15 or even 20/10 — they can see from 20 feet away what a “normal” person can only see from 15 or 10 feet away. D. R. on the other hand is severely nearsighted and measures worse than 20/200 without correction — without my glasses on, I can only see at 20 feet what “normal” people can see from 200 feet or even further away. 20/20 is the low end of “normal”; if you see at least 20/20, then an eye doctor wouldn’t prescribe you any glasses.

Decimals

What’s special about “20 feet”? Not much, really. It’s just been a standard testing distance since the Dutch ophthalmologist (= eye scientist) Herman Snellen came up with this measurement. In metric countries (i.e. outside the US), optometrists (= eye doctors) write 6/6 (meters) instead of 20/20. 6.00m = 19.7ft, but humans like round numbers.

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Waterproof your house before it rains

未雨绸缪

A good doctor cures an illness; a great doctor prevents an illness. When you do things right, people won’t be sure you’ve done anything at all. There’s no shortage of similar sayings in any language, yet we keep coming up with new ways to say it because we keep thinking “it’s fine at the moment” and fail to plan ahead. Case in point: <gestures broadly at everything>.

How long ago do you think humans first had this thought? At least 2,700 years ago, according to today’s chengyu. Egyptians were still making sphinxes then, and China was in one of its earliest recorded dynasties.

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一句话，一个主动词

中文里逗号和句号的区别主要在于语义。教育部《标点符号用法》里多次使用类似“意义上有密切关系”、“表达相对完整意义”、“前后有较大停顿”等语句描述标点用法，地二觉得实际使用也确实如此。参看以下例句：

(1) 夏夜很静谧，只有月光经过树梢来到大地的脚步声。（钱钟书《夏夜》）
(2) 那年冬天，祖母死了，父亲的差使也交卸了，正是祸不单行的日子。（朱自清《背影》）

因为“夏夜”和“那年冬天”是贯穿全句的主题，所以一直使用逗号直到主题结束，一个句号结句。这样的用法在英文中是行不通的，因为英文对“句”的概念有一个严格的语法要求：一句话，一个主动词。

什么是主动词

主动词（意为“核心动词”，不是“主动的词”）就是一句话中随人称、时态会发生改变的那个动词。例如：

(3) I saw him walk into the supermarket.
(4) He wants me to talk to him.

以上两句中，加粗部分是主动词，斜体部分不是。注意加粗部分会随着人称、时态发生改变：

(3a) I have seen him walk into the supermarket.
(3b) She sees him walk into the supermarket.
(4a) They want me to talk to him.
(4b) She wanted me to talk to him.

而斜体部分不会：

(3c) I saw her walk into the supermarket.
(3d) I saw them walk into the supermarket.
(4c) He wants her to talk to them.
(4d) He wants them to talk to me.

“主动词”是地二这里自己创造的一个名称（语法上正式名称叫“谓语动词”）。一个动词是不是主动词，看它在一句话里怎么用，不是说字典里可以查到，这个词是主动词，那个词不是。

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Silver linings have linings too

塞翁失马

Did you know that “silver lining” comes from the phrase “every cloud has a silver lining”, which in turn comes from a John Milton poem written in 1634? Milton wrote:

Was I deceived, or did a sable cloud
Turn forth her silver lining on the night?
I did not err; there does a sable cloud
Turn forth her silver lining on the night,
And casts a gleam over this tufted grove.

Now, I have no idea what a tufted grove is, but I know Mr. Milton only went one level deep. Want more plot twists? Our chengyu today has you covered. (“Sable” means dark.)

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Jishi or jishi?

Open up a pinyin IME and type in “jishi”. You’ll see a large amount of options:

A list of words all pronounced "jishi". — That’s not even all of it

Most of them are pronounced with different tones, and those with the same tones are usually different enough that, in context, people will have no trouble understanding which one you mean. Still, this is a comical amount of options even for Chinese. Shall we take a look at some of them?

记事 👩‍💻 👨‍💻 📝

(jì shì) take notes; lit. “record events”

Modern Chinese words often have a “2 + 2 = 2” pattern; that is, combine a two-character word with another two-character word, and you get a new two-character word. Here, 记录 (jì lù, to record) and 事情 (shì qíng, things, events) combine into 记事, meaning “to take notes”. A notebook is called 记事本 (běn, small books).

The emojis… well the Apple IME shows you related emojis when you type a word, so I thought to include them here. Could be a good memory aid.

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Who moved my sword?

刻舟求剑

I was a kid when Who Moved My Cheese came out. I don’t remember much about the book; I think there was some cheese and cheese-loving mice, and one of the mice got upset when the cheese disappeared and demanded (to no one in particular) that the cheese be returned. I remember thinking “it’s ridiculous”, not appreciating that the ridiculousness was the point of the story. The other half of the moral — that we often behave like this fool of a mouse in real life — was completely lost on me.

There’s a chengyu based on a similar story. Only there’s a sword instead of cheese, a man instead of mice, and it was written not twenty years ago, but two thousand years ago. And more ridiculous.

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