Because nobody does this. Nobody counts ordinary things starting from zero. Nobody counts their ten fingers, which are the first things we count, as 0 through 9. It just doesn’t happen.
I would like to point out that the issue of a possible Year Zero only occurs when you establish a proleptic calendar, that is, a calendar that generalizes your dating system to before the starting point. That is a much more sophisticated thing to do than just establishing a calendar, and some calendars never do it – regnal calendars, for example (since in the West they’re used for affairs of state, there’s no point using them for anything that happened before there was a state).
It’s not arbitrary though. It is based on the inherent meaning of “one” and “first.” You could come up with an ordinal system that started with zero, but why? You might as well start with -1th or -4.5th or 3.14th.
The problem arises because when you’re measuring years you are used to counting parts, not the whole
In a calendar the year 1 represents all time and any fraction of that time.
We don’t say we have part of a finger, or part of a donut.
For instance, if I have a dozen donuts and someone took ONE bite out of ONE donut and then I asked you to count them. You’d say “12 donuts.” Or maybe 12 donuts minus a bite.
When we measure dates we understand the year 1 means any time from 0 to the end of year 1. OR any fraction of that time.
Notice little kids say “I’m five and a half.” Once you get to a certain point, you no longer say that.
A year old is “understood” to mean COMPLETED one year AT LEAST.
So you’re really comparing apples and organges. Yes they are both fruit but they are different measures.
Time on a calendar is measured different from other things.
Since time is random anyway it doesn’t matter how we count it as long as everyone agrees on that defintion so we can all be coordinated
You’re right that nobody does this; the convention in English and other languages was set differently. And that’s fine. My point was only that it’s not conceptually impossible to justify zero-based counting as a natural system; whereas one-based counting is based on the question “How many things are previous to or equal to this?”, zero-based counting is based on the question “How many things are previous to this?”. Both are pretty natural questions, but for (understandable) historical reasons, the former is the one which humanity found itself thinking about first.
“How many things are previous to this?” is a pretty natural question, I would think, which would yield a zero-based counting system. Presumably, no similarly natural question would yield a -1th or 3.14th based counting system.
I am not claiming that people should adopt zero-based counting; I am not claiming that one-based counting is flawed. I am simply claiming that zero-based counting is every bit as conceptually permissible as one-based counting; whereas the latter is based on counting the size of the collection of objects <= the ordinal position of interest, the former is based on counting the size of the collection of objects < the ordinal position of interest. Both natural questions…
It’s conceptually permissible in the sense that it is logically consistent, and doesn’t fall over. But it’s not intuitive; it ignores the meaning and implication of “zero”.
As I said before, “zero” indicates not a specific value, but the absence of any value. To call something the zeroth element of an order or array would imply that it had no value or status as an element of the array; that it was not, in fact, an element of the array at all. And this would be wrong.
You can attempt to justify it by saying that “zero” points, not to the item itself, but to the (hypothetical) item that comes immediately before it, which is not a member of the array. But there’s no obvious reason why we should describe this item by pointing to a characteristic of another item.
Moreover by the same logic there could be a large number of items that could be called the “zeroth” item in the array, If I line up three apples on the table and count them, right to left, using your system I would call the first one the zeroth apple of the line. But all of the apples in the line over there on the counter could equally be called the zeroth apple of the line on the table, since the apple next to each of them is not part of the line on the table. Whereas under the current ordinal system, there is one and only one apple that can properly be called the “first” in the line.
It doesn’t ignore that meaning. It uses it: the item called the “zeroth” would be the one which came after zero many predecessors. The item called the “oneth” would be the one which came after one many predecessors. The item called the “twoth” would be the which came after two many predecessors. And so on.
Huh? 0 is as much a specific value as 1 or 2; it just happens to be the value which denotes how many things are in an empty collection. That doesn’t make zero not a value, any more than it makes 2 into a pair of values.
I’m not pointing to another item; I’m pointing to a collection of items, and counting how many are within that collection.
