The Number Museum
Americans say it is 68 degrees. Europeans say it is 20. They are both right, and they are talking about the same pleasant afternoon.
Two thermometers. Two sets of numbers. Two centuries of confusion.
But there is one temperature - just one - where the argument stops, and both scales read exactly the same.
It is bitterly, dangerously cold.
It is −40.
Our story starts with a man who made things out of glass.
Daniel Gabriel Fahrenheit was born in 1686 in Danzig (today's Gdańsk, in Poland) and spent most of his working life in the Dutch Republic, building scientific instruments. Thermometers in his day were unreliable: two of them, side by side, might disagree. Fahrenheit set out to make ones that matched - and he became one of the first to build thermometers filled with mercury.
In 1724, he described his temperature scale. He chose his fixed points with care:
Later refinements shifted things slightly - which is why body temperature is usually given today as 98.6 °F, and water boils at 212 °F.
Danzig, circa 1724. The ice and salt stayed cold enough to be useful.
Eighteen years later, in the Swedish university town of Uppsala, an astronomer had a cleaner idea.
Anders Celsius wanted a scale built on just two natural landmarks: the freezing point and the boiling point of water, with 100 steps in between. He published it in 1742. But there was a twist that surprises almost everyone.
In Celsius's original scale, water boiled at 0 and froze at 100.
It was upside down. The colder it got, the higher the number went. Nobody knows for certain why he chose it that way.
Celsius died of tuberculosis in 1744, aged just 42. Within a year or so, his scale had been flipped the right way up - 0 for freezing, 100 for boiling. The flip is most often credited to the famous Swedish naturalist Carl Linnaeus, or to Celsius's own student Mårten Strömer.
For about two centuries, it was usually called "centigrade" - meaning "a hundred steps." Only in 1948 did the scale officially take Celsius's name.
Uppsala, 1742. It took someone else to turn it around.
An accidental anagram
Fahrenheit's scale arrived in 1724. Celsius's in 1742. The two years use exactly the same four digits. And if you put either one through the famous "biggest digits minus smallest digits" trick from our 6174 page, you get there in a single step:
7421 − 1247 = 6174
So now the world had two scales, and they disagree almost everywhere. Here is why.
Between freezing and boiling, Celsius uses 100 steps. Fahrenheit uses 180 (from 32 up to 212). So every Celsius degree is a bigger step - worth 1.8 Fahrenheit degrees.
And they do not start in the same place, either. Where Celsius says 0, Fahrenheit already says 32.
It is like two ladders leaning against the same wall: one with widely spaced rungs, one with narrow ones, and their bottom rungs at different heights. On most of the wall, the rung numbers do not match.
But are there any heights where they do?
Same wall. Different rungs. One gap to close.
Let's walk down from freezing and watch the gap between the two numbers.
| °C | °F | Gap |
|---|---|---|
| 0 | 32 | Fahrenheit is 32 ahead |
| −10 | 14 | now just 24 ahead |
| −20 | −4 | 16 ahead |
| −30 | −22 | only 8 ahead |
| −40 | −40 | the gap is gone |
Every time Celsius drops 1 degree, Fahrenheit drops 1.8. So Fahrenheit closes the gap by 0.8 every degree. It starts 32 degrees ahead. And 32 ÷ 0.8 = 40.
Forty degrees below freezing, the two ladders finally meet on the same rung.
If you like algebra, here is the one line:
F = 1.8 × C + 32, and if F and C are the same number, that number has to be −40.
It is the only place they ever agree. Go colder, and they part ways again - with Fahrenheit now the lower number.
°F starts higher up the hill. Forty steps later, they are level.
−40 is not just a number on paper. For some people, it is winter.
In Yakutsk, in eastern Siberia - often called the coldest major city on Earth - the average low in January is about −40. Hundreds of thousands of people live there.
At −40, exposed skin can freeze in minutes. Breath crackles. Car tyres stiffen. Boiling water thrown into the air can burst into a cloud of ice.
And in places like this, nobody needs to ask which scale the weather forecast is using.
Yakutsk in January. The number on the sign is the same in any language.
The thermometer that gives up first
Fahrenheit's famous mercury freezes solid at about −38.8 °C (about −37.9 °F) - just short of −40. So an old mercury thermometer cannot even show the one temperature where the two scales agree. In very cold places, thermometers filled with coloured alcohol are used instead.
The world never fully settled the argument. Most countries use Celsius. The United States and a handful of others still use Fahrenheit for daily weather.
But −40 tells us something quietly important.
Scales are human inventions. Where zero sits, how big a degree is - those are choices made by people like Fahrenheit and Celsius, for their own good reasons.
The cold itself does not care. At −40, the air is exactly as cold whichever number you prefer.
And right there, where it is cold enough to freeze mercury, our two inventions briefly admit it.
The cold does not negotiate. The scales do.
−40 is one of those facts people love to share: at a party, in a classroom, in a winter weather report.
Partly because it sounds like a trick.
Partly because anyone can check it with a calculator in seconds.
And partly because it hides a tiny human drama: a Dutch instrument-maker with his salt and ice, a Swedish astronomer whose scale began upside down, and two centuries of people converting back and forth - except, just once, at the bottom of the thermometer.
They never met. But they agreed on one thing in the end.
Here is why −40 matters:
The whole story, in one cabinet drawer.
Two men, two scales, two centuries of converting.
−40 is the one temperature nobody needs to convert.
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