Calendrical Complications

Tags: #SocialScience/History

The Problem

Time intervals – such as decades, centuries, or millennia – can be enumerated in order to denote particular time periods in a given calendrical system.^[1]

The natural way to implement such a system is to start at a year 0, and count up. Let's count years in decimal and consider decades:

\begin{matrix} Decade & | & Years \\ First & : & 00 to 09 \\ Second & : & 10 to 19 \\ Third & : & 20 to 29 \\ Fourth & : & 30 to 39 \\ ⋮ & ⋮ \end{matrix}

We see that the tens digit is always one less than the ordinal in question; the first decade has a 0 in the tens, the second has 1, the third 2, etc. This means that phrases like "00s", "10s", "20s", etc· align with the decades. The same works for centuries with the hundreds digit and millennia with the thousands digit:

\begin{matrix} Interval & | & Years \\ N th decade & : & 10 (N - 1) to 10 N - 1 \\ N th century & : & 100 (N - 1) to 100 N - 1 \\ N th millennium & : & 1000 (N - 1) to 1000 N - 1 \end{matrix}

How wonderful! So what's the issue?

Recall that we started with the assumption that we begin at a year 0. Sadly, this is not the case for the Gregorian calendar that is the international standard today – instead, it starts at year 1.^[2] That means that all time intervals are shifted by one and thus no longer align with the digits:

\begin{matrix} Decade (A·D) & | & Years (A·D) \\ First & : & 01 to 10 \\ Second & : & 11 to 20 \\ Third & : & 21 to 30 \\ Fourth & : & 31 to 40 \\ ⋮ & ⋮ \end{matrix}

This routinely causes confusion amongst people.^[1:1] I personally recall online discourse in 2019 about whether or not 2020 would mark a new decade. Most people assumed it would – we'd be going from the 2010s to the 2020s, after all – but pedants who knew of the one-year-offset insisted that the next decade would not arrive until 2021.

I will refer to the traditional year-1 definition as de jure (from Latin dē jūre "from law"), and the popular year-0 (digit-aligned) one as de facto (from Latin dē factō "from fact").^[3]

For communicators, it's a dilemma in the proper sense of the word:

Using the de jure definition is technically correct, but obtuse and generally misunderstood.
Using the de facto definition is elegant and widely understood, but technically incorrect (and will be misunderstood by experts and pedants).

I do not believe either solution is acceptable – we must break the dilemma itself. I propose a way to unambiguously distinguish between the two definitions.

My Proposed Solution

The modern Gregorian system has two equivalent labels for years:^[2:1]

Anno Domini (A·D), with Before Christ (B·C) for years prior to 1 A·D.
Common Era (C·E), with Before Common Era (B·C·E) for years prior to 1 C·E.

There is no functional distinction between these two – they are exactly identical. (The latter is merely the secularized version of the former.)

What I propose is to leave the Anno Domini system as it is (following the de jure traditional definitions), while amending the Common Era system in this way:

Start at 0 C·E ( = 1 B·C), so that C·E now unambiguously follows the de facto system.
Drop B·C·E (since 1 B·C·E is now 0 C·E) and allow negative years (like ISO 8601).

So then the first decade C·E would refer 0 C·E to 99 C·E range that people expect, and similarly for other time periods:

\begin{matrix} Decade (C·E) & | & Years (C·E) \\ First & : & 00 to 09 \\ Second & : & 10 to 19 \\ Third & : & 20 to 29 \\ Fourth & : & 30 to 39 \\ ⋮ & ⋮ \end{matrix}

Note that C·E still matches A·D for all non-negative years, so they are still equivalent for normal year counting. Only non-positive years have changes. Negative years may seem confusing, but are really simpler to work with – consider this question:

How many years passed between 1 Jan, 100 B·C and 1 Jan, 100 A·D ?

You'd think it's 200 years, but it's actually just 199 because there's no 0 A·D! With negative years, no such issue arises:

How many years passed between 1 Jan, –99 C·E and 1 Jan, 100 C·E ?

To refer to time periods before the common era, we can similarly negate our ordinals to count backwards; the negative first decade C·E would be 0 C·E to –9 C·E. Saying negative is a bit cumbersome though, so I propose the prefix ante- ^[4] instead:

\begin{matrix} Decade (C·E) & | & Years (C·E) \\ Ante-First & : & - 09 to 00 \\ Ante-Second & : & - 19 to - 10 \\ Ante-Third & : & - 29 to - 20 \\ Ante-Fourth & : & - 39 to - 30 \\ ⋮ & ⋮ \end{matrix}

This does exactly what we wanted! We can now unambiguously communicate which system – de jure or de facto – we are using by choosing A·D or C·E respectively. Of course, since this is just a suggestion on my part so far, there is currently nobody (except myself) who understands that this is how I use these labels. However, anyone who adopts this system (including myself) can now be unambiguous in principle, and point confused readers to this article for clarification if needed. I certainly consider it a success!

Ordinals and Roman Numerals

You might have noticed that I chose to spell out all the ordinals in this article. (I wrote first instead of 1st.) This is because I like to use Roman numerals for ordinals (which count order) and standard Hindu-Arabic numerals for cardinals (which count amounts).

IIInd Century A·D: 101 A·D to 200 A·D.
–IVth Century C·E: –399 C·E to –300 C·E.

Most sources say that the ordinals are first, second, third, etc and cardinals are one, two, three, etc. In reality, however, the two are often confused. Consider this sentence:

You are number three in the waiting list.

This uses a "cardinal" three to denote a position in a list – it's being used as an ordinal! Similarly, consider this sentence:

Juggling a third ball seemed intimidating.

This one is slightly more ambiguous, but I'd argue that third here is acting like a cardinal, not an ordinal. The indefinite article a shows that it doesn't matter what ball was the third one – the amount was the issue, so it's a cardinal.

Hence I allow both III and IIIrd for ordinals and 3 and 3rd for cardinals:

You are number III in the waiting list.
I finished in IIIrd place.
I had 3 shirts that needed washing.
Juggling a 3rd ball seemed intimidating.

This keeps the numerical concepts separated from the words themselves. Of course in many cases the distinction is ambiguous ^[5], so both variants are permissible. Years are a good example of this – do they count the amount of time that's passed or do they enumerate the years ? I think both are valid interpretations, so I'm happy to accept both 2026 C·E and MMXXVI C·E.

Appendix

Thanks for reading, and have a nice day!

A lonely page, it seems...

Century - Wikipedia ↩︎ ↩︎
Anno Domini - Wikipedia ↩︎ ↩︎
De facto and de jure - Wikipedia, long vowels based on IPA listed there and confirmed by https://alatius.com/macronizer/. ↩︎
Like in A·M = Ante Meridien, lit· "before noon". In some English accents ante- sounds the same as anti-, but this doesn't cause ambiguity since both mean essentially the same thing in this context. ↩︎
Cardinals and ordinals map to each other perfectly for finite amounts, see How to Count Past Infinity by Vsauce. ↩︎