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

Transcriber: tom carter Reviewer: Bedirhan Cinar

翻译人员: Minji Seo 校对人员: Yolanda Zhang

As you can imagine, 400 years ago,

如同你想象的那样，400 年前，

在一望无际的大海上航行， 是件十分困难的事。

navigating the open ocean was difficult.

The winds and currents pushed and pulled ships off course,

风和海浪把船往前推、 也会往后拉，

and so sailors based their directions on the port they left,

所以水手需要借由出航前的方向感，

attempting to maintain an accurate record of the ship's direction and the distance sailed.

尝试精准地记录 船的方向和航行距离。

This process was known as dead reckoning,

这个过程被称做航位推算 （直译：死亡估计）。

because being just half a degree off could result in sailing right past the island that lay several miles just over the horizon.

因为半度的误差都会导致和小岛擦身而过， 尽管这小岛就在地平线另一端而已。

This was an easy mistake to make.

这是很容易犯的错误。

Thankfully, three inventions made modern navigation possible:

所幸，有三样发明 让现代航海变为可能。

sextants, clocks and the mathematics necessary to perform the required calculations quickly and easily.

六分仪、时钟、以及 能提供快速简单算法的数学理论。

All are important. Without the right tools, many sailors would be reluctant to sail too far from the sight of land.

三者都很重要。没有正确的工具， 水手们就会对太远的航行感到望而生畏。

John Bird, an instrument maker in London,

John Bird，一位伦敦的工具制造者，

made the first device that could measure the angle between the sun and the horizon during the day,

制造了第一个可以在白天 测量太阳仰角的仪器，

called a sextant.

叫做六分仪。

知道这个仰角很重要，可以将它与 同时间在英国观察到的太阳仰角进行比较。

Knowing this angle was important, because it could be compared to the angle back in England at the exact same time.

Comparing these two angles was necessary to determine the longitude of the ship.

比较的结果对定位 船只所在的经度有着至关重要的作用。

Clocks came next.

接着时钟问世了。

In 1761, John Harrison, an English clockmaker and carpenter,

1761年时，John Harrison，一位英国的 时钟制造者以及木匠，

built a clock that could keep accurate time at sea.

建造了一具在海上也能 保持时间精准的时钟。

The timepiece that could maintain accurate time while on a pitching, yawing deck in harsh conditions

这个就算在船只左右颠簸的恶劣环境下、 也能维持正确时间的定时器，

was necessary in order to know the time back in England.

对于知道何时返航回英国十分必要。

There was one catch though:

但有一个隐忧：

since such a timepiece was handmade, it was very expensive.

因为这样的定时器是手工制造的， 所以非常昂贵。

So an alternate method using lunar measurements and intense calculations was often used to cut costs.

因此，为了节省开销，月象观测配合 大量计算就成了常见的替代方案。

The calculations to determine a ship's location for each measurement could take hours.

利用计算来判断船所在的位置， 要花上好几小时。

But sextants and clocks weren't useful unless sailors could use these tools to determine their position.

然而在水手们学会利用六分仪和时钟 来判断方位之前，它们并没有太大用处。

Fortunately, in the 1600s, an amateur mathematician had invented the missing piece.

所幸，在十七世纪，一位业余数学家 补足了那些缺陷。

John Napier toiled for more than 20 years in his castle in Scotland to develop logarithms, a calculation device.

John Napier 在他位于苏格兰的城堡中 钻研 20 余年，发展了“对数”这个计算工具。

Napier's ideas on logarithms involved the form of one over E and the constant 10 to the seventh power.

Napier 关于对数的想法涉及 自然对数 e 的倒数和 10 的7次方这个常数。

Algebra in the early 1600s was not fully developed,

代数在十七世纪并还没有得到完全发展，

and Napier's logarithm of one did not equal zero.

而 Napier 的对数代入 1 时， 并不等于 0。

This made the calculations much less convenient than logarithms with a base of 10.

这使得它的计算， 比起以10为底的对数麻烦许多。

Henry Briggs, a famous mathematician at Gresham College in London,

Henry Briggs，一位伦敦格雷沙姆学院 有名的数学家,

read Napier's work in 1614, and the following year made the long journey to Edinburgh to meet Napier.

读了 Napier 在 1614 年的著作后，来年就 不远千里地到爱丁堡拜访 Napier。

Briggs showed up unannounced at Napier's castle door

Briggs 毫无征兆地出现在 Napier 的城堡门口，

and suggested that John switch the base and form of his logarithms into something much simpler.

然后建议他将原本的底数 换成较简单的数字。

They both agreed that a base of 10 with the log of one equal to zero

他们一致认为以10为底、 并将 log(1) 设为 0

would greatly simplify everyday calculations.

会大大简化日常所需的计算。

Today we remember these as Briggs Common Logarithms.

这就是我们今日所熟知的 Briggs 常用对数。

Until the development of electric calculating machines in the 20th century,

一直到二十世纪 发展出电子计算器之前,

any calculations involving multiplication, division, powers, and extraction of roots with large and small numbers

所有涉及大小数字的乘法、除法、 指数以及根号这些运算

were done using logarithms.

都离不开对数。

The history of logarithms isn't just a lesson in math.

对数的历史并不只是一堂数学课。

There were many players responsible for successful navigation.

有许多人对成功的航海技术 做出了贡献。

Instrument makers, astronomers, mathematicians,

工具制造者、天文学家、数学家、

and of course sailors.

当然，还有水手们。

Creativity isn't only about going deep into one's field of work,

创造力并不只是在 自己的领域内不断深入，

it's about cross-pollination between disciplines too.

也应该是不同领域之间的相辅相成。