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.

Example

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

FROM

1 true economist to 1000 propagandists

TO

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.

The context of a document (1)

Providing context is an often-neglected part of writing. As we write and edit a document, we tend to concentrate almost all our attention on finishing the document and almost none on providing the context.

But context is crucially important: it helps your prospective readers decide whether to read or skip your document and it helps your readers better understand the content of your document.

When a prospective reader encounters your document, he wants to know the answers to several questions; for example:

Is this for me? That is, what type of reader is this document for?

What will I gain by reading this?

Is this document too elementary for me, just right for me, or too advanced for me?

What background knowledge, if any, do I need to have in order to understand the content in this document?

How does this document relate to other documents? What other documents, if any, should I read first? Is the document part of a series or collection?

Readers don’t ask these questions out loud. They may not even ask them consciously. But they do ask them, and look for the answers.

Careful writers and editors provide those answers. That is why, for example, a research paper usually begins with an abstract; a non-fiction book usually begins with an introduction; the dust jacket of a Michael Connelly novel prominently displays the name(s) of the Connelly hero(es) the novel is about; a press release includes a headline and sometimes a subhead; and most Web sites have an “about” page.

Unfortunately, many writers do a poor job of providing context – especially when writing for the Web. To illustrate how badly we often fail at providing context on the Web, I’ll show you an example, just as I encountered it and reacted to it.

Example

While doing research on verb forms, I landed on this page. From the logo in the top left corner of the page, I could see that I was on a page of Entrepreneur magazine. The page included an article that had appeared in a journal called Language, Learning & Technology. The title of the article, “Focus-on-form through collaborative scaffolding in expert-to-novice online interaction,” had a distinctly academic tone to it.

The first sentence of the article, even more laden with jargon than the title, confirmed that the article was indeed academic:

“The following discussion highlights the amount of scaffolding, the use of L1, the role of the expert that affected how the learners socially co-constructed L2 knowledge with their expert partners during synchronous CMC.”

I glanced again at the top left corner of the page. Yes, this article was appearing in Entrepreneur. But why? What could this academic, technical research have to do with entrepreneurship?

Then I looked at the line of small type above the article:

Home > Business Journals > Language, Learning & Technology

I clicked on “Business Journals” and landed on a page that introduced Entrepreneur’s database of business and trade journals. The introduction said:

“Browse our database of over 200 business and trade journals. Find up-to-date, industry-specific information on a broad range of business issues and news events.”

So, the article on “focus-on-form through collaborative scaffolding” appears on Entrepreneur’s Web site because Language, Learning & Technology, the whole journal, is on Entrepreneur’s Web site. But that still doesn’t explain how this journal would interest entrepreneurs. The journal does not seem to cover business issues or news events at all.

I scrolled down to the L page and found the listing for Language, Learning & Technology. In a Category column, the listing said, “Computers and office automation industries.”

I surfed around until I found an “about” page for the journal. Here it is. It says the journal “seeks to disseminate research … on issues related to technology and language education.”

It is possible that there are entrepreneurs who develop or market language-education technology (or would like to do so in the future) and feel the need to keep up with the kinds of research that the journal publishes. But, from working with hundreds of entrepreneurs, I know that this possibility is extremely unlikely. Most entrepreneurs are too busy to read articles in Entrepreneur, let alone articles in arcane trade journals.

I didn’t find any further context, so I made a guess:

Entrepreneur wanted to provide a helpful database of publications that may interest entrepreneurs. (I applaud this.)

Entrepreneur wanted its database to be wide-ranging. (I applaud this, too.)

But Entrepreneur’s database is so wide that it inevitably includes some arcane journals. Language, Learning & Technology is one of them.

Of course, I could be wrong. I often am. But I was forced to make a guess because neither Entrepreneur nor Language, Learning & Technology provided the context I needed. (If either did in fact provide the context, I did not find it.)

The Takeaway: Take responsibility for providing the context of the documents you write or edit. Don’t make readers guess the context; they are likely to guess wrong. Take some time to imagine the context questions your target readers may silently ask when they encounter your document. Answer those questions clearly and candidly. From decades of experience, I assure you that this effort will pay off, by gaining you more readers and preventing time-wasting confusion.

Placement of modifiers (6)

Misplaced modifiers will annoy your readers. So will dangling modifiers. So will modifiers that could be misplaced modifiers or dangling modifiers.

Here’s an example from The Wall Street Journal. In an online news alert today, the Journal reported recent decisions of the Supreme Court of the United States. The last item in the alert was this:

“Justices have yet to rule on a case involving a New Haven, Conn., decision to scrap the results of a firefighter test over race. The court is expected to release its decision by next week.”

