**How to enjoy yourself with numbers – or: what some people quarrel about.**

I did so on purpose when I included best wishes for the new decade in all the cards I sent to my friends wishing them a Happy New Year.

It was done deliberately because I knew quite well that some people think the new decade can only correctly start with January, 1st, 2011, just like the new (third) millennium basically did not start before January, 1st, 2001.

As a consequence (just like it happened ten years ago when I sent best wishes for the new millennium), I again received an email with roughly the following content (here are just some passages):

“contrary to what is postulated often and by various media, the 31st of December 2009 did not mark the end of a decade. Instead, we are still in the first decade of the 21st century, which is at the same time the beginning of the 3rd millennium. Please remember: both the 21st century and the 3rd millennium started on January, 1st, 2001 (not, as some people say, on January, 1st, 2000).

See also the wikipedia *article*

What ended with December, 31st, 2009 are the so-called “zero-years”, i.e. (in this case) the years 2000 to 2009″

I had to defend myself. My first idea was: I simply move the start of my series of numbers down by one, introducing a “year 0” per definition in the same way as you can introduce the zero when talking natural numbers. Then I can feel free to continue calling the 1st of January 2010 the start of a new decade.

However, this is not as easy as it looks, because the number zero was “unknown” in Europe before the 13th century. Before that, the set of the natural numbers only included numerals bigger than zero. The Romans did not know the numeral zero at all, which is why the Roman letters for numerals have no character for zero. On the other hand (also in the IT sense), a space character (as the term says it) is also a character). And, of course, you can also use such a character as a numeral, for example for zero. Incidentally, in the primitive Roman number system, a zero would not make sense, anyway – except maybe in order to represent the term “zero” (nulla, nullum, nullus?).

The background of this idle discussion is that there has never been a “year zero”. The year 1 after Christ (+1) followed directly after the year 1 before Christ (-1). I guess nobody knows exactly if Jesus was born in the year 1 after Christ or in the year 1 before Christ. He cannot have been born in the year 0, because there was no year 0. To conclude that Jesus was not born at all because there was, after all, no year 0, is, of course, logically spoken, also nonsense.

If I started my definition with the year ZERO, the first decade after Christ would have been only 9 years. The same is true for the first century after Christ, which would have been only 99 years, etc. Which would mean that when the calendar says 2010, we are living in the year 2010, yet only 2009 years after Christ was born?

Isn’t all this quite confusing? Besides, it is total nonsense. Just like the discussion if the number zero is part of the natural numbers.

Of course, you also find an article in wikipedia on the natural numbers. The definition is:

The **set** of natural numbers,

dependent on the definition, contains

either the positive cardinal numbers

or the non-negative numbers

To me, this latter definition sounds good. I presume it is also the modern one, as opposed to the former one, which is historical and archaic. Our professor of analysis at TUM, Dr. Leutbecher demonstrated in a surprisingly simple way in his lectures why the zero is “of course” a natural number. His proof: he asked us to put 5 DM (I heard his lecture in the early 1970ies) on the table and announced that he was now going to prove that zero is, indeed, a natural number.

I find it incorrect to use the term “non-negative” cardinal numbers for defining natural numbers. At the time the set N is defined, you do not even know that there will be negative numbers. The set of the negative numbers extends the natural numbers to become the integer numbers. You achieve this by executing the operation “minus” on the natural numbers. In the same way, you get group, ring, field …

All of this is, of course, a humorous, perhaps confusing, yet totally useless discussion. Because most of the people living in our culture group (incidentally, most people living in this world do not belong to our culture group – and they may have totally different (calendar) problems) decided by their celebration with an absolute majority that the night between December, 31st, 1999 and January, 1st, 2000, was the beginning of a new millennium!

This democratic majority vote (or would the modern term today be Crowd Sourcing?)** determined that, likewise, the new decade started on January, 1st, 2010. And that is why I will also wish everybody a happy new decade on January, 1st, 2020!**

Naturally, I can only do that if I am still able to at the time.

RMD

(translated by EG)

P.S.

Ionly wrote this because I am totally fascinated by what wonderful kinds of things some people on this world are capable of finding interesting and wishing to prove. Formerly, this would have been called “mental onanism”. No longer today. I think it would be more recommendable if we used our mental energy for thinking about the latest Club of Rome report (see also my article on the presentation by Martin Lees).

P.S.1

The picture was taken by Rolo Zollner. He took it for one April fool’s joke in the IF blog.