If it’s zero degrees outside and it becomes twice as cold it was before, what is the temperature?
Usually it’s presented as a joke. I’d like to consider some alternative interpretations.
1) It could literally mean the number denoting temperature divided by two. This has a number of unfortunate features. For one, it depends on the temperature scale. Half of zero is zero, but if you’re at zero Celsius you’re not at zero Fahrenheit. Worse, if the temperature is less than zero then half the temperature is going to be hotter.
2) It could mean the number for the temperature divided by two, but only in the Kelvin scale. Since it’s not possible to drop below absolute zero, you don’t have to worry about half the temperature being warmer. The scale is a little inconvenient though – half of room temperature in Kelvin is colder than dry ice.
3) It could mean the average speed of the gas molecules in air divided by two. Unfortunately this means the number for temperature actually drops by a factor of 4 on the Kelvin scale.
4) It could mean half of the thermal radiative power output via the Stefan-Boltzmann law. Twice as cold means a Kelvin temperature falling by a factor of roughly 0.84, which would mean a day at the freezing point of water falls to negative 46 degrees Fahrenheit / negative 43 Celsius.
I think the last one is my favorite, as it keeps the temperatures human-scale. It’s a little contrived though.
Comments? I’d love to hear if you have any suggestions for better interpretations.