Tag Archives: numbers

Digital enhancement for numbers (Go figures!)

This article was originally published on The Editors’ Weekly, the blog of Editors Canada

At the ACES conference in Providence, Rhode Island, in late March, the Associated Press announced changes to their recommendations for handling numbers and debated some others.

About sixty percent of those present gasped when one of the recommendations was made – in fact, it might have been 70 percent. No, I’m going with 80% of those in attendance. But it made perfect sense to me. Continue reading

Look! It’s a noun! It’s an adjective! It’s a number! No, it’s…

My latest piece for The Week is an introduction to that double-agent class of words, there in the numbers but not of the numbers: quantifiers.

Singular or plural? It’s complicated.

At sixes and sevens about nine and 10

A colleague raised a common issue: she had chosen to use Canadian Press style for a website with health information, and it left her with stuff such as “at ages six to nine, you will use 10–20% more.” What to do about those mixed and inconsistent numbers when they show up together like that?

I’ll tell you what: Don’t follow Canadian Press style. Or any other style like it, when it comes to numbers.

In many ways, CP style is appropriate only for newspapers. For instance, usages such as “$9-million” are not standard English but have a justification in the narrow columns of a newspaper. CP style rules for spelling out numbers, however, are not appropriate for newspapers. Nor for most other nonfiction, in fact.

Long ago, when teaching test prep for the GRE, GMAT, LSAT, and SAT, I realized that numerals communicate more directly, immediately, and effectively to the reader, stay better in the mind, and leap off the page much more readily. In any work that is being referred to for facts, numerals are more effective for all magnitudes, not just for 10 and higher. And in a context that is as space-sensitive as a newspaper, the only reasons for preferring spelled-out numbers are prissiness and dogged traditionalism. That’s it. Adhering to their rules produces not only the example above but even worse things, rubbish such as “He is facing an eight- to 20-year sentence” and “seven in 10 people.” There is nothing about this is that is helpful to the reader; it is distracting and impedes comprehension and retention.

And how about starting sentences with numerals? The standard argument is that the reader somehow won’t know you’re starting a sentence. Why? Numerals stand out as much as capital letters. There’s a space after the period – a suitably large one in a modern proportional font, too – so no one will mistake it for a decimal.

Look, do you really prefer this:

Nineteen-eighty-four was a bad year. Eight out of 10 members of the club faced jail time ranging from six to 20 years.

to this:

1984 was a bad year. 7 out of 10 members of the club faced jail time ranging from 5 to 20 years.

Really. Which leaps off the page and into your brain more readily? Which sticks in your mind better? Quick, tell me (try it without looking first, then just at a glance): How many out of 10 members in the second example? And in the first? And what was the jail time range in the first? And in the second?

If you’re communicating factual information where the numbers matter, use numerals. Don’t worry, people will still remember how to spell them even if you don’t spell them out. You are not contributing to the decline of literacy. You are facilitating the communication of information.

Will some readers complain if you don’t spell out the low numbers? Yes – the kind of reader who is more interested in making sure that everyone follows their personal set of rules than in the actual communication being effected. These are not readers to take any account of; almost nobody even likes them. Most readers just want the facts.

The only numeral that is problematic, in fact, is 1, and that’s because it looks like l and I, especially in some type faces. For my own house style at the company where I work, I have set the rule to be that we use numerals for all numbers in all contexts except where 1 appears by itself, in which case we spell it out for clarity. We make occasional exceptions with idiomatic phrases, where the numeral would look odd (no need to be at 6s and 7s about that). Otherwise, it’s all numerals, and that makes it much more effective and usable.

You will note I said “most other nonfiction.” For works that are more narrative in style, such as many biographies and most fiction, numerals may stick out quite a bit in the flow, since – as noted – they leap off the page and communicate much more quickly. In a story they can be like sudden spurts of water in a steady stream (or like your tap after the water’s been off and air has gotten into the line). So I don’t take issue with the literary habit of spelling out up to ninety-nine and, in dialogue, even higher. But in informational material – such as health data – I strongly advocate all numerals all the time.

And the Canadian Press ought to smarten up and do so as well. Until they do, though, effective editors will do better to ignore their prescriptions. After all, the name of the game is effective communication, not “Who’s following the holy writ?”

