Central principles

The meaning of zero

Doesn’t zero just mean ‘nothing’?

Measurements such as length, mass, liquid volume and capacity, and time intervals, are examples of what are called ratio scales. These are scales where the ratio of two quantities has a real meaning. For example, if a child is 90 cm tall and an adult is 180 cm tall, we can legitimately compare the two heights by means of ratio, stating that the adult is twice as tall as the child. Similarly, we can compare masses, capacities and time intervals by ratio.

However, recorded time is not like this: it would make no sense to compare, say, 6 o’clock with 2 o’clock by saying that one is three times the other. This is an example of what is called an interval scale. Comparisons can only be made by reference to the difference (the interval) between two measurements, for example, saying that 6 o’clock is 4 hours later than 2 o’clock. Of course, you can compare the measurements in a ratio scale by reference to difference (for example, the adult is 20 cm taller than the child), but the point about an interval scale is that you cannot do it by ratio, you can only use difference.

Temperature measured in oC (the Celsius scale) or oF (the Fahrenheit scale) is another example of an interval scale. It would be meaningless to assert that 15 oC is three times as hot as 5 oC; the two temperatures should be compared by their difference.

The interesting mathematical point here is that the thing that really distinguishes a ratio scale from an interval scale is that in a ratio scale the zero means nothing, but in an interval scale it does not! When the recorded time is ‘zero hours’, time has not disappeared. When the temperature is ‘zero degrees’, there is still a temperature out there and we can feel it! But a length of ‘zero metres’ is no length, a mass of ‘zero grams’ is nothing: a bottle holding ‘zero millilitres’ of wine is empty; a time interval of ‘zero seconds’ is no time at all. Think about it!