Where do math symbols come from? - John David Walters

翻译人员: nisi J 校对人员: Ruilin Yao

In the 16th century, the mathematician Robert Recorde

十六世纪的时候， 数学家罗伯特·雷考德

wrote a book called "The Whetstone of Witte"

写了一本叫做《砺智石》的书，

to teach English students algebra.

以教授英国学生代数。

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

但是他为一遍遍 写“等于”两个字而感到疲惫。

His solution?

他的解决方法是什么呢？

He replaced those words with two parallel horizontal line segments

他用两个平行的水平线段 替代了“等于”这个词。

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

因为在他的眼中， 没有更相等的两个事物了。

Could he have used four line segments instead of two?

他可以用四条而非两条线段吗？

Of course.

当然。

Could he have used vertical line segments?

他可以用两条竖线吗？

In fact, some people did.

实际上，的确有人用了。

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

等号并非一定要长成今天这样。

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

某个时间起，它突然就 火了起来，有点像流行用语。

More and more mathematicians began to use it,

越来越多的数学家开始使用它，

and eventually, it became a standard symbol for equality.

最终，它成为了“等于”的标准符号。

Math is full of symbols.

数学里到处都是符号。

Lines,

线，

dots,

点，

arrows,

箭头，

English letters,

英语字母，

Greek letters,

希腊字母，

superscripts,

上标，

subscripts.

下标。

It can look like an illegible jumble.

有时候看起来杂乱无章。

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

觉得这么大量的符号有点恐怖很正常，

and to wonder where they all came from.

也自然想知道它们都从哪来。

Sometimes, as Recorde himself noted about his equals sign,

有时候，就像雷考得 注意到关于他的等号一样，

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

这个符号和它所代表 的东西之间有恰当的一致性。

Another example of that is the plus sign for addition,

另一个例子就是加法的加号，

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

起源于拉丁et（&），“和”的缩写。

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

有些时候，符号的选择就随性一点，

such as when a mathematician named Christian Kramp

例如当数学家基斯顿·卡曼

introduced the exclamation mark for factorials

推行用感叹号来表示阶乘，

just because he needed a shorthand for expressions like this.

仅因为他需要一个 这种表达式的简写。

In fact, all of these symbols were invented or adopted

实际上，这些符号都是由

by mathematicians who wanted to avoid repeating themselves

不想老是痛殴重复或写很多词

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

描述数学思想的数学家发明或选用的。

Many of the symbols used in mathematics are letters,

数学中使用的许多符号都是字母,

usually from the Latin alphabet or Greek.

拉丁字幕或是希腊字幕。

Characters are often found representing quantities that are unknown,

符号一般用于表达未知数，

and the relationships between variables.

以及变量之间的关系。

They also stand in for specific numbers that show up frequently

它们也表示某些经常出现的

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

用小数点式不可能或者 很难写的特定数字。

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

数集以及整个式子 也可以用字母表示。

Other symbols are used to represent operations.

其他符号被用来表示运算。

Some of these are especially valuable as shorthand

其中有一些作为缩写尤为重要，

because they condense repeated operations into a single expression.

因为他们能把重复的运算 浓缩到一个简单的表达式。

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

同一个数字的重复相加被缩写成乘法，

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

所以不会占用不必要的位置。

A number multiplied by itself is indicated with an exponent

数字的自相乘用指数

that tells you how many times to repeat the operation.

来表示重复运算多少次。

And a long string of sequential terms added together

然后，一系列的数字相加

is collapsed into a capital sigma.

缩写为大写的合集符号。

These symbols shorten lengthy calculations to smaller terms

这些符号把冗长的 计算过程简化成较小的

that are much easier to manipulate.

更容易处理的项。

Symbols can also provide succinct instructions

符号也可以提供

about how to perform calculations.

关于计算的简明指导。

Consider the following set of operations on a number.

想象接下来的一系列运算。

Take some number that you're thinking of,

在脑海中选一个数字，

multiply it by two,

乘以二，

subtract one from the result,

结果减一，

multiply the result of that by itself,

结果和自己相乘，

divide the result of that by three,

结果除以三，

and then add one to get the final output.

然后再加一以得到最终答案。

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

如果没有符号，我们就要 面对这样的大块文字。

With them, we have a compact, elegant expression.

有了符号，我们有了简洁， 优雅的表达方式。

Sometimes, as with equals,

有时候，就像等号，

these symbols communicate meaning through form.

这些符号通过形式传达意义。

Many, however, are arbitrary.

然而，许多符号是很随意的。

Understanding them is a matter of memorizing what they mean

要了解它们，记住它们的意思就好了，

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

并在不同的场景下使用，直到把它们 牢牢得记住，就像任何其他语言一样。

If we were to encounter an alien civilization,

如果我们遇到了外星文明，

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

他们八成有完全不同的符号。

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

可是如果他们像我们一样得思考， 他们八成也有许多符号。

And their symbols may even correspond directly to ours.

这些符号或许和我们的相呼应。

They'd have their own multiplication sign,

他们也会有自己的乘号，

symbol for pi,

代表圆周率的 π，

and, of course, equals.

当然还有等于号。