Where do math symbols come from? - John David Walters

譯者: Helen Chang 審譯者: S Sung

In the 16th century, the mathematician Robert Recorde

十六世紀數學家羅伯特 · 雷科爾德

wrote a book called "The Whetstone of Witte"

寫了一本書叫「礪智石」

to teach English students algebra.

教英國學生代數

But he was getting tired of writing the words "is equal to" over and over.

但是他厭倦了一遍又一遍地寫「等於」

His solution?

他怎麼解決呢？

He replaced those words with two parallel horizontal line segments

他用兩條水平的平行線段取代這詞

because the way he saw it, no two things can be more equal.

因為他認為沒有其他兩物更平等了

Could he have used four line segments instead of two?

他可以用四條線段代替兩條嗎？

Of course.

當然可以

Could he have used vertical line segments?

他可以使用垂直線段嗎？

In fact, some people did.

其實真有人這樣做

There's no reason why the equals sign had to look the way it does today.

沒有理由等號非得是今天這個樣子

At some point, it just caught on, sort of like a meme.

它起步的時間點恰好，有點像是模因 （meme：一種文化傳播形式）

More and more mathematicians began to use it,

越來越多的數學家開始用它

and eventually, it became a standard symbol for equality.

最終它成為等於的標準符號

Math is full of symbols.

數學裡充滿著符號

Lines,

線、點、箭頭

dots,

arrows,

English letters,

英文字母、希臘字母

Greek letters,

superscripts,

上標、下標

subscripts.

It can look like an illegible jumble.

看似難以辨認的大雜燴

It's normal to find this wealth of symbols a little intimidating

覺得這麼多符號很嚇人是正常的

and to wonder where they all came from.

想知道它們的起源也是

Sometimes, as Recorde himself noted about his equals sign,

就像雷科爾德他自己提到的等號一樣

there's an apt conformity between the symbol and what it represents.

有時符號和它所代表的內容相當一致

Another example of that is the plus sign for addition,

另一個例子是「加號」

which originated from a condensing of the Latin word et meaning and.

起源於縮簡的拉丁字 et 意思是「和」

Sometimes, however, the choice of symbol is more arbitrary,

有時候符號是任意選的

such as when a mathematician named Christian Kramp

例如數學家克里斯蒂安 · 克蘭普

introduced the exclamation mark for factorials

採用驚嘆號代表階乘

just because he needed a shorthand for expressions like this.

只因為他需要階乘的速記表達方式

In fact, all of these symbols were invented or adopted

事實上所有這些符號的發明或被採用

by mathematicians who wanted to avoid repeating themselves

是因為數學家想要避免一再地重複

or having to use a lot of words to write out mathematical ideas.

要不然就得用很多字來表達數學想法

Many of the symbols used in mathematics are letters,

許多被使用的數學符號是字母

usually from the Latin alphabet or Greek.

通常來自拉丁字母或希臘字母

Characters are often found representing quantities that are unknown,

字符經常被發現用來代表未知的數量

and the relationships between variables.

和變量之間的關係

They also stand in for specific numbers that show up frequently

它們也代表經常出現的具體數字

but would be cumbersome or impossible to fully write out in decimal form.

但以十進制形式完整地寫出來 很麻煩或是不可能

Sets of numbers and whole equations can be represented with letters, too.

也可以用字母來表示 一組數字和整個方程式

Other symbols are used to represent operations.

其他的符號被用來代表運算

Some of these are especially valuable as shorthand

其中一些作為簡寫特別有價值

because they condense repeated operations into a single expression.

因為重複的操作被壓縮成 單一的表達式

The repeated addition of the same number is abbreviated with a multiplication sign

重複加相同的數字用乘號來簡寫

so it doesn't take up more space than it has to.

就不會佔用更多的空間

A number multiplied by itself is indicated with an exponent

數字自乘用指數

that tells you how many times to repeat the operation.

來表示重複操作了多少次

And a long string of sequential terms added together

一連串的連續加法

is collapsed into a capital sigma.

濃縮成大寫的 Σ（sigma）

These symbols shorten lengthy calculations to smaller terms

這些符號把冗長的計算 縮短成簡短的術語

that are much easier to manipulate.

因而更容易操作

Symbols can also provide succinct instructions

符號也可以提供

about how to perform calculations.

如何執行計算的簡潔指示

Consider the following set of operations on a number.

考慮以下的數字操作

Take some number that you're thinking of,

拿一些你想到的數字

multiply it by two,

乘以二

subtract one from the result,

減去一

multiply the result of that by itself,

把結果自乘

divide the result of that by three,

把那結果除以三

and then add one to get the final output.

然後加一，得出最終的結果

Without our symbols and conventions, we'd be faced with this block of text.

若沒有慣用的符號 我們將看到這堆文字

With them, we have a compact, elegant expression.

用了符號就會有精簡優雅的表達式

Sometimes, as with equals,

有時候和等號一樣

these symbols communicate meaning through form.

這些符號通過形式來表達意思

Many, however, are arbitrary.

然而有許多符號是任意選定的

Understanding them is a matter of memorizing what they mean

所以了解和記住它們的意思

and applying them in different contexts until they stick, as with any language.

並在不同的情況下應用它們 直到熟稔，就像學任何語言一樣

If we were to encounter an alien civilization,

如果我們遇到外星的文明

they'd probably have a totally different set of symbols.

他們可能會有完全不同的符號集

But if they think anything like us, they'd probably have symbols.

但如果他們的思維與我們類似 他們可能也會有符號

And their symbols may even correspond directly to ours.

甚至他們的符號能夠直接對應我們的

They'd have their own multiplication sign,

他們會有自己的乘法符號

symbol for pi,

pi （π）的符號

and, of course, equals.

當然還會有等號