3 ms·

> 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 pro

by kbd 7y ago

> 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 7y ago
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 7y ago
  I’m constantly baffled by the way people hold that paper up as some sort of objective proof that 0 based indexing is superior.
  - kbd 7y ago
    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".
  - kazinator 7y ago
    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?
goto11 7y ago
> 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 7y ago
  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 7y ago
    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 7y ago
      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 https://news.ycombinator.com/item?id=20425500

by kbd 7y ago

iamed2 7y ago

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 7y ago
I’m constantly baffled by the way people hold that paper up as some sort of objective proof that 0 based indexing is superior.
- kbd 7y ago
  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".
- kazinator 7y ago
  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?

goto11 7y ago

> 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 7y ago
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 7y ago
  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 7y ago
    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 https://news.ycombinator.com/item?id=20425500