Monday, June 29, 2009

Writing, logic and numbers (3)

If we wish to keep our writing clear, we have to be careful when writing about numbers. To do that, we don’t need to acquire a deeper knowledge of mathematics; all we need to do is take a few moments to pay close attention to the numbers we are discussing.

This post is specifically about numbers in the form of ratios. A dictionary definition of ratio is:

“A relationship between two quantities, normally expressed as the quotient of one divided by the other: The ratio of 7 to 4 is written 7:4 or 7/4.”

When writing about ratios, the most important thing is to get the logic right; that is, correctly match the numbers to the words. Unfortunately, we sometimes fail to do this.


For example, here is an excerpt from an article published this morning:

“Economics is well known as the Dismal Science. In my opinion it is more dismal than ever as the world economy is being looted, pillaged, and run into the ground by a group of frauds and hucksters. The intellectual cover for this heist is being provided by people who call themselves economists but are really propagandists. Perhaps in these times the best quantitative measure of health for a society is the ration of true economists to propagandists. I would estimate that it is more than 1 to a 1000 today reflecting the current dire circumstances.”

The word ration is probably a typographical error; the writer likely means ratio. Also, he does not need the word a before 1000. And, in formal writing such as this, he should use the form 1:1000 or 1/1000.

But, setting all those details aside, let’s take a look at his logic: He wishes to say that for every true economist there are one thousand propagandists. So, when he states the ratio as 1 to 1000, he has the right numbers in the right places. That is, his numbers match his words. Good.

However, he goes astray when he uses the comparative phrase more than. From the context of his remarks (he is complaining that there are too few true economists and too many propagandists), we can safely assume that he means to say that he would estimate that the ratio of true economists to propagandists is less than 1:1000.

To be clearer, he could have inverted the ratio, changing it


1 true economist to 1000 propagandists


1000 propagandists to 1 true economist

Then he could have said

I would estimate that it is more than 1000:1 today, reflecting the current dire circumstances.

This form is easier for the reader to grasp.

The Takeaway: When setting up a ratio, be careful of three things: (1) Make sure that you are matching the right numbers with the right words. For example, if you say there are “two girls for every boy,” as in the 1963 hit song, “Surf City," performed by Jan and Dean (photo), the ratio of girls to boys is 2:1. (2) When you use comparative adjectives and phrases such as higher, more than, lower, and less than, remember that you are referring to the first number in the ratio. For example, if you say, “the ratio this summer is more than 2 to 1,” or “the ratio this summer is higher,” you are saying that there are now more than two girls for every boy. (3) If you decide to invert a ratio, make sure you invert both the numbers and the words. For example, if you want to state that the Surf City ratio is “one boy for every two girls,” the ratio of boys to girls is 1:2.

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