Johannes Gebauer wrote:
For the same reason there is no year 0. 0 is the point in between the year -1 and the year +1. Midnight of the 31st December in the year -1 _is_ zero, but one minute later is in fact the 1st January of the year 1.
to which Owain Sutton rejoined:
You give medieval astronomers too much credit. There's no year zero because nobody made one (the AD system was created retrospectively, don't forget.) If a year zero did exist, you'd be arguing that it would be ludicrous to leap from -1 to +1.
but which causes me to observe that I understand first, that there was no general distinction two millenia ago between "mathematicians" and "astronomers", and second, that there was generally no concept of "zero" in any numbering system then in use. I seem to remember that the first incidence of the occurence of the concept of "zero" as a number was by the Mayans, and occurred as recently as 1500 years ago, or so. The Hindu's in India developed the idea of a number "zero" at about the same time, or a little later, and it was introduced to the West by the Arabs during the height of Arab culture about 1000 years ago..
Second, the issue of whether or not there can be a measure zero, is a no more than a matter of where one begins measuring something, and how one measures it. It is convention in the U.S. to have measuring devices six inches long with zero at one end, and six at the other. It is only convention that the rule is not numbered from -2 to 3, or from or from six to twelve. And as a practical matter, I can tell at a glance when someone is measuring a one inch long item, whether they are trained as a carpenter or machinist, by the way they use a rule. Most people using a six inch ruler to measure off one inch, will use the endpoint (zero) as a starting point; trained carpenters and machinists (at least those in my acquaintance) start with the "1" mark because the distance between the "1" and the "2" are less likely to vary than the distance between the end of the rule and the "1" mark.
The idea of a measure designated "zero" is a matter of order. If you have an established, ordered set of items, whether of letters, numbers, people, measures of music, or laws of thermodynamics, and discover a need to add something to the beginning of the string, you are faced with the choice of inventing a new new number, or re-numbering the string. I would submit that if you have an ordered sequence of measures of music, named beginning with "one", and "two", and named in accordance with a rule which says that the name of the next item added to the final end of the string is the derived by assigning as a name the name of the number that is one higher than the previous last measure, and then are confronted with the need to add a measure at the beginning of the string, you will apply the same rule, that is, that the name of the new "first" measure will be the name of the old first measure less one, then you have measure "zero".
Science, by the way, is not protected against exactly this type of issue. When I was in high school, I was taught that there were three laws of thermodynamics. In college, a few years later, I was taught that there were four, because it was realized that there was a necessary precondition to the other three. Since there already was a longstanding tradition of referring to the original three as the first, second and third laws of thermodynamics, and since the original three depended upon the newly stated fourth, this fourth law ["If 'A' is in thermodynamic equilibrium with 'B', and 'B' is in thermodynamic equilibrium with 'C', then 'A' is in thermodynamic equillibrium with 'C'."] was named the "Zeroth law thermodynamics"
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