I’m not saying “This apple is the zero-th apple because of some property of the particular (non-existent) apple which precedes it”. I’m saying “This apple is the zero-th apple, in this manner of speaking, because the number of apples which precede it is zero, just like this other apple is the 8-th apple, in this manner of speaking, because the number of apples which precede it is 8.”
Huh? You’re making up some weird system other than the one I’m talking about.
In the “zero-based” system, I call an apple the k-th when the collection of apples prior to it has size k. In the “one-based” system, you call an apple the k-th when the collection of applies prior to or including it has size k. These two counts always differ by exactly one. It’s not like the “zero-based” system can diverge far from the “one-based” system and go completely off the rails; the two are yoked together.
There’s two separate concepts at play here: cardinal size (how many things are in this collection?) and ordinal position (which position in an ordered series is this?). These two aren’t the same thing; they are different concepts. However, one can set up a correspondence between them. To do so, we need to find a way to turn an ordinal position into a collection whose cardinality to measure; in the “one-based” system, the collection we choose is “All positions <= this one”, whereas in the “zero-based” system, the collection we choose is “All positions < this one”. That’s the only difference, and both are equally justifiable ways to naturally transform from ordinal positions into cardinalities.
Another way to put it:
Supposing one had a fence with a bunch of posts along it at a uniform distance, and one wanted to label the fenceposts in series. One way of labelling any given post would by announcing how many posts were prior to or equal to it (One-based indexing: “I’m calling this the 5-th post, because there are 5 posts prior to or equal to it. The very first post, I’ll call the 1-th one, since there is just 1 post prior to or equal to it.”), but another way would be by announcing its distance from the start of the fence (Zero-based indexing: “Actually, I’ll call it the 4-th post, since it’s at a distance of 4 fence-links from the start of the fence. The very first post I’ll call the 0-th one, since it’s at a distance of 0 fence-links from the start of the fence.”).
Both are equally natural, justifiable methods of labelling positions in the series of fenceposts.
I don’t agree here. There is an inherent meaning of the term “fourth” and it’s not “there are four before this.” I’m not saying you can’t index in the manner you describe, but you can’t do that and use the traditional terminology of ordinals.
I… agree with you. I’m not saying that “fourth” does mean, in English as it actually exists, “the position with four predecessors”. Obviously, it doesn’t. Nobody who speaks English speaks like that.
I’m just saying that had a language developed its standard terminology to correlate the term for “the ordinal position of E in the series A B C D E” with the term for “the cardinal size of {X, Y, Z, W}” rather than with the term for “the cardinal size of {X, Y, Z, W, V}”, this would be perfectly natural and justifiable.
As it happens, this is not the route English took. I have no disagreement with that undeniable fact. But it’s not because one-based indexing uses a correspondence which is somehow more logical and essential than the one used in zero-based indexing. It’s just a contingent fact about the particulars of this language, that it happened to go with one natural correspondence rather than another.
Well, do we know if any other language handes the matter differently? In particular, since Indian culture has had the concept of zero since God knows when, and does in fact have calendar systems that start at zero, not one, do we know how ordinals relate to cardinals in the various Indian languages?
That is, we agree on what the traditional terminology of ordinals is; it would be extraordinarily silly to pretend not to know this. My point is only that this traditional terminology has no canonical status other than that it happens, as a matter of contingent historical fact, to be the traditional. The other system being discussed is equally as well-motivated, on its own merits. It just happens to not be the traditional one. It could have been, but it wasn’t. That’s a fact about humans and numbers.
“Indian culture” didn’t gain the concept of zero as a number until far after it had standardized its basic number-names, same as us; after all, both English and the northern Indian languages derive from the same Proto-Indo-European language ancestor, which already had well developed number terms. Pretty much every human culture reached the concept of “zero as a number” far after they’d already started developing their basic number terms, for the same reasons; again, this is just a fact about human psychology and not about numbers themselves.
(Note that even in English, we can see how certain concepts arose later than others: the names for “first” and “second” have nothing to do with “one” and “two”, just as “half” has nothing to do with “two”; the names only begin to be developed uniformly from 3 on)
