was forced into a cruel challenge by a corrupt lord.

被貪腐的君王逼迫要參加一殘酷的挑戰。

William's son was to be executed

威廉的兒子會被處決，

unless William could shoot an apple off his head.

除非威廉可以射到在他頭上的蘋果。

William succeeded, but let's imagine two variations on the tale.

威廉成功了，但讓我們來想像看看這故事的兩個不同可能。

In the first variation,

第一種情形，

the lord hires a bandit to steal William's trusty crossbow,

君王雇用一名強盜去偷威廉慣用信賴的弩，

so he is forced to borrow an inferior one from a peasant.

因此他被迫從農夫那借一次等的弓。

However, the borrowed crossbow isn't adjusted perfectly,

然而，借來的弩並沒有被很完美地調整，

and William finds that his practice shots

且威廉發現他的試射

cluster in a tight spread beneath the bullseye.

都集中在靶心下面。

Fortunately, he has time to correct for it before it's too late.

幸運地，在一切太遲之前他有時間做修正。

Variation two:

第二種情形：

William begins to doubt his skills in the long hours before the challenge

威廉在挑戰前的漫長時間裡，開始質疑自己的技術

and his hand develops a tremor.

且他的手開始顫抖。

His practice shots still cluster around the apple

他的試射仍然聚集在蘋果周圍，

but in a random pattern.

但是散佈的很隨機。

Occasionally, he hits the apple,

偶然，他也能擊中蘋果，

but with the wobble, there is no guarantee of a bullseye.

但隨著搖晃，並沒有辦法保證正中靶心。

He must settle his nervous hand

他必須使他緊張的手平靜

and restore the certainty in his aim to save his son.

為了拯救他的兒子，他必須找回他的命中率。

At the heart of these variations are two terms often used interchangeably:

這些變化中的核心，是兩個很常被互相替換的單字：

accuracy and precision.

精密度和準確度。

The distinction between the two

這兩者間的區分

is actually critical for many scientific endeavours.

實際上對許多科學努力至關重要。

Accuracy involves how close you come to the correct result.

精度牽扯到你離正確的結果多近。

Your accuracy improves with tools that are calibrated correctly

隨著工具被準確地調教，你的精度會提升

and that you're well-trained on.

你有受到好好的訓練也會。

Precision, on the other hand,

另一方面，準度

is how consistently you can get that result using the same method.

是你用同一種方式得到的結果有多高的一致性

Your precision improves with more finely incremented tools that require less estimation.

隨著更多更精緻的工具的增加，其講求更少的估計，你的準度隨之提升。

The story of the stolen crossbow was one of precision without accuracy.

弩被偷的故事主要關乎準度，而非精度。

William got the same wrong result each time he fired.

威廉在每次射擊後得到同樣的錯誤結果。

The variation with the shaky hand was one of accuracy without precision.

而關於手搖晃的情形，則是關乎精度而非準度的。

William's bolts clustered around the correct result,

威廉的靶聚集在正確結果周圍，

but without certainty of a bullseye for any given shot.

但在每一次的射擊中，缺乏正中準心的把握。

You can probably get away with low accuracy

對於日常生活，低精度

or low precision in everyday tasks.

與低準度是不會有太大影響

But engineers and researchers often require accuracy

但是工程師和研究人員時常要求有微觀水平水準的準確性，

on microscopic levels with a high certainty of being right every time.

必須有高度把握每次都正確。

Factories and labs increase precision

工廠和實驗室透過更好的設備及更精細的製程

through better equipment and more detailed procedures.

提升準度。

These improvements can be expensive, so managers must decide

這樣的改進可能所費不貲，因此主管必須決定

what the acceptable uncertainty for each project is.

每個專案中的不確定性能被接受的程度。

However, investments in precision

然而，在準度上面投資

can take us beyond what was previously possible,

可以帶我們超越先前的可能性，

even as far as Mars.

甚至可以帶領我們到火星。

It may surprise you that NASA does not know exactly where

可能會令你震驚的是，國際太空總署並不知道

their probes are going to touch down on another planet.

他們的探測器在另一顆星球確實的著陸地點。

Predicting where they will land requires extensive calculations fed by measurements

預測他們的著陸點需要使用測量結果做多方面的計算

that don't always have a precise answer.

其不總是有準確的答案

How does the Martian atmosphere's density change at different elevations?

火星的大氣密度如何在不同高度發生變化？

What angle will the probe hit the atmosphere at?

探測器會以什麼角度進入大氣？

What will be the speed of the probe upon entry?

探測器進入大氣前的速度會是多少？

Computer simulators run thousands of different landing scenarios,

電腦模擬跑出上千種不同的著陸情境，

mixing and matching values for all of the variables.

混和並配對這些值，以得到所有的可能性。

Weighing all the possibilities,

衡量所有的可能性，

the computer spits out the potential area of impact in the form of a landing ellipse.

電腦會以著陸橢圓的形式算出所有潛在的衝擊區域

In 1976, the landing ellipse for the Mars Viking Lander

在1976年，維京一號火星登陸器的著陸橢圓

was 62 x 174 miles, nearly the area of New Jersey.

尺寸為 62 x 174 英里，其大小接近紐澤西州。

With such a limitation,

在這樣的限制下，

NASA had to ignore many interesting but risky landing areas.

NASA 不得不忽視許多有趣但有風險的著陸區。

Since then, new information about the Martian atmosphere,

從那時開始，關於火星大氣的新資訊

improved spacecraft technology,

改進了太空科技，

and more powerful computer simulations have drastically reduced uncertainty.

且更多強大的電腦模擬徹底地降低了不確定性。

In 2012, the landing ellipse for the Curiosity Lander

在2012年，好奇號的著陸橢圓

was only 4 miles wide by 12 miles long,

只有4英里寬，12英里長，

an area more than 200 times smaller than Viking's.

此尺寸比維京1號的小超過200倍。

This allowed NASA to target a specific spot in Gale Crater,

這讓NASA可以鎖定蓋爾撞擊坑上一特定的點，

a previously un-landable area of high scientific interest.

這是先前無法登陸，但有高度科學重要性的區域。

While we ultimately strive for accuracy,

當我們最終為了精度努力，

precision reflects our certainty of reliably achieving it.

準度反映著我們有把握實現的確定性。

With these two principles in mind,

只要在心中記住這兩個主要的原則，

we can shoot for the stars

我們可以射中星星

and be confident of hitting them every time.

並有信心每一次都可以擊中。