[kbd]

I can't believe I'm jumping into the inevitable 1-based indexing discussion, but I'm surprised to see you say that one-based indexing results in "less "+ 1" or "- 1" things in your code". Most arguments I've seen come out to "it's fine" (certainly) or "it's more comfortable for mathematicians" (which I can't speak to).

Besides Dijkstra's classic paper[1] showing why 0-based indexing is superior, in practice I find myself grateful for 0-based indexing in Python because of how slices and things just work out without needing +1/-1.

I'd like to understand. Could you give an example of when 1-based indexing works out better than 0-based?

[1] http://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF

[mruts]

The classic example is getting the last element of an array. With 1-based indexing the length of the array is the index of the last element. It has a nice symmetry to it.

Also I find it elegant that for 1-indexing that the start and end value for slices are both inclusive, instead of the first one being inclusive and the last being exclusive.

Also, isn’t it just weird that the index of an element is one less than it’s “standard” index? Like if I take the first nth elements of a list, it would stand to reason that the nth element should be the last element, right?

The reason for zero indexing is historical, related to pointer offsets. I don’t think anyone chose them to be easier for people. They just made them that way because it maps closer to how contiguous values in arrays are accessed.

Also, with 1-indexing I can multiply numbers by arrays and get reasonable offsets. 3 x 1 is three, so I would get the third element of the list. But with 0-indexing, I have 0 x 3 which gives me the same element, clearly inconsistent.

There are some good reasons for 0-indexing and I have been using it in every language for my entire career. The amount of code I’ve written in Julia is marginal compared to my 0-indexing experience, so I might be missing something.

One nice this about 0-indexing is that I can slice a list in half with the same midpoint. For example a Python array with 10 elements:

fst, snd = arr[0:5], arr[5:10]

A little nicer than:

fst, snd = arr[1:5], arr[6:10]

Though you could have inclusive slices with 0-indexing, but it would be inconvenient and suffer from the same problem as 1-indexing.

[kbd]

> The classic example is getting the last element of an array.

Good point, in Python I don't notice that the last element is arr[len(arr)-1] because Python provides arr[-1]. I think in general your point is that it's natural for the nth element to be arr[n].

> The reason for zero indexing is historical, related to pointer offsets.

There is that, but Dijkstra's paper makes the case from first-principles that the closed, open interval of [0,n) for sequences is the most appropriate.

> with 1-indexing I can multiply numbers by arrays... 3 x 1 is three...

Sorry, I don't understand this. It makes sense that the point I don't understand is probably most-related to why Julia chose its indexing scheme and why Matlab et al. do the same.

> One nice this about 0-indexing is that I can slice a list in half with the same midpoint.

Yeah, arr[0:index] + arr[index:len(arr)] is the full list. And to your point earlier ("if I take the first nth elements of a list"), len(arr[:n]) == n seems natural.

Edit: I've been trying to formalize why Python's indexing scheme, along with its negative-indexing, is optimal (slight pseudocode):

    l = ['a','b','c']
    n = len(l)
    i = -n
    while i < n:
        print(l[i++])

prints "a b c a b c". That code makes no reference to any bound but 'n', nor any constants (1,0) or offsets, yet it iterates over the list twice through its range (first negative indices then positive).

[iamed2]

Dijkstra's write-up is full of subjective aesthetic judgements that certain things are ugly. I personally don't find `1:0` for an empty sequence to be ugly, and I do find using `1:1` to refer to an empty sequence and `1:2` to refer to the sequence `{1}` to be ugly. I would encourage everyone to read over his reasoning and see if you agree with his aesthetic judgements.

[eigenspace]

I’m constantly baffled by the way people hold that paper up as some sort of objective proof that 0 based indexing is superior.

[kazinator]

Zero based indexing objectively has various convenient properties which one-based indexing doesn't.

The value of convenience over inconvenience isn't objectively better, that's all.

Objectively speaking, if I find the least positive residue of some integer modulo M, I get a value from 0 to M-1. If my M-sized array is from 0 to M-1, that is objectively convenient:

  hash_table[hash(string) % table_size]

Objectively speaking, if I have some files in a directory and I give them zero based names like file000, file001, ... then I can objectively refer to the first volume of ten using the single pattern file00?, and the next volume as file01?. If they are numbered from 001, I need file00? file010 to match the first ten. For the next ten, the file01? pattern unfortunately matches file010 so I objectively need some way to exclude it.

