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0 pointsmruts6y ago0 comments

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.

0 comments

kbd6y 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).

iamed26y 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.

eigenspace6y 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.

4 more replies

goto116y 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!

kbd6y 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).

1 more reply

jpeloquin6y ago

> 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.

mrutsOP6y ago

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.

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