Zeroth — Why the Century Number Is One More Than the Year Number

2012.09.03   prev     next

WHY are the 1800s called the “nineteenth century?” Why are the 1900s called the “twentieth century?” The answer is a fundamental mistake that was made, very early in the history of mathematics, in deciding how to number things. It would be too much trouble to fix it now, so we’re pretty much stuck with it.

It’s not because they started with the year 1. It would have been better to start with the year 0, but if we had done so, we would still have the same problem with century names. We can see this because:

“nineteenth century”  =  1801 through 1900

But if they had started with the year 0, then:

“nineteenth century”  =  1800 through 1899

So the 1800s would still be called the “nineteenth century.” It would be a little more consistent, since all hundred years of that century would start with “18”. (And no year of the form “18xx” would belong to a different century.) But the question of why the 1800s is called the “nineteenth century” would remain.

Index Zero

In most modern computer programming languages, if you define a list of objects as having five items, then those items are indexed 0, 1, 2, 3, and 4. Why is that? The reason is that since there are ten digits, you should be able to index ten items with a single digit. But those digits are:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

They are not indexed as follows:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

because the last number in that sequence, “10,” is composed of two digits. And the digit 0 (by itself) is not being used.

Similarly, you should be able to index a hundred items with two digits, and they are indexed:

00, 01, 02, ... 97, 98, 99

They are not indexed as follows:

01, 02, 03, ... 98, 99, 100

because, again, the last number in that sequence “100,” is composed of three digits. And the two-digit combination “00” is not being used.

When humans first discovered numbers and counting, the number 0 wasn’t initially recognized as a number, because “zero items” is synonymous with “nothing to count.” The idea that you have items to count implies that there is at least one item. So they started their counting system with 1. And when they had five items, they indexed them this way:

1, 2, 3, 4, 5

When they had ten items, they indexed them:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

And so naturally, the word for the item that comes at the very start of a list became “first” (1st). And the word for the item that comes immediately after the very start of the list became “second” (2nd).

The word “zeroth” (0th) was never invented. Nobody knows of such a word.

If we had indexed five items this way:

0, 1, 2, 3, 4

Then we would call the starting item in a list the “zeroth” (0th) item. And we would call the item that comes immediately after the starting item “first” (1st). And the next item would be called “second” (2nd). Etc.

“Zeroth” (0th) would be synonymous with “the starting item” (the way “first” is in our actual usage).

“First” (1st) would be synonymous with “the item immediately after the starting item” (the way “second” is in our actual usage).

If we had done it that way (and started with year 0 for good measure), then the centuries would be named as follows:

0-99  =  “zeroth century”
100-199  =  “first century”
200-299  =  “second century”
...
1700-1799  =  “seventeenth century”
1800-1899  =  “eighteenth century”
1900-1999  =  “nineteenth century”
2000-2099  =  “twentieth century”
2100-2199  =  “twenty-first century”

It would all make sense, and the one-off naming would not exist.

Of course, it’s unrealistic to expect everybody to switch over now, especially with all that has already been written under the current system of century names. Plus it would be incredibly hard to get people to stop thinking of the word “first” as meaning “the starting item,” much less replace it with the strange, new word “zeroth.”

But now you know: That’s why the century number is one-off.

See also:  Pi — Diameter vs. Radius

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