201612190530偏遠的島民早在著名數學家之前就發明了二進制系統

http://www.ancient-origins.net/news-evolution-human-origins/remote-islanders-invented-binary-number-system-famous-mathematician

 


Remote islanders invented binary number system before famous mathematician

偏遠的島民早在著名數學家之前就發明了二進制系統

 

Mangareva is home to just 2,000 inhabitants. The island is a tiny 18 square kilometres and is located halfway between Easter Island and Tahiti. Yet on this small, remote island, the ancient inhabitants were more mathematically advanced than the rest of Europe when they invented a numerical system for trading.

曼加瑞瓦島上居住著大約2000多名島民。這是一座僅有18平方公里的小島,坐落在復活節島和大溪地島之間。然而,在這座微不足道的偏僻小島上的居民為了進行交易而發明的數字系統甚至要比歐洲還要更加先進。

 

Research conducted last year and published in the journal Proceedings of the National Academy of Sciences, revealed that the indigenous people of the Polynesian Island invented a binary number system , similar to the one used by computers to calculate, centuries before Western mathematicians did. Andrea Bender, a cognitive scientist at the University of Bergen in Norway, and her colleague Sieghard Beller, were studying the Mangarevans when they noticed that the inhabitants had words for the numbers 1 to 10, but for numbers 20 to 80 they used a binary system, with separate, one-word terms for 20, 40, and 80. For really large numbers, they used powers of 10 up to at least 10 million.

根據於去年進行並發表在《美國國家科學院院刊》的研究,波利尼西亞群島的原住民其實發明過一種二進制數字系統,非常類似於計算機的計算方式,不過卻是早在西方數學家好幾個世紀之前。挪威卑爾根大學的認知科學家,安德烈・本德爾和她的同事西格德・貝勒在研究曼加瑞瓦人的時候發現,這些島民有1到10的數字,但從20到80他們使用的都是二進制,20,40還有80本身則有單獨的數字。對於真的非常大的數字,他們也可以使用10到至少1000萬這樣的計算方式。

 


The remote island of Mangareva. Source: Wikipedia

偏僻的曼加瑞瓦島

 

"Those were probably the numbers that were most frequent in their trading and redistribution systems," said Bender. "For that specific range, it was helpful to have these binary steps that make mental arithmetic much easier — they didn't have a writing or notational system, so they had to do everything in their mind."

“這些可能是他們的交易和分配體系裡最常見的數字了,”本德爾說。“面對特定的範圍,有了這些二進制步驟就能讓心算變得更容易——他們沒有寫作或符號系統,所以他們只能用腦袋來處理面對的問題。”

 

One of the most famous mathematicians of the 17 th century, Gottfried Wilhelm Leibniz, is known to have invented a binary numeral system. Nowadays, binary numbers – where each position is written as a 0 or 1 – form the foundation of all modern computing systems. But the study showed that the Manareva islanders were using a combined decimal and binary system which had died out by the mid-1400s.

其中一位17世紀最聲名遠播的數學家,哥特佛萊德・威廉・萊布尼茲,是眾所週知的二進制發明者。在現行的二進制下——每個數目的位置都是由0或1來表示——這構成了現代計算機系統的基礎。但現在的研究卻表明,曼加瑞瓦人其實早就在使用十進制與二進制的組合系統,但它們到了14世紀中葉就佚失了。

 


Gottfried Willhelm Leibniz

哥特佛萊德・威廉・萊布尼茲

 

The Mangarevans traded across long distances for items such as turtles, octopuses, coconut and breadfruit with people on the Marquesas Islands, Hawaii and the islands around Tahiti. It is believed that the binary system helped ancient people to keep track of their trading activities. What is more surprising is that they were able to use a complex number system without needing notation.

曼加瑞瓦人經常與馬克薩斯群島,夏威夷還有大溪地島一帶上的島民進行以海龜、章魚、椰子還有麵包果為主的遠航貿易。據說,這樣的二進制系統也有助於古人計算他們的交易活動。更讓人吃驚的是,他們能夠在完全沒有任何符號的情況下使用這套數字系統。

 

The numbering scheme may be the only known example of an extensive binary numeral system that predates Leibniz.

這可能是在萊布尼茲之前最早應用二進制數字系統的實例。

 

By April Holloway

 

 

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