Seeing book sections or chapters starting with zero, always confuses me. I know that this convention is probably inspired by the fact that the addresses of memory locations start with zero. But that case was due to that fact one of the combination of the voltages can be all zeros. So, it's actually the count of combinations, and I don't think it can be used for ordinal enumeration of worldly things such as book chapters, or while talking about the spans in space and time (decades, centuries, miles etc). There is no zeroth century, there is no zeroth mile and there is no zeroth chapter. In case the chapter numbers are not meant be ordinal, then I think it would be odd to call Chapter 3 as fourth chapter.
If you’re at a corner and someone asks for directions, you say “three blocks that way”. That means three blocks starting from here.
Then what do you call “here”?
The name for where you start from in this scenario is usually not required because it’s obvious what you mean and everyone understands the first block means you have to first walk a block, not that where you start is the first block.
So in that sense yes we have a zeroth chapter. That’s when you’re at the beginning of the first one but haven’t read all the way.
"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.
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.
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.
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.
The first element in a collection at address 15 is at address 15. The offset of an element from the start is addr-start, so 15-15=0 for the first, 16-15=1 for the second, etc.
that's why we start from 0, not because of voltages, at least in compsci.
This is all mostly about cuts and spans in a continuum. Cuts can be numbered starting with zero, but spans can't be. Book chapters are spans of content.
Usually the chapter 0 is preliminary or prerequisite material. It makes sense in an obvious and intuitive way if you want an ordinal "before the first", even if that sense isn't a rigorous mathematical one (although I think there's no problem with it).
I guess the practice was influenced by computer science - I don't know of an example that precedes it, but one fairly early one I've found is Bishop and Goldberg's Tensor Analysis on Manifolds from 1968, with a chapter 0 on set theory and topology. Back then the authors felt the need to justify their numbering in the preface:
"The initial chapter has been numbered 0 because it logically precedes the main topics"
Quite straightforward.
There's also the "zeroth law of thermodynamics", which was explicitly identified long after the first, second, and third laws, but was felt more primary or basic, hence the need for an "ordinal before the first"
The reason is that, for an array (or vector), you find the memory position for the i-th element with the base address + i*word_length. And the first element is in the base address - so has index 0.
It has memory offset 0, which we use as the array index for convenience so that there's no distinction between a memory offset-base and the corresponding array index-base. That's what happens when your arrays are barely different from pointers, as in C. If your arrays aren't just a stand-in for raw pointers, then there's little reason to require 0-based indexing. You can use more natural indexes based on your particular application, and many languages do allow arbitrary indices.
Building floor numbers in at least a few countries I’m aware of start from zero or “G” ( or the local language equivalent for “ground“) with 1 being the first story above the ground.
I think you’re just biased to think that starting must “naturally” begin with 1.
Zero is just a good a place to start and some people do start counting from zero.
The floor number case arises so because traditionally it is the count of "built" floors. So, ground is technically not a floor in that sense. Also, if the floor indicates a separation (cut) between the living spaces, ground floor can be numbered as zero, just like the start point of a measuring tape is numbered as zero.
Zero is not an ordinal number. There can be a vector element indexed with zero, but it is not "zeroth" element. Book chapter numbers are ordinal numbers.
Just the convenience of having an ordinal number to say? Rather than saying "chapter 0, chapter 1, chapter 2" one can say "the fourth chapter"? Or is it the fact that the chapter with number 4 has 3 chapters preceding it?
On first glance I find this all rather meaningless pedantry.
If I use ordinal numbers to count, then counting tells me the number of objects. Sometimes I want to know the number of objects.
EDIT: Yeah, I don't know why book chapter labels shouldn't start with "0". It seems fine to me. They could use letters instead of numbers for all I care.
When I'm counting letters it's more convenient to go "one, two, three." When I'm finding the offset between letters it's more convenient to go "zero, one, two." Neither of these methods is going to displace the other.
Definitions are fine, and I agree that "A" is the first letter. But that's no use to people who need to think clearly about the offset between "A" and "C" right now. Should I tell them they're wrong, they have to count to three and then subtract one? Because the dictionary says so?
Offset is an answer to the question "where does Nth memory location start from?". The answer is "after N-1 locations". It's the count of locations that need to be skipped by the reader, to reach the start of Nth memory location.
I don't know but I feel like you are making a point out of something arbitrary. When I listen to an audio book, everyone always says: "Chapter 1", not "the first chapter" so why is this important?
I think extreme attention to to arbitrary meaningless details is how we ended up with most rules in language that we are starting to collectively detest.
