A brief history of numerical systems - Alessandra King

翻译人员: Ruilin Yao 校对人员: Cissy Yun

One, two, three, four, five, six, seven, eight, nine, and zero.

1,2,3,4,5,6,7,8,9,0

With just these ten symbols, we can write any rational number imaginable.

只用这十个符号， 我们可以写出任何有理数

But why these particular symbols?

但是为什么是这几个符号呢？

Why ten of them?

为什么有十个？

And why do we arrange them the way we do?

而为什么人们会按照这样的方式排列它们呢？

Numbers have been a fact of life throughout recorded history.

有史以来，数字一直是生活中必不可少的

Early humans likely counted animals in a flock or members in a tribe

最早人们通常用身体的某部分或计数标记

using body parts or tally marks.

来表示一群动物或部落的人的数量

But as the complexity of life increased, along with the number of things to count,

但是随着生活越来越复杂 需要数的数量也不断增加

these methods were no longer sufficient.

这些方法不再够用了

So as they developed,

随着不同文明的发展，

different civilizations came up with ways of recording higher numbers.

人们想出了很多用了记录更多数量的办法。

Many of these systems,

很多数字系统，

like Greek,

Hebrew,

比如希腊数字

希伯来数字

and Egyptian numerals,

以及埃及数字

were just extensions of tally marks

只是原来计数标记的加强版

with new symbols added to represent larger magnitudes of value.

加入了用来代表更高数量级的新符号

Each symbol was repeated as many times as necessary and all were added together.

每个符号都尽可能多次重复使用再把它们加起来

Roman numerals added another twist.

罗马数字添加了另一种方式

If a numeral appeared before one with a higher value,

如果1前面有一个值更大的数字

it would be subtracted rather than added.

它们会被相减，而不会被相加

But even with this innovation,

但尽管有了这种创新

it was still a cumbersome method for writing large numbers.

对较大的数字来说 这依旧是种累赘的方法

The way to a more useful and elegant system

有一种更有用更优雅的方式

lay in something called positional notation.

称为定位数系

Previous number systems needed to draw many symbols repeatedly

之前的数字系统需要不断重复地画很多符号

and invent a new symbol for each larger magnitude.

而且每一个更大的数量级都需要引入新的符号

But a positional system could reuse the same symbols,

但是定位数系可以重复使用同样的符号，

assigning them different values based on their position in the sequence.

根据它们的位置赋予它们不同的值

Several civilizations developed positional notation independently,

一些社会文明发展了自己的定位数系

including the Babylonians,

其中包括巴比伦人

the Ancient Chinese,

古中国人

and the Aztecs.

还有阿芝特克人

By the 8th century, Indian mathematicians had perfected such a system

到了第八世纪，印度数学家完善了一种记数制

and over the next several centuries,

它在接下来的几个世纪中

Arab merchants, scholars, and conquerors began to spread it into Europe.

被阿拉伯商人，学者和征服者传到了欧洲

This was a decimal, or base ten, system,

这就是十进制

which could represent any number using only ten unique glyphs.

一种可以只用十个独特的图像字符 就能表示出任何数字的方法

The positions of these symbols indicate different powers of ten,

这些字符的位置表明了10的不同次方，

starting on the right and increasing as we move left.

从右开始，次方数向左不断递增。

For example, the number 316

比如数字316，

reads as 6x10^0

读成 6乘以10的0次方

plus 1x10^1

加上 1乘以10的1次方

plus 3x10^2.

加上 3乘以10的2次方。

A key breakthrough of this system,

这个方法的一个巨大突破是

which was also independently developed by the Mayans,

同时也被玛雅人发明了的

was the number zero.

数字0.

Older positional notation systems that lacked this symbol

旧的定位数系没有这个符号，

would leave a blank in its place,

便会在那个位置留一个空格，

making it hard to distinguish between 63 and 603,

这让63和603，12和120

or 12 and 120.

难以区分

The understanding of zero as both a value and a placeholder

0这既是一个值又是一个占位符的特质

made for reliable and consistent notation.

让它成为一个可靠，一致的符号

Of course, it's possible to use any ten symbols

当然，也可以用任何十个符号

to represent the numerals zero through nine.

来代替数字0到9.

For a long time, the glyphs varied regionally.

很长一段时间 图像字符在各地区不断变化发展着

Most scholars agree that our current digits

大多数学者认为我们如今的数字

evolved from those used in the North African Maghreb region

是从北非阿拉伯王国马格里布地区曾用过的符号

of the Arab Empire.

进化而来的

And by the 15th century, what we now know as the Hindu-Arabic numeral system

到十五世纪 我们现在日常所熟悉的阿拉伯数字体系

had replaced Roman numerals in everyday life

已经取代了罗马数字

to become the most commonly used number system in the world.

变成了世界上最常用的数字系统。

So why did the Hindu-Arabic system, along with so many others,

那为什么阿拉伯数字系统和其他的一些

use base ten?

都用十进制呢？

The most likely answer is the simplest.

最可能的答案是因为它是最简单的。

That also explains why the Aztecs used a base 20, or vigesimal system.

这也解释了阿芝特克人使用二十进制的原因

But other bases are possible, too.

但是其他进制也是可以用的

Babylonian numerals were sexigesimal, or base 60.

巴比伦数字是六十进制

Any many people think that a base 12, or duodecimal system,

很多人认为十二进制

would be a good idea.

也挺好的

Like 60, 12 is a highly composite number that can be divided by two,

12和60都是因数很多的合数，它们可以被2，

three,

被3，

four,

and six,

被4，

被6整除，

making it much better for representing common fractions.

用这些数来表示共同因数更好一些

In fact, both systems appear in our everyday lives,

事实上，我们日常生活中存在很多数字系统，

from how we measure degrees and time,

从测量角度和时间，

to common measurements, like a dozen or a gross.

到日常的计量单位，比如一打。 （a dozen意为12个，a gross意为144个）

And, of course, the base two, or binary system,

当然，二进制

is used in all of our digital devices,

也被使用于所有的电子设备。

though programmers also use base eight and base 16 for more compact notation.

尽管程序员也将八进制和十六进制用于更精简的表达。

So the next time you use a large number,

所以下一次你使用一个很大的数字时，

think of the massive quantity captured in just these few symbols,

想想你仅用了这几个符号就获得了一个如此大的量，

and see if you can come up with a different way to represent it.

也试试看你是否能用不同的方式把它表达出来。