The writer of this alert has left it up to the reader to guess which noun or verb the prepositional phrase over race modifies.

If it modifies to rule, case, decision, to scrap, or results, then over race is a misplaced modifier.

If it modifies a noun or verb that does not appear in the same sentence, then over race is a dangling modifier.

If it modifies test, which immediately precedes it in the sentence, then over race is neither a misplaced modifier nor a dangling modifier. However, the reader is left to guess the logic: what kind of test is a “test over race”?

The Takeaway: Respect your readers’ time and intelligence. Avoid misplaced modifiers and dangling modifiers. Place every modifier close to the word being modified. And be sure the logic of your modifiers is clear.

The vague antecedent (2)

Another weakness to avoid, if you want to make your writing clear, is the vague antecedent. An antecedent is a noun (a word, phrase or clause) that a pronoun refers to. The antecedent should precede the pronoun.* The antecedent should be clear, not vague. In summary: every pronoun should have an easily identifiable noun as its antecedent.

When writers leave antecedents vague, they confuse their readers. They also create unintentional humor, which can distract their readers.

The advertisement pictured above contains a good example of a vague antecedent. In the sentence at the bottom of the ad, what did the writer intend as the antecedent of the pronoun it? Why was that antecedent not immediately clear to the reader? What caused the unintentional humor?

To be clear, the writer of the ad should have written something like this:

Buying a new car? Let us detail your current car before you sell it or trade it in. After we finish, you’ll like your car so much you might even decide to keep it.

The Takeaway: Avoid vague antecedents. Every pronoun should have an easily identifiable noun (a word, phrase or clause) as its antecedent. Don’t make your readers guess which noun you mean. That’s bad manners and bad marketing.

*The English word antecedent comes from Latin for going before.

Using commas correctly (1)

When using “because” following a negative statement, be sure to use a comma before “because.” If you don’t use a comma in a construction like this, your reader may not correctly understand your meaning – at least on first reading.

Example

For example, consider this sentence:

“The idea was that if borrowers defaulted in payments on their loans, investors wouldn’t lose their money because the federal government would cover the losses.”

By failing to use a comma before “because,” the writer incorrectly implies that investors would lose their money, but that they would lose it for some reason other than that “the federal government would cover the losses.” The writer should have used a comma after “investors wouldn’t lose their money” and before “because.”

The sentence would then read:

The idea was that if borrowers defaulted in payments on their loans, investors wouldn’t lose their money, because the federal government would cover the losses.

Example

This headline is a similar example of a failure to use commas correctly:

“Biologists Won’t Meet in Louisiana Because of State Law on Teaching Evolution”

By omitting the comma, the headline writer incorrectly implies that the biologists will meet in Louisiana, but not because of that law.

The headline should have read:

Biologists Won’t Meet in Louisiana, Because of State Law on Teaching Evolution

In each of these two cases, the typical reader will read the sentence, perceive the implication as implausible, re-read the sentence, recognize that the writer should have used a comma before “because,” and finally perceive the correct meaning of the sentence.

One could argue that this is a small matter, and that almost every reader will eventually figure out the correct meaning. That may be true. But some readers will not figure it out. And some will become distracted and will stop reading. And the readers who do figure it out will assume that the writer did not know the rule or was being inconsiderate or careless. And they will know that he has wasted their time.

Why invite all those undesirable outcomes when it is so easy to do it correctly?

The Takeaway: When you are using “because” following a negative statement, use a comma before “because.” If you don’t use a comma in a construction like this, your reader may not correctly understand your meaning.

Mixed metaphors (1)

Mixed metaphors can confuse and amuse your readers. If you are aiming for clear writing, you don’t want to confuse your readers, or unintentionally amuse them. You don’t want to make them slow down to wonder why you mixed two or more metaphors. You don’t want to do anything to distract their attention from the flow of your main argument.

Definition

A mixed metaphor is a series of two or more metaphors that become incongruous when combined.

Example

For example, in an article today on the effect of the depression on Las Vegas strip clubs, the writer includes this sentence:

“And investors are not the only ones getting hammered by the softness in the bump and grind industry.”

The incongruity is that people are being “hammered” (a metaphor for “being damaged financially”) by “softness” (a metaphor for “depression”). Readers are amused by the thought of a soft hammer.

But this mixed metaphor is not only incongruous; it is also illogical. Compare it, for example, to the classic mixed metaphor “barnacles on the wheels of progress” – the incongruity is that in reality barnacles attach themselves to the hulls of ships, not to the wheels of land-based vehicles.

