Note: Although I'd side with EWD on this one (for now, at least), I don't intend to reference it as an "appeal to authority", but as an example of someone producing a reasonable, properly worded and thought-through argument on the topic, which I've not really seen since. I'd be very interested in what similar arguments would look like from the other perspective. If someone would like to convince me, feel free give me a link to some reasoning :)
Also: I personally find "it's always been like this" to be a terrible argument in either case. Those are the reason we weren't able to standardize for one system of units, for example. In the Swiss army, there's a saying that is used to explain the various idiotic decisions and the bogus explications thereof a soldier has to endure:
Ist so weil ist so, bleibt so weil war so.
Things are like that because they are like that.
All stays that way because it was that way.
I have my opinion, and that is that zero is the proper number to start enumerations on, not just in programming, but for everything.
Everyone starts counting objects at 1. Zero means an absence of objects to count or list. I count that there are 7 cars in the lot. The first one is 1. If there were 0 cars, I would not have any to enumerate over. If I make a list, I always number the first one as 1 (or A). If there was nothing on my list, I would have nothing (0) to number.
Word processors start list numbering at 1. Printers number the first page as 1. Kids are taught to count starting with one, using one finger. I feel like this is only an argument because we have zero-based indexing in mainstream programming languages, although maybe there are some mathematicians who think otherwise?
I don't take programming languages as a reference point. It's the other way around. I try to figure out what the most natural, principled, and elegant way would be, and I would base my programming language on that, if I were to design one.
> Zero means an absence of objects to count or list. I count that there are 7 cars in the lot. The first one is 1. If there were 0 cars, I would not have any to enumerate over. If I make a list, I always number the first one as 1 (or A). If there was nothing on my list, I would have nothing (0) to number.
We should distinguish between two uses of the natural numbers, I think:
0. _Ordinal numbers_, for assigning labels to things. "This is car 3." 1. _Cardinal numbers_, for saying how many things there are. "There are 7 cars."
The relationship between the two would be that the number of cars is the number that is next in line when you have called out the indices (0, 1, 2, 3, 4, 5, 6) of all the cars.
> Word processors start list numbering at 1. Printers number the first page as 1. Kids are taught to count starting with one, using one finger. I feel like this is only an argument because we have zero-based indexing in mainstream programming languages
What is the most common isn't what determines, for me, what is the most proper. I will play along and use 1-based indexing when I have too, but in my heart I know how I think it should _really_ be.
> maybe there are some mathematicians who think otherwise?
Yes, though starting numberings on 1 is still common (maybe the most common). Zero is at least recognised as a natural number nowadays. Historically, this wasn't the case. Apparently, Peano started on 1 in his axioms for the natural numbers [0], and zero, as far as I understand, hardly had the status of being a number at all during much of Greek and Roman antiquity [1].
[0] https://en.wikipedia.org/wiki/Peano_axioms#Formulation [1] https://en.wikipedia.org/wiki/0#Classical_antiquity
But who thinks that way? I just see 7 cars, not an indexed listing. And anyway, the 0 indexed car doesn't exist.
The question for me is what one _should_ do, not what is usually done.