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As the story goes,
the legendary marksman William Tell
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was forced into a cruel challenge
by a corrupt lord.
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William's son was to be executed
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unless William could shoot
an apple off his head.
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William succeeded, but let's imagine
two variations on the tale.
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In the first variation,
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the lord hires a bandit to steal
William's trusty crossbow,
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so he is forced to borrow
an inferior one from a peasant.
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However, the borrowed crossbow
isn't adjusted perfectly,
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and William finds that his practice shots
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cluster in a tight spread
beneath the bullseye.
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Fortunately, he has time
to correct for it before its too late.
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Variation two:
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William begins to doubt his skills
in the long hours before the challenge
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and his hand develops a tremor.
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His practice shots still cluster
around the apple
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but in a random pattern.
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Occasionally, he hits the apple,
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but with the wobble,
there is no guarantee of a bullseye.
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He must settle his nervous hand
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and restore the certainty in his aim
to save his son.
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At the heart of these variations
are two terms often used interchangeably:
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accuracy and precision.
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The distinction between the two
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is actually critical
for many scientific endeavours.
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Accuracy involves how close you come
to the correct result.
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Your accuracy improves with tools
that are calibrated correctly
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and that you're well trained on.
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Precision, on the other hand,
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is how consistently you can get
that result using the same method.
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Your precision improves
with more finely incremented tools
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that require less estimation.
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The story of the stolen crossbow
was one of precision without accuracy.
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William got the same wrong result
each time he fired.
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The variation with the shaky hand
was one of accuracy without precision.
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William's bolts clustered
around the correct result,
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but without certainty of a bullseye
for any given shot.
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You can probably get away
with low accuracy
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or low precision in everyday tasks.
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But engineers and researchers
often require accuracy
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on microscopic levels with
a high certainty of being right everytime.
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Factories and labs increase precision
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through better equipment
and more detailed procedures.
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These improvements can be expensive,
so managers must decide
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what the acceptable uncertainty
for each project is.
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However, investments in precision
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can take us beyond
what was previously possible,
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even as far as Mars.
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It may surprise you that NASA
does not know exactly where
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their probes are going to touch down
on another planet.
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Predicting where they will land
requires extensive calculations
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fed by measurements
that don't always have a precise answer.
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How does the Martian atmosphere's density
change at different elevations?
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What angle will the probe
hit the atmosphere at?
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What will be the speed
of the probe upon entry?
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Computer simulators run thousands
of different landing scenarios,
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mixing and matching values
for all of the variables.
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Weighing all the possibilities,
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the computer spits out
the potential area of impact
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in the form of a landing ellipse.
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In 1976, the landing ellipse
for the Mars Viking Lander
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was 62 x 174 miles,
nearly the area of New Jersey.
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With such a limitation,
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NASA had to ignore many interesting
but risky landing areas.
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Since then, new information
about the Martian atmosphere,
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improved spacecraft technology,
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and more powerful computer simulations
have drastically reduced uncertainty.
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In 2012, the landing ellipse
for the Curiosity Lander
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was only 4 miles wide by 12 miles long,
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an area more than 200 times
smaller than Viking's.
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This allowed NASA to target
a specific spot in Gale Crater,
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a previously un-landable area
of high scientific interest.
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While we ultimately strive for accuracy,
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precision reflects our certainty
of reliably achieving it.
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With these two principles in mind,
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we can shoot for the stars
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and be confident
of hitting them every time.