wrote a book called "The Whetstone of Witte"

寫了一本書叫「The Whetstone of Witte」

to teach English students algebra.

用來教英國學生代數

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

但他實在是厭倦了不斷重複寫「等於」

His solution?

他的解決方法是什麼呢?

He replaced those words with two parallel horizontal line segments

他用兩槓平行線取代了那些字

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

因為他認為沒有兩個東西比這更均等了

Could he have used four line segments instead of two?

那可以用四槓而不是兩槓嗎？

Of course.

當然可以

Could he have used vertical line segments?

他可以用垂直線嗎？

In fact, some people did.

的確有些人是這麼做的

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

現今還沒有理由解釋為何等於符號看起來是這樣子

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

在某些層面，這就是個流行，像是網路用語

More and more mathematicians began to use it,

越來越多數學家使用這個符號

and eventually, it became a standard symbol for equality.

最後，它終於變成了「相等」的標準符號

Math is full of symbols.

數學中充滿了符號

Lines,

線條、

dots,

點、

arrows,

箭號、

English letters,

英文字母、

Greek letters,

希臘字母、

superscripts,

上標符號、

subscripts.

下標符號

It can look like an illegible jumble.

就如同一堆難辨認的雜物

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

看到無數的符號令人有點膽怯是正常的

and to wonder where they all came from.

接著我們會好奇他們是從哪來的

Sometimes, as Recorde himself noted about his equals sign,

有時，就 Recorde 本人關於等於符號的紀錄

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

符號與所代表的意義之間是有跡可循的

Another example of that is the plus sign for addition,

另一個例子就是加號

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

它源自於拉丁文 et 的縮寫，意指「以及」

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

然而，有時符號的採用卻過於隨意

such as when a mathematician named Christian Kramp

像是當一位名叫 Christian Kramp 的數學家

introduced the exclamation mark for factorials

為了階乘而介紹驚嘆號的符號

just because he needed a shorthand for expressions like this.

只是因為他需要一個比較簡短的表示方法而已

In fact, all of these symbols were invented or adopted

其實，這些符號

by mathematicians who wanted to avoid repeating themselves

都是為了避免重覆使用或不斷書寫以表現數學概念

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

而被創造或採用的

Many of the symbols used in mathematics are letters,

許多數學家用的符號都是

usually from the Latin alphabet or Greek.

來自拉丁或希臘的字母

Characters are often found representing quantities that are unknown,

字元通常都用來表示未知的數量

and the relationships between variables.

以及變數之間的關係

They also stand in for specific numbers that show up frequently

它們也代表一些出現頻率很高的特定數字

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

但寫下來會過於冗長或是不可能全部寫出來的小數點

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

一整套的數字和整個等式也可以用字母代表

Other symbols are used to represent operations.

其他符號則用來表示

Some of these are especially valuable as shorthand

有些符號對於縮減運算非常有幫助

because they condense repeated operations into a single expression.

因為他們將重覆的運算過程縮減成一個符號

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

重覆加上的數字用乘法符號縮減

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

這樣就不用占用太多空間

A number multiplied by itself is indicated with an exponent

重覆相乘倍增用指數表示

that tells you how many times to repeat the operation.

它會告訴你運算中要重覆相乘幾次

And a long string of sequential terms added together

而一連串連續的數字相加

is collapsed into a capital sigma.

則分解成一個大寫的 sigma

These symbols shorten lengthy calculations to smaller terms

這些符號將冗長的算式縮短成較小的形式

that are much easier to manipulate.

更加方便運用

Symbols can also provide succinct instructions

符號還可以簡潔扼要的

about how to perform calculations.

指示要如何呈現算式

Consider the following set of operations on a number.

設想以下的數字運算

Take some number that you're thinking of,

取一個你想的數字

multiply it by two,

乘二

subtract one from the result,

減一

multiply the result of that by itself,

算出的結果相乘

divide the result of that by three,

再除以三

and then add one to get the final output.

然後加一得出最後的結果

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

沒有我們的符號和公式，我們會面臨一大堆的文字內容

With them, we have a compact, elegant expression.

運用符號，我們可以有個簡潔優雅的呈現方式

Sometimes, as with equals,

有時，使用等號

these symbols communicate meaning through form.

透過公式這些符號的傳達就有意義

Many, however, are arbitrary.

但是太多則很難閱讀

Understanding them is a matter of memorizing what they mean

要了解它們就要將它們背下來

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

在不同的運算中使用它們直到像是語言一樣經久難忘

If we were to encounter an alien civilization,

如果我們遇到了外來文明

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

他們很可能擁有跟我們完全不一樣的符號

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

但假如他們任何東西都跟我們想的一樣，他們可能會有符號

And their symbols may even correspond directly to ours.

而且他們的符號或許可以跟我們的相對應

They'd have their own multiplication sign,

他們會有自己的乘法符號

symbol for pi,

圓周率的符號

and, of course, equals.

當然還有等號