Objectively speaking, if I have zero based indices to a 3D array, I can find the address of an element <i, j, k> using the homogeneous Ai + Bj + Ck rather than Ai + Bj + Ck + D, which objectively adds an extra term.

Objectively speaking, the zero-based byte index B can be converted to a four byte word index using B / 4 (truncating division), and within that word, the zero-based byte local offset is B % 4. Objectively speaking, the same conversion from 1-based bytes to 1-based words requires (B-1)/4+1 and (B-1)%4+1, which is objectively more syntax and more nodes in the abstract syntax tree.

There is no reason I should like shorter, simpler, faster; that's a purely subjective aesthetic. After all, a short poem isn't better than a long one; a bacterium isn't better than a rhinoceros; and so on.

Hey, how about those one-based music intervals? C to E is a major third and all that? We have a diatonic scale with seven notes, right? As we ascend, whenever we cycle through seven notes, we have passed ... one more octave. And to invert an interval, we subtract from ... why, nine of course! And a fifth stacked on top of a fifth is a major ninth. There is objectively more cruft in 1 based music theory than 0 based. But there is no accounting for people liking it that way, right?

[eigenspace]

You do realize that there are approximately just as many use cases where 1 based indexing is more natural and involves less operations, right? It’s highly problem and context dependant.

But I’m not trying it make the point that 0 based or 1 based is better or worse than the other. I’m just saying that it’s a borderline immaterial difference for most use-cases and Julia gives many many tools for getting around any problems that may arise when a certain indexing scheme is awkward.

The 0 or 1 based debate is one of the most boring and pedantic arguments one can have and I do my best to ridicule people when they try to start it.

[goto11]

"Objectively speaking" there are pros and cons to each system. The largest pro of 0-based indexing is of course that it can correspond to a memory address plus an offset, which is the reason C (and derived languages) use 0-based.

But it is also an objective fact that using 1-based indexing means that the index corresponds to the ordinal numbers, e.g. index 1 is the first element, index 2 is the second element and so on. This also have a number of convenient properties.

For example February is the 2. month, so if you have a list of the names of the months, you would expect month_names[2] to be February. With zero-based you would have to do month_names[month_number - 1]. And if you want to get the month number from the name, you would have to do month_names.index_of(month_name) + 1. Be careful not to switch up the +1 and -1!

As for music theory, a third is called so because it spans three half-notes. It describe the size of a range which is independent of the offset of the indices. By the same token decades are 10 years (not 9) and centuries are 100 years (not 99).

[goto11]

I think people get tricked by his way of building an argument. He structures it rhetorically almost like it is a mathematical proof, but if you read carefully the central argument is that it is "nicer"...in the particular example he picked. But if you don't pay attention it might feel like he "proves" that 0-based is universally better.

Then he goes on weird diatribes like the one about "corporate religion". I'm not sure, but I think he is trying to say that people who question his dubious logic are "sheeple".

[kbd]

I wasn't arguing so much that it was "objective proof", but that in contrast to "The reason for zero indexing is historical, related to pointer offsets. I don’t think anyone chose them to be easier for people.", I was pointing out that there are arguments for it as well. It's not just because "the address of an array is also the address of its first element in C".

[pjmlp]

Because of the author. If it had been someone else no one would use it as such.

[goto11]

> Dijkstra's paper makes the case from first-principles that the closed, open interval of [0,n) for sequences is the most appropriate

He argues that it is the most appropriate when indexing into an array of the natural numbers starting with 0. If the array in question started with 1, one-based indexing would be most appropriate following exactly the same logic!

[kbd]

I don't think that's a correct reading. You're talking about this section, correct?

> When dealing with a sequence of length N, the elements of which we wish to distinguish by subscript, the next vexing question is what subscript value to assign to its starting element. Adhering to convention a) yields, when starting with subscript 1, the subscript range 1 ≤ i < N+1; starting with 0, however, gives the nicer range 0 ≤ i < N.

He never specifies the contents of the array, he's talking about subscripts (i.e. indexes).

[goto11]

You may be right, but in that case, why is the second range "nicer"? AFACT it is because he explicitly adds 1 in the first example but implicitly subtract 1 in the second, which makes it looks cleaner. If you want the N'th element of an array, the range in the first example is N ≤ i < N+1 while in the second it is N-1 ≤ i < N. Written out like that, I don't see how the second is obviously nicer.

