# There is no year zero!

I realise that in writing this post I am wasting my time, pissing against the wind, banging my head against a brick wall and all the other colourful expressions in the English language that describe embarking on a hopeless endeavour but I am renowned for being a pedantic curmudgeon and so I soldier on into the jaws of disappointment and defeat. I shall attempt to explain carefully and I hope clearly why the 31st of December of the year 2019 does not mark the end of the second decade of the 21st century. I know, I know but I must.

The core of the problem lies in the fact that we possess two basic sets of counting numbers, cardinals and ordinals. Now cardinals have nothing to do with the Holy Roman Catholic Church, a family of birds or a baseball team from St. Louis but are the numbers we use to say how many items there are in a group, a collection, a heap or as the mathematician prefer to call it a set. Let us look at a well-known example:

I’ll sing you twelve, O

Green grow the rushes, O

Twelve for the twelve Apostles

Eleven for the eleven who went to heaven,

Ten for the ten commandments,

Nine for the nine bright shiners,

Eight for the April Rainers.

Seven for the seven stars in the sky,

Six for the six proud walkers,

Five for the symbols at your door,

Four for the Gospel makers,

Three, three, the rivals,

Two, two, the lily-white boys,

Clothed all in green, O

One is one and all alone

And evermore shall be so.

This is the final round of an old English counting song the meaning of several lines of which remain intriguingly obscure. Starting with the fourth line from the top we have a set of 12 Apostles i.e. the original twelve follower of Jesus. One line further in, we have a set of 11, who went to heaven, presumably the Apostles minus Judas Iscariot. And so we proceed, each line refers to a group or set giving to number contained in it.

In everyday life we use cardinal numbers all the time. I bought 6 eggs today. There are 28 children in Johnny’s class. My car has 4 wheels and so on and so forth. The cardinal numbers also contain the number zero (0), which indicates that a particular group or set under discussion contain no items at all. There are currently zero kings of France. We can carry out all the usually simple arithmetical operations–addition, subtraction, multiplication and division–on the cardinal numbers including zero, with the exception that we can’t divide by zero; mathematicians say division by zero is not defined. So if Johnny’s class with its 28 members are joined by Jenny’s class with 27 members for the school trip there will be 55 children on the bus. I’m sure you can think up lots of other examples yourselves.

Ordinal numbers have a different function, there signify the position of items in a list, row, series etc. We also use different names for ordinal numbers to cardinal numbers, so instead of one, two three four…, we say first, second, third, fourth…etc. an example would be, Johnny was the fifth person in his class to get the flu this winter. Now, in the ordinal numbers there is no zero, it would be a contradiction in terms, as it can’t exist. Occasionally when there is an existing ordered list of principles or laws people will talk about the ‘zeroeth’ law, meaning one that wasn’t originally included but that they think should precede the existing ones.

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. Whichever system of counting years one uses, Gregorian, Jewish, Muslim, Persian, Chinese, Hindu or whatever there is and never can be a year zero, it is, as stated abve, a contradiction in terms and cannot exist. Therefore the first decade, that is a group of ten year, in your calendrical system consists of the years one to ten or the first year to the tenth year, the second decade the years eleven to twenty or the eleventh year to the twentieth year and so on. The first century, that is a group of one hundred years, consists of the years one to one hundred or the first year to the one-hundredth year. First millennium, that is one thousand years, consists of the years one to one thousand or the first year to the one-thousandth year.

Going back to our starting point the first decade of the 21st century started on the 1st January 2001 and finished on the 31st December 2010. 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.

Filed under Calendrics, History of Mathematics, Myths of Science

### 16 responses to “There is no year zero!”

1. Michael Traynor

Unless your habitual answer to ‘What year is it?’ is in the form ‘The two-thousand nineteenth.’ you are hoist by your own petard, Thony.

• I suggest you actually read what I wrote at the beginning of the beginning of the penultimate paragraph and then reconsider your comment.

2. A delightful post, precisely because the question, “Could there logically be a year 0?” depends on implicit (or explicit) assumptions, and so both sides can feel clothed in absolute righteousness. (I accept of course that Thony’s position comports better with history, as he explains thoroughly in the linked post “Something is wrong on the internet”.)

A pity this blog wasn’t around in 2000!

• Gita Dunbar

As I recall, there were many people around at the time making the same sort of argument, albeit without using the ‘cardinal’ and ‘ordinal’ reasoning … at least I don’t remember such. Anyway, nobody listened then and I doubt anyone much will listen now.

