## 60% Hotter

Posted by Neal on October 25, 2007

A few years ago, I wrote about phrases like *ten times less*, and how something like this makes sense only if you interpret is as something like, “one tenth as much”. This week, Jan Freeman writes about the same issue in her column, and notes that not only is the fractional interpretation easily understood; people have been saying “X times less” to mean “1/X as much” for at least two centuries. Nevertheless, she warns that it is still possible to make numerical comparisons that make no sense, and gives some examples. To them, let me add these, which I got from Doug’s DVD of *Before the Dinosaurs: Walking with Monsters*.

In the segment on the early Permian Period, it states that the average global temperature was “20% colder than today.” In the segment on the late Permian Period, it states that the average global temperature was “60% hotter than today.” Before I say more about these statements, let me talk about measuring length. To say something is X% longer or shorter than something else is not a problem, whether you’re measuring in inches, centimeters, or anything else. You add or subtract X% to or from the original number, and it doesn’t matter whether the number is 1 inch or 2.54 centimeters because both scales are starting from the same zero, an agreed-upon absolute minimum length.

But unless you’re using the Kelvin scale, where absolute zero really is zero, it doesn’t make sense to make any comparison by multiplying the degrees by some fraction or percentage. If the temperature were 0 degrees Celsius, then 20% colder or 60% hotter would still be 0 degrees Celsius. But take the same temperature and name it with the Kelvin scale — 273.15 kelvin — and then 20% colder and 60% hotter are (respectively) 218.52 kelvin and 437.04 kelvin. The video doesn’t say which temperature scale the writers have in mind, but I’m guessing it’s not Kelvin. If it is, please disregard this post.

## Philip Whitman said

You are correct. When you are saying something is 20% warmer or colder than something else, you have to use an absolute temperature scale to represent proportonal accuracy, either degrees Kelvin (a Kelvin degree is equal to a Centigrade degree, but the zero is at a different place on the scale) or a Rankine degree (a Rankine degree is equal to a Fahenrenheit degree, but the zero is at a different place on the scale).

## Neal said

I never realized there was a scale with Fahrenheit-sized degrees with zero at absolute zero. I wonder why the nifty online temperature conversion calculator I found didn’t bother to include it.