A brief history of banned numbers - Alessandra King

譯者: YUYI TONG 審譯者: Helen Chang

人們說筆鋒比劍尖更利

They say the pen is mightier than the sword,

and authorities have often agreed.

而統治者們也普遍同意這個說法

From outlawed religious tracts and revolutionary manifestos

從非法的宗教刊物和革命宣言

to censored and burned books,

到被刪減和燒毀的書籍身上

we know the potential power of words to overturn the social order.

我們可以看出語言 在推翻社會秩序方面的潛力

But as strange as it may seem,

但奇怪的是

some numbers have also been considered dangerous enough to ban.

有些數字也被認為危險而需要被禁

Our distant ancestors long counted objects using simple tally marks.

我們古老的祖先一直使用 簡單的標記來計算物品

But as they developed agriculture and began living together in larger groups,

但當他們開始發展農業及群居生活

this was no longer enough.

這些標記便不能滿足需求

As numbers grew more complex,

當數字發展得越來越複雜

people began not just using them, but thinking about what they are

人們便不再只是使用它們 而是開始思考它們的是什麼

and how they work.

以及它們如何運作

And by 600 B.C.E. in Ancient Greece, the study of numbers was well-developed.

到了公元前 600 年 古希臘的數字研究已經非常發達

The mathematician Pythagoras and his school of followers

數學家畢達哥拉斯及其學派的追隨者

found numerical patterns in shapes, music, and the stars.

發現了圖形、音樂和 星體的數字規律

For them, mathematics held the deepest secrets of the universe.

對他們來說 數學是宇宙中最深奧的秘密

But one Pythagorean named Hippasus discovered something disturbing.

一個畢達哥拉斯學派的門生希帕索斯 卻發現了一樣令人不安的東西

Some quantities, like the diagonal of a square with sides of length one

一些數值

例如邊長為 1 之正方體的對角線

couldn't be expressed by any combination of whole numbers or fractions,

無論多小

都不能用任何整數 或分數的組合來表達

no matter how small.

These numbers, which we call irrational numbers,

這些數字，我們稱為無理數

were perceived as a threat

它被認為是一個對於

to the Pythagorean's notion of a perfect universe.

畢達哥拉斯完美宇宙概念的威脅

They imagined a reality that could be described

他們曾認為可以用理性和數字規律

with rational, numerical patterns.

來描述現實世界

Historians write that Hippasus was exhiled for publicizing his findings,

歷史學家寫道， 希帕索斯因為宣揚他的發現而被流放

while legends claim he was drowned as punishment from the gods.

但傳說指他被溺死，作為神對其的懲罰

While irrational numbers upset philosophers,

在無理數令哲學家不安的同時

later mathematical inventions would draw attention

其後的數學發明也同樣引起了

政治和宗教領袖的注意

from political and religious authorities, as well.

In the Middle Ages, while Europe was still using Roman numerals,

在中世紀， 當歐洲還在使用羅馬數字時

other cultures had developed positional systems

其他文明已經發展出位值系統

that included a symbol for zero.

當中包括 0 的符號

When Arab travelers brought this system to the bustling maritime cities of Italy,

當阿拉伯旅行家把這套系統 帶回繁華的沿海城市意大利時

its advantages for merchants and bankers was clear.

這套系統的確為商人 和銀行人員帶來了好處

But the authorities were more wary.

但統治者對此還是比較謹慎

Hindu-Arabic numerals were considered easier to forge or alter,

印度 - 阿拉伯數字被認為 較容易偽造或更改

especially since they were less familiar to customers than to merchants.

特別是因為客人 不像商家那樣熟悉這種數字

And the concept of zero opened the door to negative numbers

0 的概念也在一個

對借貸還很謹慎的年代

and the recording of debt

at a time when moneylending was regarded with suspicion.

開啓了負數和欠債記錄的大門

In the 13th century, Florence banned the use of Hindu-Arabic numerals

在 13 世紀，佛羅倫斯當局 禁止使用印度 - 阿拉伯數字

for record keeping.

用作記錄用途

And though they soon proved too useful to ignore,

雖然之後人們發現它實在很有用

controversies over zero and negative numbers

但對於 0 和負數的爭議

continued for a long time.

仍然持續了很長一段時間

Negative numbers were dismissed as absurd

到了 19 世紀

well into the 19th century.

負數仍被斥為荒謬的存在

And prominent mathematicians, like Gerolamo Cardano,

一些優秀的數學家， 比如吉羅拉莫·卡爾達諾

avoided using zero,

會避免使用 0

even though it would have made it much easier to find solutions

即使運用 0 能更容易找到

to cubic and the quartic equations.

立方和四次方程的解法

Even today it's illegal to use some numbers for different reasons.

即使到了今天，有些數字仍因為 不同原因而不能合法使用

有些是因為它們代表的東西而被禁止

Some are banned because of what they represent.

For example, governments have prohibited the display of numbers

比如，政府禁止展示一些

that have symbolic meaning,

具象徵意義的數字

such as the date of a revolution

像是革命的日期

or connections to oppositional political figures or parties.

或是與反政府的人有關聯的數字

Other numbers are potentially illegal because of the information they carry.

另外還有些是因其所含的信息 而被視作非法

Just about any information,

幾乎任何資訊

whether text,

不管是文字

image,

圖像

video,

or executable programs can be translated into a string of numbers.

影像

還是執行計劃都可以 被翻譯成一串數字

But this means that protected information,

但這代表受保護的資訊

whether copyrights,

比如版權

proprietary materials,

產權文件

or state secrets

還是國家機密等

can also be represented as numbers,

也都可以用數字來代表

so possessing or publishing these numbers may be treated as a criminal offense.

所以掌握或發佈這些數字 都可能被視為犯罪

This idea gathered attention in 2001

這種想法在 2001 年引起了注意

when code that could be used to decrypt DVDs

因為當時用於解密 DVD 的代碼

was widely shared and distributed in the form of a large prime number.

以一種大質數的形式 被廣泛分享和發佈

The idea of illegal numbers may sound absurd,

非法數字的概念聽起來可能很荒謬

but like words,

但就如文字一樣

written numbers are a way of expressing concepts and information.

數字也是一種表達概念和資訊的方法

And in a world where calculations and algorithms

在一個計算和算法

shape more and more of our lives,

越來越塑造我們生活的世界裡

the mathematician's pencil grows stronger by the day.

數學家的筆也會變得日益強大