Monday, December 21, 2009

Decades, Centuries, and Names (an extended rant)

They're at it again. Time has a story about the search for a name for the decade of 2000-2009, and with 2010 bearing down upon us, we're going to be hearing from all the crazies. People who don't know the difference between cardinal and ordinal numbers, between decades and centuries, between names and nicknames.

Let's go over it again, slowly. And please remember that Don has a B.A. in Math.

Cardinal numbers are used to indicate quantity; they are the normal integers that we're used to: 0, 1, 2, 3, 4, 5, and so on infinitely.

Ordinal numbers are used to indicate order or sequence: First, second, third, fourth, fifth, and so on infinitely. Ordinal numbers are position: there is no "zeroth" or "negative-seventeenth."

All right then. Here's the rub. In the modern U.S. we generally refer to centuries (100-year periods) by ordinal numbers (i.e. "the 21st century"), and to decades (10-year periods) by cardinal numbers (i.e. "the 1990s").

You probably remember the heated arguments about the turn of the century. Some people thought the 21st century should start with the year 2000, others thought it should start with the year 2001. The 2001 folks were technically correct (all together now: "...which is the best kind of correct") because "the First century" started with the year 1 (there was no year 0) and finished at the end of 100, the "second century" started with 101 and continued thru 200, and (stay with me here) "the twenty-first century" started with the year 2001 and will continue thru 2100.

Note that the 2000 fanciers, while technically incorrect, were still off by only 1%. That's an astonishingly low error rate.

This, incidentally, is why we have the confusing pattern of calling years that start with 19xx "the twentieth century" and years that start with "20xx" "the twenty-first century."

(Here at Meerkat Meade we adopted an inclusive strategy: we decided to phase in the 21st century during the whole year 2000. We figure that turning a century is a lot harder than turning an oil tanker, and they take miles and miles to turn. For us, the century started turning on Jan 1 2000 and was finished by January 1, 2001.)

Of course, 1999/2000/2001 was also a change of millennium. We don't have a standard way of referring to millennia. Sometimes we call this current one "the third millennium" (ordinal) and sometimes we call it "the 2000s" (cardinal.) To be technically correct, "the third millennium" started on 2001 and runs thru 3000. while "the 2000s" started in 2000 and run through 2099.

(Actually, at Meerkat Meade we prefer to use the Holocene calendar, which sets the year 0 at the start of the Holocene period in the year 10,000 BCE. This year is 12,009 H.E. [Holocene Epoch], and we are in the 13th millennium or the 121st century, both of which started on January 1, 12,000.)

Now let's talk about decades.

As I said above, we generally name decades cardinally: the 1950s, the '70s, etc. Only in flowery, stilted, or overly legal language do we say something like "the third decade of the twentieth century" (ordinal) rather than "the 1920s" (cardinal). Thus, the 1970s started with 1970 and ran thru 1979, the 1980s ran 1980-1989, etc.

Problem is, people who don't think about what they're saying (and they are legion) remember the technically correct argument that "centuries start with the 01 year because there was no year 0" and apply it (incorrectly) to decades and millennia.

For example, the following letter from a very stupid child appeared in the December 21, 2009 issue of Time:

Even 5-year-olds know that when counting anything -- toes, fingers, or years -- we begin with one, not zero. The first decade of this millennium began with the year 2001, and the last year of the first decade of this millennium will be next year, 2010. The millennium began with the year 2001. Why is this so difficult for adults to grasp? -Anna Link, Falls Church, VA

Because, Anna, adults do not generally refer to decades in the same stilted, pretentious way that you do. Nor, to be technically correct, did the article you're commenting upon: The '00s: Goodbye (at Last) to the Decade from Hell. Even 5-year-olds (to borrow a phrase) know that "the '00s" began in '00 (duh) and end in '09.

And to point out your technically incorrectness (the worst kind of incorrectness), since "this millennium" started (cardinally) in 2000, the "first decade of this millennium" ran from 2000 thru 2009 -- not 2001-2010 as you say. Too bad, Anna. If you'd only been pedantic enough to say "the first decade of the third millennium," you'd at least have been partially correct...instead of revealing yourself to the nation as a dunderhead who cannot tell the difference between 10 years, 100 years, and 1,000 years.

Oh, well, you were educated in Virginia, so perhaps expecting you to have knowledge of numbers greater than 4 is asking too much. Go back to your nonevolutionary world created in 4004 BCE (wouldn't that make today part of "the eighth millennium" which runs from 1998 thru 2097? The "second decade" of that millennium, in fact, which started in 2007 and runs though 2018?)