• Actually astronomers do use a year zero when they need to relate events such as eclipses to conventional dating (year 0 is 1 BCE). Here’s Fred Espenak’s explanation.

https://eclipse.gsfc.nasa.gov/SEhelp/dates.html

Also, astronomers have long got around the problem by pushing the starting date of the calendar back to a time before there were any observations. This led to the Julian Day Number system:

https://en.wikipedia.org/wiki/Julian_day

Note that Julian days start at noon GMT (so that european astronomers didn’t have to change day number during an observing session).

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4. Carl Vehse

This topic brings to mind the legendary Lutheran theologian, Franz Bibfeldt, whose writings first came to light in some last-minute creative footnote padding in a Concordia Seminary-St. Louis term paper in 1947.

Excerpted from the University of Chicago Magazine February 1995, article, “The Unbearable Lightness of Being Bibfeldt“:

Chronologers admit,” says the Encyclopaedia Britannica, “no year between 1 B.C. and A.D. 1.” By reckoning in this manner, notes the Encyclopaedia, “there is an interruption in the regular succession of the numbers.” For chronologers, this merely fouled up the leap years. But Robin Lovin-a former U of C professor who is now dean of the Perkins School of Theology at Southern Methodist University-brings home the impact of this on the common 1-B.C.. man, who probably found himself uncommonly inebriated on the eve of such a noteworthy new year. “One minute you’re a full year before Christ,” notes Lovin, “and then, BOOM, one minute later, you’re into the first year of the Christian era, with nothing in between.”…

The only modern scholar to tackle this issue is the more-or-less University of Chicago-based German theologian Franz Bibfeldt, who in 1927 submitted his doctoral thesis to the University of Worms on “The Problem of the Year Zero.” Like most truly innovative works, Bibfeldt’s thesis was not initially well received. But Bibfeldt scholars do find in it early signs of the overarching theme that came to dominate all subsequent efforts of the man who is perhaps the most adaptable intellectual of our century: the search for the missing middle.

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6. Jacob Kanev

This is exactly right. Obviously, there was one year before the year of Christ’s birth, directly followed by one year after the year of Christ’s birth. There has never been a year of Christ’s birth, and the logical conclusion can’t be anything else than that Christ was never born. Or maybe he was, and the people who made the calendar several years later wanted to cover something up? What dirty secret is lurking here? Why was year zero removed? What did really happen? And if we find out, should we tell the Christians?

• Carl Vehse

Numbering the years with the use of A.D. (anno Domini and B.C. (before Christ) was started in the Western world in 525 A.D. and became more widely used after 800 A.D. This was well before the number zero was recognized, especially for its cardinal use. By then, of course, it was too late to add the extra “zeroth year.”

• The AD dating system was indeed created in 625 CE but first came not general use in the late 8th century. However, BC dating doesn’t really come into general use until the 17th century.

7. After the XKCD comic today I googled to understand this better and found your post. I appreciate you taking the time to write this up. (XKCD Link – https://xkcd.com/2249/ )

• Jim Harrison

Are we in the 20’s now? As far as politics are concerned, it sure feels like the 30’s.

8. Scott Woodford

Of course there is no year Zero. Dionysius of Exiguus has been called stupid or ignorant because he didn’t start our calendar with a year Zero. I think he would have started with year one even if he had known about zero. Modern timelines use a zero to separate negative units from positive ones. But in this case the zero is a just a point the same as other numbers. Zero does not take a whole year. To measure an amount of time, a span, we have a start point and an end point. Dionysius may not have called it zero, but he must have started at a point, and ended twelve months later creating year One. Even today we measure things without needing a zero. Most of the twelve inch rulers I have seen do not have a zero. The left edge of the ruler is a flush starting point so a carpenter can go to an inside corner wall and get a true measurement from the corner. A tape measure can do that plus the tab at the tip ensures the tape starts at the edge of a two by four. There is no zero there either. In fact you can make a functional timeline by putting two tape measures tip to tip and stretch the tapes out in opposite directions. No zero is needed.
Here is another argument for starting with year one. We like round numbers and we like the sound of counting from zero. When we count tangible things we start with one, but the zero is assumed. Suppose I had ten dollars in my pocket. To confirm that I would lay them on a counter one at a time as I count them. Of course the counter is empty to start so I don’t start with zero. I start with one, two, three and so on. I might say I start with the first dollar, then the second, third etcetera until I get the the tenth.
Now lets suppose that I have a a bunch of dimes in my pocket. I clear away my bills and start counting dimes;ten cents, twenty, thirty up to ninety. I might say to myself I have zero dollars so far, so I must be on my zeroth dollar. What happens when that tenth dime hits the counter? We have just as much cash on the counter as the first bill. Are the ten dimes suddenly my first dollar in dimes? The truth is that all the dimes were part of the first dollar; even the first dime. Years work the same way. From the first nanosecond of whenever we start, it is part of the first year. Should we call it year One or year Zero? I choose the former!