Writing, logic and numbers (2)

In a recent post, I discussed the need to pay close attention to logic when writing about numbers, especially when comparing numbers. In that post I explained, with examples, how to say that one number is larger than another.

Today’s post looks in the opposite direction: how to say that one number is smaller than another.

Example

An article about the 2008 presidential campaign carried the headline, “McCain’s Crowd Disturbingly Small, Ten Times Less Than Planned For.”

In the text of the story we learn that the crowd consisted of about 1,000 people and that campaign organizers had expected ten times that number of people. In other words, 10,000 were planned for and 1,000 showed up.

Therefore the headline, in effect, says that 1,000 is “Ten Times Less Than” 10,000. But this is illogical. Consider:

One times 10,000 = 10,000.
Ten times 10,000 = 100,000.
Therefore, ten times less than 10,000 = 10,000 minus 100,000 = negative 90,000.

The idea of negative people is absurd. It would be correct to say:

McCain’s Crowd Disturbingly Small, One-Tenth the Size Planned For.

It would also be correct to say:

McCain’s Crowd Disturbingly Small, 0.90 Times Less Than Planned For.

But for numbers less than 1, most people are more comfortable with percentages. So:

McCain’s Crowd Disturbingly Small, 90% Less Than Planned for.

The Takeaway: When writing, always use logic and numbers carefully. Remember that the phrase times less than and the phrase less than are not interchangeable.