Folks ... cardinal and ordinal numbers both have "just so" stories to support them. We're unlikely to eliminate either one of them today.

"here" is definitely not a zeroth block. As soon you start walking, you are in the first block. However, if you are numbering the separations (cuts) between the blocks, you can number that "here" as zero.

Ok as soon as you start walking your are in the first block, I agree. So then where are you before that? What block were you at before you started moving, when you were giving directions?

What is the name of the block from which you left to enter the first block? Before you started walking I mean.

And mustn’t that block be before that other first? When we move from where we start we count up, so then mustn’t an earlier block be counting down? Counting down would mean a number smaller than one.

And are blocks not counted in units, as whole numbers?

So would it not be the case that one block less than 1 must be by necessity the zeroth block?

In other words if you agree that “as soon as you start walking, you are in the first block”, then you must also agree that before you left you began in the zeroth block.

How else could it be interpreted?

Before starting to walk, you were at the start of the first block, not at zeroth block. There is no block prior to first block. Otherwise that block would be called as first block.

Think of jogging on a road. When you are at the beginning of the road, you are at the start of the first mile, not in the zeroth mile. It doesn't have one more mile prior to first mile.

The patient-0 terminology arose from a misreading of the label patient-O, where O is the letter O.

When numbering discrete elements you usually start with 1, so first is 1, second is 2 etc.

Indexes in C are not ordinal numbers though, they should be thought of as offsets or distances from the first element. So [0] is 0 steps away from the first element, hence the first element. The confusion arise when you think these indices are actually ordinal numbers.

I agree with all of this.

The original discussion was regarding there's no such thing as a zeroth X, and what I've been trying to say this whole time is sure there is, it's the beginning. Which is why you start counting time from 0.

Interesting about patient-O though. I didn't know that.

My previous comment may have seemed snarky, but that wasn't my intention. I tried to originally write something that didn't seem sarcastic but it was just long.

The best way to explain my point was to just to agree and then list the contradictions that arise, e.g. The day starts at 12:01 since there's no zeroth minute, etc... and that unfortunately has the effect of looking like snark.

OK but I’m not sure I get your point then. Are you saying Edwin Aldrin was the first man on the moon because Neil Armstrong was the zeroth?

Not at all. Neil and buzz were first and second astronauts on the moon.

If we ask who was on the moon before them then the answer is nobody.

I think that’s agreeable. So then what am I talking about? It’s just counting.

I’m going to explain this to whomever is interested, and anyone is free to tell me where I made a mistake, in which case I will thank them for the correction.

When we talk about counting we say we are talking about things like numbers. We also talk about things, because you count things. And so counting is numbers of things. Like the number of ways to combine two dice rolls is a problem for counting.

One property of counting is that the numbers and the thing counted are separate. In other words the thing being counted does not matter when we are counting, as long as they are countable. I think that much is clear. Numbers work the same regardless of the thing being counted.

So let’s then define how counting works. Let’s say the cardinality of a set determines the “nth-ness” of the number, and the kinds of things the set holds inside is how we determine the thing we’re counting. Together, the type of thing the set holds + it’s cardinality is how we say the nth-ness of the thing being counted.

Remember the thing and the number are separate from each other, and that the count ability is also crucial. It’s the cardinality that determines the nth-ness of the count.

So then let’s count astronauts using our rule and determine who is the nth astronaut. Neil is first because when he landed on a moon, the set of all moon landers had a cardinality of 1. And buzz is second because when he landed on the moon the size of the set of moon landers is 2. Size of a set and cardinality are the same.

A set can also be empty. This set has a cardinality of 0.

So what was the set of moon landers before Neil? It was empty. In other words, there was nobody on the moon. So if we apply our rule we say that nobody was the zeroth person on the moon.

You might say that doesn’t make sense because nobody isn’t a person, but the problem is that’s a concern for the thing and not the number. We said they are separate things.

In this case we are only really interested in the nth-ness of the number and the kind of thing the set holds.

While nobody is not a person, the empty set itself definitely exists and it definitely has a cardinality of 0.

So the zeroth person on the moon was nobody. The zeroth mile is no mile. The zeroth century is no century. Some of the these things might make sense to you and some might not. But the sense that they have or don’t have in those case stem from how we think about the thing and less about the number.

I’ll give my final example.

An experiment starts at time t0. The zeroth second. Each second that is completed grows the size of our set of seconds. Nonetheless when the experiment began the set was empty. That was the zeroth second.

It’s not an actual second, but that doesn’t matter you can still count it. No second doesn’t exist but the empty set of second does and it can be counted. And in fact it’s really hard to explain counting at all if you don’t have a concept of zeroth.

That is why a zero-day exploit is called what it is because not one full day has passed since its existence has been revealed. Would first day also work, yes that’s fine colloquially but zeroth day is definitely not wrong is what I’m saying.

That is why we start the day at 00:00 in military time. Because what the time of a day means is the size of the set of hours, minutes, second, etc… that have passed. But the count starts at the empty set.

Here’s a very funny and confusing example: The day you are born is not your first “birth day”, because a “birth day” means anniversary of your birth. However the day you are born is the empty set from which that count begins. Birth day in this sense is an overloaded term in English but in many languages it’s literally called birth anniversary.

Anyways, that’s what I have to say. Probably much more than anyone wanted or needed but I hope it was at least clear what I think. If I’m mistaken then let me know.

Clearly there is some contradiction if you claim the first chapter in a book is the “zeroth” chapter but the first man on the moon in the first man.

That's a neat way of thinking.