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数学是怎么为海上的船导航的? – 译学馆
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数学是怎么为海上的船导航的?

How does math guide our ships at sea? - George Christoph

你可以想象,400年前
As you can imagine, 400 years ago,
在外海航行是一件很难的事情。
navigating the open ocean was difficult.
风和洋流会使船偏离航向
The winds and currents pushed and pulled ships off course,
所以水手们通过他们离开的港口位置来辨别方向
and so sailors based their directions on the port they left,
试图去精确地记录船的航行方向及距离
attempting to maintain an accurate record of the ship’s direction and the distance sailed.
这一过程被称为死亡计算
This process was known as dead reckoning,
仅仅半度的偏差很可能导致船只恰好错过了在海平面数英里之外的岛屿
because being just half a degree off could result in sailing right past the island that lay several miles just over the horizon.
很容易犯这样的错误
This was an easy mistake to make.
值得庆幸的是三个发明让现代航海成为了可能
Thankfully, three inventions made modern navigation possible:
六分仪,钟表,和能够满足快速简单计算的数学
sextants, clocks and the mathematics necessary to perform the required calculations quickly and easily.
所有的发明都很重要,没有正确的方法与工具,很多水手不愿意远航出海。
All are important. Without the right tools, many sailors would be reluctant to sail too far from the sight of land.
约翰伯德是伦敦的一名设备制造者
John Bird, an instrument maker in London,
他制造出了第一个可以精确测量太阳和海平面之间角度的装置
made the first device that could measure the angle between the sun and the horizon during the day,
这种装置就是六分仪
called a sextant.
知道这个角度非常重要,因为可以用来与同一时间出现在英格兰的角度相比较。
Knowing this angle was important, because it could be compared to the angle back in England at the exact same time.
通过比较这两个角度可以确定船所在位置的经度。
Comparing these two angles was necessary to determine the longitude of the ship.
接下来谈谈钟表。
Clocks came next.
在1761年,哈里森约翰,英国的制表人兼木匠,
In 1761, John Harrison, an English clockmaker and carpenter,
制造出了一个能在海上保持精准时间的钟表。
built a clock that could keep accurate time at sea.
可以在恶劣的条件下 摇摆、偏航的甲板上维持精确结果的计时器
The timepiece that could maintain accurate time while on a pitching, yawing deck in harsh conditions
知道回英格兰的时间是有必要的
was necessary in order to know the time back in England.
不过有一个条件
There was one catch though:
因为这样的手表是手工制作的,所以很昂贵
since such a timepiece was handmade, it was very expensive.
所以采用月历计时并精确计算的方法被广泛采用以降低成本
So an alternate method using lunar measurements and intense calculations was often used to cut costs.
这种定位船只位置的计算方法往往耗费几个小时
The calculations to determine a ship’s location for each measurement could take hours.
但是除非水手们会使用这些工具来确定位置否则六分仪和钟表都是没用的。
But sextants and clocks weren’t useful unless sailors could use these tools to determine their position.
幸运的是,在1600s,一个业余数学家已经发明了这一时无两的部分
Fortunately, in the 1600s, an amateur mathematician had invented the missing piece.
约翰内珀在他苏格兰城堡里花费了超过20年的时间发展了一种计算工具,对数。
John Napier toiled for more than 20 years in his castle in Scotland to develop logarithms, a calculation device.
内珀的对数思想包括1比e和常数10的七次方
Napier’s ideas on logarithms involved the form of one over E and the constant 10 to the seventh power.
在17世纪早期,代数还没有得到很好的发展。
Algebra in the early 1600s was not fully developed,
内珀的对数理论认为1的对数不是0
and Napier’s logarithm of one did not equal zero.
这与计算以10为底的对数相比并没有让计算更加方便
This made the calculations much less convenient than logarithms with a base of 10.
亨利·布里格斯是格雷沙姆大学的著名数学家
Henry Briggs, a famous mathematician at Gresham College in London,
在1614年读了内珀的著作后,他于第二年踏上了去往爱丁堡的路途。
read Napier’s work in 1614, and the following year made the long journey to Edinburgh to meet Napier.
Briggs在没有通知内珀的情况下就出现在了他城堡的门前。
Briggs showed up unannounced at Napier’s castle door
并建议约翰将对数的底和形式变得更加简单一些
and suggested that John switch the base and form of his logarithms into something much simpler.
他们一直同意以10为底1的对数是0
They both agreed that a base of 10 with the log of one equal to zero
这将大大简化日常计算
would greatly simplify everyday calculations.
今天我们将它记为布里格斯常用对数
Today we remember these as Briggs Common Logarithms.
直到20世纪电子计算器的发展
Until the development of electric calculating machines in the 20th century,
涉及乘 除 幂及根的情况计算情况
any calculations involving multiplication, division, powers, and extraction of roots with large and small numbers
都可以用对数解决
were done using logarithms.
对数的发展不仅是数学史史上的一步
The history of logarithms isn’t just a lesson in math.
在航海导航中有着至关重要的作用
There were many players responsible for successful navigation.
对工具制造者,天文学家,数学家都是如此
Instrument makers, astronomers, mathematicians,
水手更是受益匪浅
and of course sailors.
创造力不仅是在一个领悟做深入研究
Creativity isn’t only about going deep into one’s field of work,
交叉领悟同样重要
it’s about cross-pollination between disciplines too.

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