This warmth has been the source of some irritating newspaper headlines:

The Mirror has a headline with: “temperatures soar to twice the average for March”

BBC New reports that the Daily Telegraph (which possibly should know better) says : “a barbecue weekend is in prospect, with temperatures double the usual for March.”No, the temperature hasn’t doubled. If it

*had*doubled, if would be nearer 300°C!

If something doubles in size, units don’t matter. Something can double in length from 1 metre to 2 metres, or equally from 100 cm to 200 cm, or even from 3.28 feet to 6.56 feet.

0°C, 0°F and 0K are all different temperatures (yes, there is no degree symbol when using the absolute kelvin units) |

Things are even weirder if we used the Delisle scale (an obsolete and peculiar temperature scale where the freezing point of water is 150°D, and the boiling point is 0°D, so

*higher*numbers are

*colder*temperatures). 10°C is 135°D; “doubling” this gives 270°D, which is -80°C, whereas 20°C is 120°D. (Although it may seem weird for numbers to go down as temperatures go up, Delisle was not alone: this is the direction the original Celsius scale went, with freezing being 100, and boiling being 0.)

So why does doubling work for lengths, but not for temperatures? What’s different about the temperatures is that they have an

*arbitrary zero*point. 0 metres means no length, but 0°C doesn’t mean no heat. There’s nothing special, temperature-wise, about the freezing point of water; it’s an arbitrary zero point (as evidenced by the fact that the Fahrenheit scale chooses a completely different arbitrary zero point).

To be able to do the multiplication and get a meaningful doubling, we need a true zero point for temperature, the absolute temperature, measured on the Kelvin scale (or the Rankine scale if you prefer those good old small Fahrenheit-sized degrees). There is another condition: the scale needs to be linear (rather than say logarithmic, like acidity, sound loudness, or star brightness); temperature is a linear scale, so that’s okay. (If you want to play around with temperature scales, there’s a nice temperature units converter on the web, although it says °K, when it should be just K).

Let’s look at that doubling calculation again, now using an absolute scale. 10°C is 283K (rounded to the nearest degree, since that 10°C isn’t supposed to be very precise). Then 283K x 2 = 566K – this time, a meaningful calculation. And 566K is 293°C, which is worryingly hot for March!

The same data, graphed with an arbitrary zero and a true zero on the y axis |

This trick of an arbitrary zero leading to nonsensical comparisons like “temperatures double” is used all the time in “presentation graphics” (often in newspapers!) with misleading

*y*axes. If the

*y*axis doesn’t show a true zero (or worse yet, is unlabelled), then beware!

Note that we

*can*do this kind of multiplication if we are talking about temperature

*differences*, no matter what the scale. A

*rise*of 20°C

*is*twice a rise of 10°C. (A rise of 10°C is a rise of 18°F; a rise of 20°C is a rise of 36°F ). Rises work this way because a rise of 0°C, which is also a rise of 0°F, is a true zero.

However, newspapers can even mangle this! Several decades ago (although I doubt things have improved today) I saw a newspaper report that included the immortal phrase: “a rise of 1°C (33°F)”.

## No comments:

## Post a Comment