Year Zero

Awhile back, the BBC website History Extra had a post that included this tidbit:

AD 0… the date that never was

The AD years of the Christian calendar are counted from the year of Jesus Christ’s birth, and, as the number zero was then unknown to the west, Dionysius began his new Christian era as AD 1, not AD 0. …

This evoked the ire of the noted historian Thony Christie. In a post Something is Wrong on the Internet, he explained:

It was common practice to number the years according to the reign of the current monarch, emperor, despot or whatever. So for example the year that we know as 47 BCE would have been the third year of the reign of Gaius Julius Caesar.

Thus Dionysius Exiguus (Dennis the Short) would say that some event occurred in (say) “the 3rd Year of Our Lord”; in Latin, “Anno Domini”, hence AD.

For this discussion, focus your attention on the so-called ordinal number “3rd”. Zero as a cardinal number has been around a long time, but the ordinal “zeroth” remains rather uncommon. I did a Google ngram search, and “zeroth” is almost nonexistent before about 1930. As of 2000, “zero” is nearly 200 times more frequent than “zeroth”. (The alternate spelling “zeroeth” is even scarcer.)

Nowadays one rarely explicitly uses ordinals for years. When is the last time you heard someone say, “In the US election in the 2018th year of the Common Era, the Democrats did well”? Grammatically, the phrase “the 2018 US election” contains a cardinal number, not an ordinal. Thony demurs:

This distinction between cardinal and ordinal numbers becomes confused when we talk about historical years. We refer to the year five hundred CE when in fact we should be saying the five hundredth year CE, as it is an ordinal and not a cardinal. … We are enumerating the members of an ordered set not counting the number of objects in a collection. Because this is the case there cannot be a zeroeth year. End of discussion!

(Note that we still use ordinals for centuries: “the 19th century witnessed the discovery of Maxwell’s equations”.)

In the recent post There is no year zero! Thony repeats the argument:

When we talk about years we tend to use the words for cardinal numbers but in fact we are actually talking about ordinal numbers. What we call 2019 CE or AD i.e. two thousand and nineteen is in fact the two thousand and nineteenth year of the Common Era or the two thousand and nineteenth year of Our Lord. …  [T]here is and never can be a year zero, it is, as stated abve, a contradiction in terms and cannot exist. … The second decade started on the 1st January 2011 and will end on the 31st December 2020 and not on 31st December 2019 as various innumerate people would have you believe. [My emphasis]

I love the “take no prisoners” tone. Historically Thony has a strong case. But logically—is there room for another viewpoint? When we index an ordered collection, must we start the count with 1?

Of course not! Some computer languages index arrays starting with 0; others allow you to pick the initial index. In mathematics, sometimes 0 proves more convenient, sometime 1.

For example, when von Neumann laid the foundations of the modern treatment of Cantor’s ordinal numbers, he picked 0 as the first ordinal. This allowed him to define n as the set of all its preceding ordinals: n={0,…,n-1}. This has the pleasant consequence that n contains exactly n elements. (Bold indeed anyone who calls von Neumann “innumerate”.)

OK, fine for pure math and computer programs? But what about years?

It’s no surprise that the mathematically bent regret the absence of a Year 0. After all, the universe did not begin in 1 AD. You’d want the year n BCE to correspond to the index –n, but that would result in the messed-up indexing

…, -3, -2, -1, 1, 2, 3, …

Naturally our friend Dennis didn’t worry about this. As Thony notes, “The idea of BC years or dates only came into use in Early Modern period.” (And yeah, negative numbers.)

History often saddles us with inelegant conventions. Measuring spoons! US weights and measures! Electric current! Dionysius had a good rationale for starting his scheme with 1, but that rationale has evaporated into the mists of history.

Thony was on his home turf calling out the BBC for their historical goofs. But when he claims that logically we couldn’t have indexed the years

…,-3,-2,-1,0,1,2,3,…

I fear he’s on shaky ground.

Shortly before 2000, Stephen Jay Gould wrote a book, Questioning the Millennium. He devoted the second chapter to the 2000 vs. 2001 debate. I leave the last word to him.

Some questions have no answers because we cannot get the required information. … Many of our most intense debates, however, are not resolvable by information of any kind, but arise from conflicts in values or modes of analysis. … A subset of these unresolvable debates—ultimately trivial, but capable of provoking great agitation, and thus the most frustrating of all—have no answers because they are about words and systems, rather than things.

[Added later: I just noticed that Sniffoy’s comment to Thony’s 2014 post makes much the same points. I must have read it at the time, since I replied to it!]

2 Comments

Filed under History

2 responses to “Year Zero

  1. And Gould is 100% wrong!

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