Name: 【TED-ed】數學符號從何而來？ (Where do math symbols come from? - John David Walters)
Uploaded: 2017-12-04T22:05:00.000Z
Duration: 4 min 30 s

In the 16th century, the mathematician Robert Recorde

在十六世紀，數學家 Robert Recorde

wrote a book called  "The Whetstone of Witte"

寫了一本書叫「The Whetstone of Witte」

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」

He replaced those words with two parallel horizontal line segments

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?

Could he have used vertical line segments?

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,

and eventually,  it became a standard symbol for equality.

最後，它終於變成了「相等」的標準符號

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

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,

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

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

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.

Many of the symbols used in mathematics are letters,

usually from the Latin alphabet or Greek.

Characters are often found representing quantities that are unknown,

字元通常都用來表示未知的數量

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.

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.

A number multiplied by itself is indicated with an exponent

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

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

Symbols can also provide  succinct instructions

Consider the following set of operations on a number.

Take some number that you're thinking of,

and then add one to get the final output.

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

these symbols communicate meaning through form.

透過公式這些符號的傳達就有意義

Understanding them is a matter of memorizing what they mean

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,

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,