[kbd]

Sure. Something is generally considered more elegant ("nicer") when it has fewer terms. (I'm really happy with my own argument above why Python's indexing is "optimal".) But I'd put what I think you're saying this way: Dijkstra asserts that '1 ≤ i < N+1' is worse than '0 ≤ i < N', but he's choosing his conditions carefully. '1 ≤ i ≤ N' also has no extra terms. (Though in fairness to Dijkstra, this section was after he'd already argued why closed, open ranges are better.)

I will say this though: in all the noise in this sub-thread, I never got any example in answer to my original question asking for any algorithm or formula that works out better with 1-based indexing (my original response was to its parent's claim that 1-based indexing results in fewer ±1s in practice). Except for maybe the "stride" examples[1] for which I still don't understand why the starting index is important. I say this not in victory (ha ha! zero-based indexes are clearly superior!) but in disappointment because I was hoping to gain understanding of why Julia/Matlab and others (which are more geared towards math/stats which is outside of my experience) made their indexing choice. Particularly because it's against the norm, they must have good reasons.

[1] https://news.ycombinator.com/item?id=20425500

[jpeloquin]

> Also, with 1-indexing I can multiply numbers by arrays and get reasonable offsets. 3 x 1 is three, so I would get the third element of the list. But with 0-indexing, I have 0 x 3 which gives me the same element, clearly inconsistent.

This is interesting. Suppose the task is to use this approach (index * stride) to pick every third item from a list of 9 items: [1, 2, 3, 4, 5, 6, 7, 8, 9].

With 1-indexing: Multiply the sequence of valid indices (1, 2, 3, ...) by the stride (3) and use the result to 1-index into the given list. Returns [3, 6, 9].

With 0-indexing: Multiply the sequence of valid indices (0, 1, 2, ...) by the stride (3) and use the result to 0-index into the given list. Returns [1, 4, 7].

0-indexing has the start point of the return values fixed to the origin. 1-indexing has its start point float around depending on the stride. Both work, but have different emergent properties in the given example.

[mruts]

It’s true that they both work, but I think the floating nature of the 1-indexing has some very desirable properties. If we wanted to sample from a distribution, the stride would relate to 1/n x 100 percent sampling. With 0-indexing we are always going to sample the first element. Granted this isn’t the best way to sample in the first place, so maybe it’s a contrived.

[eigenspace]

Shouldn’t Dijkstra’s paper be your 0th reference?

[nikhilsimha]

^ This is why I love hackernews!

[wodenokoto]

Looking at teaching materials, indexing in R hardly gets a mention. Student are told they get get the first element by a[1] and the twelfths element by a[12], and if you want 4th, 5th and 6th, you just ask for that range, a[4:6]

For python teaching this is almost a whole chapter, with people sharing cheat sheets and building graphics to show how slicing works what not. You don't see these things in R teaching materials.

I'm sure that for the implementation of algorithms, things might be easier with zero indexing, but for a user asking for element 4,5 and 6, 1-indexing is much, much easier on the user.

[stabbles]

In C++ you typically access arrays with unsigned integers (size_t), and a common pitfall is:

    for (size_t i = v.size() - 1; i >= 0; --i) {
      std::cout << i << ": " << v[i] << std::endl;

To fix the infinite loop you could write:

    for (size_t i = v.size(); i > 0; --i) {
      std::cout << i - 1 << ": " << v[i - 1] << std::endl;

Neither is great. Switching to signed integers might make your compiler throw warnings at you.

However, 1-based indexing does not work out well with modular arithmetic:

    # 1 based
    v[1 + (i - 1) % v.size()]

    # 0 based
    v[i % v.size()]

There's pros and cons with both schemes.

[ddragon]

Yes, and in both cases the language should provide tools so you don't have to deal directly with those edge cases. For example in Julia, for modular arithmetic with 1-based indexing there is mod1 [1], and for iterating in Julia you should use eachindex which will always work for both 0 or 1 indexed arrays.

[1] https://docs.julialang.org/en/v1/base/math/#Base.mod1

[2] https://docs.julialang.org/en/v1/base/arrays/index.html#Base...

[goto11]

I'm not really convinced by Dijkstras paper. He is basically saying indexing from zero is more natural because if you have an array of natural numbers including zero, then the range of numbers [0..n] is denoted by the index [0..n] which is logical. With 1-indexing you have have to write [1..n+1] to get the values [0..n] which is weird and ugly. Sure, but this assumes that the array in question is starting with 0 in the first place! The whole argument is begging the question.