However, there is some logic in the metaphor: if barnacles did attach themselves to wheels, they would slow the wheeled vehicles, just as they slow ships (by adding friction).

But the strip club metaphor is illogical: the softer the softness, the less effective it would be as a hammer.

While a reader stops to think these kinds of thoughts about a mixed metaphor, he is not paying attention to the main argument. He may even stop reading, because the mixed metaphor has distracted him. Every time you use a mixed metaphor, you risk losing readers.

By the way, one could argue that the strip-club mixed metaphor is an example of a triple mixed metaphor, because the, ahem, body parts that are bumped and ground in strip clubs are indeed soft.

A much clearer example of a triple mixed metaphor (which coincidentally also involves body parts) is the well-known elementary-school blooper, “A virgin forest is a place where the hand of man has never set foot.”

But that’s enough frivolity for today. Besides, I want to keep this blog rated family friendly.

The Takeaway: Unless you are being intentionally amusing, do not use mixed metaphors. It’s fairly easy to avoid using mixed metaphors: as you write, just be aware of the metaphors you are using. That is to say, don’t choose your words unconsciously. Recognize when you are using metaphors and take the time to think through their effect on your readers. It really is that easy.

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.

Avoiding redundancy (3)

In two previous posts (1), (2), about avoiding redundancy, I showed and edited real-world examples of redundancy. I explained why and how you should avoid redundancy.

Today I received a vague, rambling letter from Jon Butler (photo), Dean of the Graduate School of Arts and Sciences at Yale University. Dean Butler's letter contains a lot of redundancies; here is one:

“...shrinking funding sources have called into question our ability to sustain the forward progress of the sciences and social sciences.” (Boldface added.)

By definition, progress is forward movement.

The Takeaway: Remember, every redundancy impedes your reader. He has to stop for a few seconds and wonder, “Is this a redundancy? If not, why did the writer include this word?” The effect is cumulative; use enough redundancies and your copy will irritate all but the dullest readers. So, always try to avoid redundancy.

Avoiding redundancy (1)
Avoiding redundancy (2)

Writing, logic and numbers (1)

Pay close attention to logic when writing about numbers, especially when comparing numbers. For example, keep in mind the difference between the phrase as much as and the phrase more than.

Example

Imagine two boxes (A and B), full of office supplies. Imagine that you and I know that A weighs 12 pounds. If I say to you, “B weighs as much as A,” or “B is as heavy as A,” I mean B weighs 12 pounds.

If I say, “B weighs four times as much as A,” or “B is four times as heavy as A,” I mean B weighs 48 pounds. That is, B is equivalent to four A’s. (4A = 4x12 pounds = 48 pounds)

But if I say “B weighs four times more than A,” or “B is four times heavier than A,” I mean B weighs not 48 pounds, but 60 pounds. In other words, I mean that B is equivalent to four A’s plus A. (4A + A = 4x12 pounds + 12 pounds = 60 pounds).

Most people learn as much as, more than and other basic concepts of arithmetic in elementary school or even before elementary school. One learning method involves the manipulation of Cuisenaire rods (shown in picture above).

For example, if a pupil lays down three white rods in a line, and then one white rod and one red rod in a line parallel to the first line, and then one light-green rod parallel to the other two lines, he can easily perceive that 3 is 3 times as much as 1, and 2 times more than 1.

Journalists and PR people

Unfortunately, most journalists and PR people did not learn these concepts (or have forgotten them). They confuse as much as and more than. For example, a press release issued last Thursday begins with this headline:

“MEPs cost taxpayers five times more than UK MPs”

The second paragraph of the text contains the numbers behind the headline:

“Open Europe’s comparison finds that the European Parliament costs taxpayers a staggering £1.8 million for each MEP per year. This is in contrast to the House of Commons, which costs taxpayers £364,000 for each member….”

Now, £1.8 million divided by £364,000 is approximately 5. But this means five times as much as, not “five times more than.”

An article in the Mail Online gets the concepts right:

“[A study concluded that] women talk almost three times as much as men, with the average woman chalking up 20,000 words in a day – 13,000 more than the average man.”

If you subtract 13,000 from 20,000, you get 7,000 (the men’s rate); 20,000 is almost three times 7,000.

The Takeaway: When writing about numbers, mind your logic. For example, remember that as much as and more than are not interchangeable. Look at the numbers you are comparing and then select the correct phrase to express the comparison.

