was forced into a cruel challenge by a corrupt lord.

William's son was to be executed

unless William could shoot an apple off his head.

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

In the first variation,

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

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

However, the borrowed crossbow isn't adjusted perfectly,

and William finds that his practice shots

cluster in a tight spread beneath the bullseye.

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

Variation two:

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

and his hand develops a tremor.

His practice shots still cluster around the apple

but in a random pattern.

Occasionally, he hits the apple,

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

He must settle his nervous hand

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

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

accuracy and precision.

The distinction between the two

is actually critical for many scientific endeavours.

Accuracy involves how close you come to the correct result.

Your accuracy improves with tools that are calibrated correctly

and that you're well-trained on.

Precision, on the other hand,

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

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

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

William got the same wrong result each time he fired.

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

William's bolts clustered around the correct result,

but without certainty of a bullseye for any given shot.

You can probably get away with low accuracy

or low precision in everyday tasks.

But engineers and researchers often require accuracy

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

Factories and labs increase precision

through better equipment and more detailed procedures.

These improvements can be expensive, so managers must decide

what the acceptable uncertainty for each project is.

However, investments in precision

can take us beyond what was previously possible,

even as far as Mars.

It may surprise you that NASA does not know exactly where

their probes are going to touch down on another planet.

Predicting where they will land requires extensive calculations fed by measurements

that don't always have a precise answer.

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

What angle will the probe hit the atmosphere at?

What will be the speed of the probe upon entry?

Computer simulators run thousands of different landing scenarios,

mixing and matching values for all of the variables.

Weighing all the possibilities,

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

In 1976, the landing ellipse for the Mars Viking Lander

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

With such a limitation,

NASA had to ignore many interesting but risky landing areas.

Since then, new information about the Martian atmosphere,

improved spacecraft technology,

and more powerful computer simulations have drastically reduced uncertainty.

In 2012, the landing ellipse for the Curiosity Lander

was only 4 miles wide by 12 miles long,

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

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

a previously un-landable area of high scientific interest.

While we ultimately strive for accuracy,

precision reflects our certainty of reliably achieving it.

With these two principles in mind,

we can shoot for the stars

and be confident of hitting them every time.