100% of these usages is wrong

I have just seen an infographic (heaven help us, yes, an infographic – generally now not actual charts but just text tarted up) with the following statements:

46% of all U.S. workers claims that they are less productive without coffee.

61% of the workers who need coffee to get through their day drinks 2 cups or more each day.

49% admits to needing coffee while on the job in the Northeast where the workday coffee ritual is the strongest.

Let’s ignore all the other issues in those sentences and just focus on the most egregious, unnatural usages: 49% of workers claims; 61% of the workers drinks; 49% admits. Ick. Just ick.

This is a classic overthink error. I see it mainly in newspapers and similar places where the writers are trying to enforce their understanding of “proper” grammar and are going against their normal speech instincts in doing so.

Percentages can apply to unitary or mass entities and they can apply to populations of entities. When you’re talking about mass or unitary entities, it’s right to use the singular: “50% of this cake is chocolate”; “50% of this collection is action figures.” Moreover, when you’re talking about average (or consistent) percentage of each individual in a set, you may use the singular, though it can sometimes be awkward to phrase it thus: “40% of her cupcakes is sugar.”

But when you’re talking about the portion of the individuals in a set of individual entities, percents are plural quantifiers. You don’t say “46% of the people here drinks coffee” unless somehow each employee has a body 46% of which (perhaps on average) drinks coffee and the other 54% of which abstains. Would you say “Half of the employees here drinks coffee”? How about “A lot of the people here drinks coffee”? Hey, a lot is singular, you know!

Which is just the point. A lot may be singular, and 46% may be a discrete quantity, but their effect on the nouns they describe is a plural quantification. Remember that a dozen is also a singular construction and a discrete quantity, and a hundred likewise, and yet you don’t invariably conjugate verbs in the singular after them: “A dozen people is coming over”? No. (But you can say “A dozen eggs sits in the basket” because you know that’s a carton.) You can say “A bunch of flowers sits by the window” because in that case a bunch is a unitary object; if you say “A bunch of people sit by the window” it means that the people may or may not be together as a unit, but there are a fair few of them in any event. (And “A bunch of people sits by the window” is an almost amusing image of a set of people so together in their grouping that they even sit as a single unit.)

It’s easy enough to see how people can get confused. Many of these things can take singular or plural depending on what are sometimes very fine nuances of meaning. I can say “100% of these usages is wrong” and mean that each usage is 100% wrong, and I can say “100% of these usages are wrong” and mean that every last one of them is wrong. But there are cases where your ear just screams: “46% of workers claims”?! No. Just no. A percentage of a population of individuals is a plural.

And really, if your analysis of grammar leads you to write something that sounds staggeringly wrong, stop and reconsider your analysis.

There’s a couple things about this…

Quick: How many things are wrong with the above sentence?

Those who know me will not be surprised when I say that it depends on the variety of English you’re using. In casual English, it’s fine, though the speaker may be aware that it’s non-standard (“not good English”). But it presents a few interesting issues. I’m going to start at the end.

I’ll leave off any real address of ending a sentence with ellipses (…), which some people dislike; I used it because I intended it to be “leading,” and that’s different from a flat-out statement.

But there are many people who will insist that a couple things is wrong and should be a couple of things. This is based on couple being a noun. The thing is, though, so is dozen, and we no longer (as we once did) say a dozen of things; so, too, is a million, and actually, in English, so too are numbers generally, though they are a special class of noun. (Numbers are not adjectives in English. Try using them in all the various places where you can use adjectives and you will see that.)

We no longer say a million of people, though we still say a milli0n of them. And couple is coming to be like other numbers, as dozen has and myriad is in the process of doing; you still can say a couple of things, but you can also say a couple things.

Can you say it when there are actually more than two things, as in fact there are with this sentence? Shouldn’t we say several things if there are three or four? Well, if you wish to be precise, yes, but several gives a sense of significant quantity, whereas couple downplays it. Like it or not, a couple is in use as an informal indefinite quantifier. True, it’s a bit weaselly. But English is a very weaselly language – or can be when we want it to be.