Placement of modifiers (5)

Clear writing requires, among many other things, the correct placement of modifiers. Incorrect modifier placement can confuse your readers. It can also introduce unintentional humor into your writing – making you look foolish.

Here’s an example, from today’s Wall Street Journal:

“Don’t Ask, Don’t Tell

“The [Supreme Court] turned down a challenge to the Pentagon policy forbidding gays and lesbians from serving openly in the military, granting a request by the Obama administration.”

The writer has placed the adverb “openly” immediately following the gerund “serving.” By placing it there, he indicates that “openly” modifies “serving.”

Therefore the writer is stating that the Pentagon allows gays and lesbians to serve in the military, but not to serve openly. That is, gays and lesbians must not do or say anything that could reveal or acknowledge that they are serving in the military.

One expects that this policy would be difficult to apply in practice:

“Hi, Mom. Hi, Dad.”

“Welcome home, Son. You look so healthy. How was basic training?”

“Mom, I don’t know what you’re talking about.”

“Basic training. You know. The Army.”

“Sorry.”

“We drove you to Fort Dix. Don’t you remember?”

“Just don’t ask me about this, OK?”

“You were so brave when you ‘came out to us.’ And you know we gave you our full support then, and we still do. Why are you afraid to talk about something as mundane as the Army?”

“I said, just drop it.”

The Takeaway: Respect your readers; place every modifier close to the word being modified. Your correct modifier placement will greatly increase the clarity of your writing. It will also help you avoid introducing unintentional humor.

Placement of modifiers (4)

The incorrect placement of modifiers is a frequent error in writing. Incorrect modifier placement can detract – either slightly or heavily, depending on the context – from the clarity of your writing. If you want to produce clear writing, you must use correct modifier placement. It’s fairly easy.

For example, incorrect modifier placement sometimes involves phrases that begin with As someone who. Here are two incorrect examples and one correct example.

INCORRECT: Misplaced Modifier (near the wrong noun or pronoun)

A contributor to an online forum writes:

“As someone who’s been writing professionally since 2002, you don’t have to tell me what a pain in the ass Microsoft autoeverything is... especially when you have to take your final copy and paste it into a publishing system that doesn’t understand all its ‘special’ characters. Sigh.”

The writer has incorrectly placed the modifying phrase, “As someone who’s been writing professionally since 2002,” immediately before the pronoun “you.” But the phrase actually refers to the writer, and therefore modifies “me.”

This kind of error is also called a misplaced modifier: the word (noun or pronoun) to be modified is included in the sentence but the modifier is placed closer to another word. This misplacement creates a false signal for the reader; the modifier appears to be modifying the wrong word. (Note also that in this case the writer increases the confusion by using “you” again in the same post, but in a different sense.)

The writer should have written something like this:

As someone who’s been writing professionally since 2002, I know what a pain …

INCORRECT: Dangling Modifier (no noun or pronoun)

On the web site of the British treasury, this comment appears:

“As someone who works in sheltered housing for young people with learning difficulties the effect of the closing of special school places particularly residential facilities seems to mean we are getting more referrals from Youth Offending Teams.”

The writer uses the modifying phrase, “As someone who works in sheltered housing for young people with learning difficulties,” but does not include in the sentence any word (noun or pronoun) that the phrase could plausibly modify.

This kind of error is also called a dangling modifier: the word to be modified is not included in the sentence, so the modifer is left “dangling.” A dangling modifier forces readers to guess what word should have been included in the sentence. In this case, most readers will guess that the word is I. The writer should have written something like this:

As someone who works in sheltered housing for young people with learning difficulties, I think that the effect …

CORRECT

On April 08, 2009, I received an email from Amazon.com that begins this way:

“Dear Amazon.com Customer,

“As someone who has purchased or rated books by Daniel Defoe, you might like to know that Sharpe's Sword: Richard Sharpe and the Salamanca Campaign, June and July 1812 is now available.”

The writer of the email has correctly placed the opening phrase, “As someone who has purchased or rated books by Daniel Defoe,” immediately before the pronoun (“you”) that the phrase modifies. The modifier is neither a misplaced modifier nor a dangling modifier. The sentence is quite clear.

The Takeaway: Respect your readers’ time and patience. Avoid misplaced modifiers and dangling modifiers. Place every modifier close to the word being modified. Your correct modifier placement will help readers move effortlessly forward through sentence after sentence. They will appreciate it (even if only unconsciously) and respect you for it. You will be recognized for your clear thinking.

Placement of modifiers (1)
Placement of modifiers (2)
Placement of modifiers (3)