Carl Friedrich Gauss Discovered Measurement Error On a Walk to School

How a simple detail in studying a path reveals the deepest statistical truths.

Thomas Willmott on Unsplash

People often think that the most amazing mathematical facts stem from them being inherently complex.

The greatest mathematician of all-time would disagree.

We all know significant figures. We know that our end calculation can’t be more accurate than our least accurate measurement.

We know that makes sense.

But why does it make sense?

Why can’t measurements be “accurate”. Why not create something to make it “exact”.

The answer came out of a boy, sometime in the late 1780s.

A poor kid from Germany, he would walk to school every morning. And walk from school back home.

One day, he started to count his steps to school. He followed a path he thought was exact.

Every time, the step count was off, just a little bit.

Curiosity getting the best of him, he looked at the philosophy of measurement itself.

We all have seen this:

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Normal distribution, also called the Gaussian distribution

Out of that tiny thought, he later developed what we know today as the normal distribution.

We also call it the “Gaussian” distribution.

Carl Friedrich Gauss discovered something wrong with observation.

He knew that every time you took a ruler to measure something, you will inherently have some “movement” in the number you choose.

In other words, something will never be exact.

Out of that tiny count of walking samples, a child bore the skeleton for observational error.

And years later, he became the forefather of error analysis, among many other things in mathematics he discovered.

So the next time you are looking at something, no matter the metric, or otherwise, you can rest assured on one thing: It is never going to be quite “exact”. Observation is always just a bit off, no matter what.

We often talk about the definitions of things we accept as solid truth, but we hardly speak about the intuition of those truths. Anytime we attempt to measure, we know we’re wrong, even if it is just by a tiny little bit.

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UC Berkeley, mathematics. Los Angeles. Long-time runner. Top writer on Quora, 100M+ total content views. New to Medium. Inquiries:

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