The interesting thing is that many of the people who will insist on a couple of will also insist, in this sentence, on There are rather than There’s. Now, if couple here really is a singular noun (like pair or brace), you might think it would take the singular. But of course with collectives we will use the plural when we are emphasizing not the totality but the mass of individuals. So There are a lot of paintings means there are many paintings, but There is a lot of paintings means that there is a lot, probably for auction: a single group.

Likewise with, for instance, the majority of voters – you may say The majority of voters decides the vote, because it is the fact of a majority that is decisive, but it is only (and not always) in newspapers and similar places where a writer is striving to be correct but doesn’t fully understand the grammar that you will see The majority of voters doesn’t want this rather than don’t want this.

So, since I have already said that a couple here is equivalent to “two”, “roughly two”, or “a few”, you would expect that it should be There are a couple rather than There’s a couple, right? And in fact in formal standard English that is so, because in formal standard English we match the number in there is/there are to the number of the predicate. But in casual English we often don’t do so, and it’s not because we’re ignorant or illiterate – it’s because it’s an arbitrary decision.

There is is really just an existential predicate, and there’s nothing other than convention that forces us to match it to the object. Spanish and other languages that use a version of “have” rather than “is” don’t do it (Hay dos cervezas sobre la mesa; Il y a deux bières sur la table); German doesn’t do it with its “give” verb (Es gibt zwei Biere auf dem Tisch); even some languages that use a version of “is” don’t do it (Tá dhá beoir ar an mbord – Irish).

Remember that what comes after there is is structurally the object. In normal usage (in English), objects have no effect on the number or person of the verb – it matches the subject. We don’t normally force the copular verb to match its object, even when adhering to the nominative object “rule”: not It am I but It is I, and not It are we but It is we… which, of course, normal people say as It is us, even when the It is empty. The famous quote from Pogo (appropriate with respect to grammatical confusion and disputes) is “We have met the enemy and he is us,” not “he are us.”

It’s just because the there in there is is just a placeholder, and not even a noun or pronoun, that we have the habit of matching the number of the verb to the object – the object is the only noun in the area, so we conclude that it must be the subject. There is also a mistaken belief that There is a person is an inversion of A person is there; this is not true – there is no spatial reference in there is. When we use there to point to a location, we have to have a location to point to, either present in context or established in text. If I say There is a mistaken belief, there is no “there” there.

In some languages, a subject isn’t even supplied for existential predicates; there’s just a verb. English doesn’t like bare verbs, so we always put something – there or it – in the subject position. Which works fine until someone stops and says “What is it? Where is there?” It gets to be like a person who starts analyzing the muscle movements in walking and finds he/she can’t remember how to simply walk anymore.

Thus, the use of there are rather than there is with plural predicates is learned behaviour, and is not truly natural – as witness the fact that even highly literate people often use the singular in casual use or unguarded moments. That doesn’t make it correct in formal English, but it does explain a couple things about it.

Math… amazing

Every so often someone will forward me one of these “amazing!” math tricks, and I will of course feel compelled to explain just how outrageously simple the math in them actually is. The latest one going around is even simpler and more obvious than most, and yet people still seem impressed by it:

Take the last two digits of the year you were born, add your age this year, and it will add up to 111. Amazing!

I have to say, I’m kind of amazed that it’s not gobsmackingly obvious to absolutely everyone who can add and subtract two digits. But so many people will do anything to avoid arithmetic, so it seems to have that “magic wand” quality pretty readily.

So OK. Say someone were to send you an email that said “The year you were born plus your age this year equals 2011 – but only this year! Amazing, huh?” Wouldn’t you find that obvious? Now, 2000–1900=100, and you were born in the 1900s (we assume no one under 12 years old got the email), and it’s 2011 now…

Put it another way: if you subtract 1900 from everything, as though 1900 were the year 0, this year would be the year 111; and if you start with the last two digits of your birth year, you’re subtracting 1900, so…

There are some really cool number tricks out there. But you don’t too often see them being passed around in emails, because different people have different definitions of “cool”.