Ahem. The point is, in general civic society we count decades cardinally. The current decade is 2000-2009, and it doesn't have a name.

That's because there isn't a common accepted name for the span of numbers 0-9. 10-10 are "the teens," 20-29 are "the twenties," and so forth -- and that's how we commonly name decades: either "the 1910s," "the 1920s," etc. or "the Teens," "the Twenties," etc.

If we try to call 2000-2009 "the 2000s," there is going to be confusion. Does that mean the decade, or the century? (We frequently do refer to centuries in ordinal fashion, as in "the 1600s" or "the 1800s.")

But there's no name like "teens, twenties, etc." for '00-'09.

Last time we faced this problem was with the 1900s. At the time, there was a generally accepted name for '01-'09: aughts. This came from the standard way of speaking numbers aloud at the time: 1807 was pronounced "eighteen-aught-seven." As people in the 1910s and 1920s started to talk about years in the period 1900-1909, it was natural that they said things like "Back in aught-four..." or "The bad storm of aught-eight." From there it was a simple generalization to call the decade "the aughts."

Nowadays, this is not the fashion. We say "eighteen-oh-seven" and "Back in oh-six..." So by analogy, we should be calling this decade "the oh's." But that's not going to stick, because there is too much potential for confusion. (In Baltimore, for example, "the O's" means "the Orioles.")

I say we should go with "aughts." And we should go back to the old way: "Back in twenty-aught-four..."

Just to make things more complicated (cue Grover: "More complicated?!"), we also talk about "naming decades" when we really mean giving a decade a nickname. These are cute sobriquets like "the Roaring Twenties" or "the Me Decade." Not every decade gets a nickname (what nickname did we give the 1910s?), and moreover, nicknames are often applied well after the fact. If the decade 2000-2009 is going to have a nickname, it's too early for us to decide on it now.

And one more thing, while I've got you here. The time is long past to drop the "two thousand" thing. Next year is not "two thousand ten" (or even worse, "two thousand and ten") -- it's "twenty-ten." 1910 wasn't "one thousand nine hundred ten," it is and always was "nineteen-ten."

We put up with this nonsense the first few years of the century (it certainly made sense to say "the year two thousand" rather than "the year twenty-oh-oh"), but we realized the problem back when everyone was calling that movie "Two Thousand and One: A Space Odyssey," and even pushed for calling the sequel "Twenty-Ten." We totally stopped being patient around 2003 (twenty-oh-three).

If nothing else, imagine the time savings from 7 billion people saying "twenty-fifteen" instead of "two thousand fifteen."

Thank you. Now go forth and celebrate the ending of the '00s, and best wishes for a safe and happy 2010 and the rest of the Teens..

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Damian Cugley said...

Thanks for this. Cardinals versus ordinals is the best way of explaining it without getting in to endless more-pedantic-than-you contests—and easily grasped by most of my mathematically literate friends, who are the only people who actually care much one way or another over 2010 versus 2011. :-)

Anonymous said...

On wikipedia right now we are having arguments over whether or not the 2010s are the 2nd decade of the 21st century or not.

We all agree that the 2010s, by definition, started in 2010 and run through 2019. We also agree (well most of us) that the 21st century technically started in 2001 and runs through 2100 due to the Year 0/1 issue.

Now, if you logically calculate the years that the phrase "2nd decade of the 21st century" describes you get 2011-2020, which is a slightly different time span than the 2010s. So, it seems that the phrase the 2010s are the second decade of the 21st century is technically incorrect.

However, an argument is now being put forward that since we always refer to decades cardinally that you need not parse the phrase "2nd decade of the 21st century" the ordinal way it seems logical to do. That in fact, it is fine to say that the first decade of the 21st century began a year earlier than the century to which it belongs and that the last decade of the 21st century ended a year earlier than the 21st century. In effect, that what is meant by a phrase like the "2nd decade of the 21st century" is simply convention and doesn't need to be 100% consistent with the logical ordinal parsing of the statement. In particular, when you try to assign decades as belonging to centuries when the former are typically demarcated cardinally and the latter ordinally, what is the proper way to do the mapping / organization?

I definitely started on the purist side that 2010s != 2nd decade of the 21st century, but I'm finding myself sucked in by the organizational and assignment argument that named decades should belong to named centuries even if their start and end dates differ by a single year. That last technicality can be pointed out as just that.

Anonymous said...

It's a matter of definition, as any real mathematician knows.