Death, taxes and measurement uncertainty

“In this world, nothing can be certain except death and taxes.” Ironically, that includes the origin of this famous quote.

It’s attributed to Benjamin Franklin, the great American statesman, scientist and signatory of the United States Declaration of Independence. Historians know Franklin used those words. We have it his 1789 letter to French physicist Jean-Baptiste Le Roy. He was a true intellectual and a polymath, the sort of man who made scientific discoveries before breakfast. He probably coined phrases like that all the time, but can we be certain he invented this one?

The answer is no. We don’t know for sure. He may have picked it up from someone else. Perhaps it was from a snippet of an overheard conversation or a debate between his fellow scholars. A little research reveals Daniel Defoe used a very similar phrase 63 years earlier. But that doesn’t give us a greater degree of certainty, Defoe may have borrowed it himself. The further back in time we go, the more uncertain we become. There are fewer records from back then and those that do exist are less reliable.

A white statue of Benjamin Franklin

The Benjamin Franklin national memorial located at the Franklin Institute, Philadelphia, PA, USA

We are surrounded by uncertainty

But what’s all this got to do with metrology? We are surrounded by uncertainty. It’s one of the defining features of our lives and the world around us. Quite a statement, but it’s easy enough to prove. Just pause for a minute and imagine a world without it.

The concept of uncertainty has affected the way we speak. When we say “more or less”, “give or take”, “in the ball park” we are expressing uncertainty. In mathematics we even have a special symbol for uncertainty. It’s the plus sign with a minus under it (±).

In science and industry, it’s the metrologists’ job to understand, quantify, and account for uncertainty. They are like cartographers charting a vast ocean of uncertainty, and somehow, against all odds, we arrive at our destination.

In metrology, 3 is a magic number…

Every measurement is subject to uncertainty, that’s why we say “measure thrice, cut once”. There’s a good deal of sense in that statement. In metrology, 3 is a magic number. A single measurement is subject to so much uncertainty, we need a second one to confirm it. If the second measurement disagrees with the first, then a third will tell us which is the closest to the true value.

In fact, 3 is a minimum. For a much better level of certainty, we need an average of many results. The more the better. According to the NPL (National Physical Laboratory), the ideal would be to find the mean from an infinite set of values (Imagine trying to square that with the boss). In reality a good number is 10, and it makes the sums easier. More results give better certainty, but it takes greater effort and with diminishing returns.

Where does uncertainty come from?

Being able to quantify uncertainty is one of the most important jobs a metrologist can do. A measurement is only complete if it comes with a statement of uncertainty. Understanding that means taking a step back and working out where the uncertainty comes from. There are many sources.

Think about a person playing a game of Golf. The chances of an average player scoring a hole-in-one on a par 3 hole are 1 in 12,750. Tough odds, I’m sure you’ll agree. But what about the same player repeating the feat during the same round? You’ve got the same club, the same ball, on the same day, same course.

A golf player taking a shot on the fairway

The odds are… wait for it… 1 in 162,562,500 (give or take).

That means if you lived for 100 years, you’d have to play more than 4000 games of golf every day to achieve it (presumably you’d be quite a good golfer after that amount of practice). With so many factors the same, the club, the ball, the golfer, why such bad odds?

Uncertainty can come from almost anywhere, especially on a breezy 18 holes. For a start, there’s the measuring process and the instrument itself. On a golf course that might be as primitive as licking your finger and sticking it into the air to check the wind direction.

The measurand (that’s the thing being measured) can be a source of uncertainty itself. Some things don’t stay the same long enough to measure. Imagine trying to measure an ice cube in warm room. Returning to our golf example, wind speed and direction are never the same for long. There are imported uncertainties (instrument calibration also has an element of uncertainty which you need to factor into your measurements).

Note: The NPL is quick to point out that an uncalibrated machine has far greater uncertainty.

There’s operator skill to consider, sampling issues (are your measurements representative) and the environment (temperature, humidity, air pressure for example). Out on the golf course, miles from the club house, the environment can make a very big difference (side note: on your next coffee break, google “animal encounters on the golf course” for some amusing examples of this).

Measurement uncertainty really can come from anywhere, even the most unexpected places. If you want to learn more about this topic, the NPL has a handy guide available free of charge here. If you enjoyed reading this blog post, check out the previous one here: What’s the difference between accuracy and precision?

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