At the very least, they could try tricks that use more than just disguised simple addition and subtraction. For instance, there are fun facts such as that your age (or any two-digit number) plus the reverse of your age (e.g., 49+94) will always be divisible by 11 (in fact, it will be 11 times the sum of the digits in your age); your age minus the reverse of your age, or the reverse of your age minus your age (e.g., 94–49) will always be divisible by 9; your age minus the sum of its digits (e.g., 49–13) will also always be divisible by 9… And the digits of any number divisible by 9 will always add up to a number divisible by 9, which means if you have any two-digit number divisible by 9 and add its digits, you will get 9 or (in the case of 99) a number the digits of which add to 9.

All of this is explainable with simple algebra on the basis that a two-digit number cen be represented as ten times a one-digit number plus another one-digit number, e.g., 49=(4×10)+9.

So for any number 10x+y (e.g., 40+9, where x=4 and y=9), the reverse will be 10y+x (e.g., 90+4), meaning if you add 10x+y (the original number) to it you get 11x+11y (e.g., 40+9+90+4=44+99), and if you subtract the reverse you get 9x–9y (e.g., (40+9)–(90+4)=40+9–90–4), and if you subtract the sum of the digits (x+y, e.g., 4+9) you get 9x (because 10x+y–(x+y)=9x, e.g., 40+9–(4+9)=36). And of course 10x+y+10y+x=11x+11y=(x+y)×11.

So assuming a person of a normal adult age, you can say

1. Take your age (e.g., 49).
2. Add the digits together (e.g., 4+9=13).
3. Subtract that from your age (e.g., 49–13=36).
4. Add the numbers of the resulting number together (e.g., 3+6).
5. The answer is 9.

Of course, you want to gussy this up with something fancy. Add in some other calculations to distract. Instead of step 5, maybe say

5. Multiply by the last two digits of the year.
6. The answer is 99. This always works!! But it will only work this year!!! And not again for a hundred years!!!! OMG it’s amazing tell all your friends!!!!11

or, if you think they can handle the math (!), say

5. Now add your age to the reverse of your age (e.g., 49+94).
6. Divide the result by the sum of the numbers in your age (the number in step 2).
7. Multiply this by the number from step 4.
8. The result is the answer to the question “Who’s the greatest hockey player of all time?”!!! OMG Gretzky rules!!! Number 99 forever!!!!

Even this is pretty straightforward for people who like to think about numbers. But there aren’t that many of us. Anyone who graduated from high school is officially able to figure this sort of thing out easily. But as long as people think math is hard and mystifying…

I suppose you could argue that the general “Numbers! Oh noooooes!” attitude people tend to have in our culture allows them actually to have fun with simple things like this, but it deprives them of the much greater fun they can have with more complex number problems, and it makes them easy marks for misleading advertising, misleading politicians, and so on. And generally vulnerable to making dumb mistakes. There’s a classic Dilbert cartoon (two of them, in fact) illustrating this – see http://search.dilbert.com/comic/40%25%20Sick.

One or two things about numbers

A colleague has encountered a sentence of the type “This will happen in one-to-two months.” She’s wondering about those hyphens.

And well she should be. They have to go. It’s not optional. Otherwise it’s presenting a type of month with the quality of “one-to-two” in the same way as “two-by-four boards” are boards with the quality of being two inches by four inches. A “moderate-to-severe infection” is “an infection that is moderate to severe”; “one to two months” is not “months that are one to two”.

In cases like this, some people are confused by the use of hyphens in something like “a two-month decline”. But this is not that. In a case like that, the head noun is “decline”, and “two-month” is hyphenated because it is part of a compound modifier. In the case of “one to two months”, “months” is the head noun and the numbers are quantifying it – they are not adjectives, they are quantifiers. That’s another point of confusion some people get into: treating numbers as though they were adjectives. (It doesn’t help that CP Style, presumably for reasons of readability in newspaper columns, prescribes, for instance, “two-million” rather than the standard “two million”.)

“One to two months” is not a set of months with the quality “one to two”; it is “one month to two months” with the first “month” removed. (A similar deletion, but of the final “months”, is seen in “a month or two”, which we don’t write “a- month -or-two”.) We can use a dash to replace “to” in, for instance, “1–2”, but we don’t use dashes (or hyphens) and “to” with number ranges.