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> an argument always has to be from aesthetics, which can include simplicity and "uglyness", but these aren't totally individual (you can get 99/100 people to a

> an argument always has to be from aesthetics, which can include simplicity and "uglyness", but these aren't totally individual (you can get 99/100 people to agree on which of two schemes is "simpler"). Putting aside the implicit claim that something as subjective as aesthetics will be agreeable by 99% of the population...is 0-based indexing simpler? Why? Your next example is...a little all over the place mathematically, if I’m being honest. I’m having trouble following it. But let me try... So you’re saying I have a 1-dimensional, ordered set S, whose elements are real numbers. It can’t be an interval, because S needs to be discrete for this to be possible computationally or even theoretically (S is uncountable if its continuous, and thus cannot be indexed). It needs to have an order to have a sense of position in the first place, so map S to the natural numbers in whatever way you choose. Now choose an element s in S. You want me to pick the first n elements from s that are “next”, for whatever your order relation is. We’ll call that relation <. In that case I would respond by saying, “Let s be an element of S, and choose an n-tuple N of elements (x_1, x_2, x_3, x_4, x_5, x_6) in *S* such that s < x_1 < x_2 < x_3 < x_4 < x_5 < x_6, and there exists no element k of S such that k in S, s < k < x_6, k not in N. Haven’t I accomplished your exercise just fine without using 0 indexing? If I were programming this, I could index the n-tuple starting with x_0 or x_1. I don’t understand the issue - what are you trying to convey here? Personally, I’d program this by defining S to be my vector or list or whatever, k to be the index of s in S, then defining my n-tuple with: N = [] for (i = 1, i <= n, i++): N.append(S[k + i]) I feel as though you only believe your example is compelling because you’re overlapping the origin with the initial index. But when you abstract your problem to the general case (as I did), then it doesn’t really seem to matter much. Your example is actually kind of a narrow edge case.

zimablue 8y ago
Hey, thanks for trying to reply substantively. You haven't understood what I was saying, which is fair enough because I didn't present it very clearly probably. The line where you start talking about something else is this: "So you’re saying I have a 1-dimensional, ordered set S, whose elements are real numbers". No, I'm not saying that. Firstly to define the question as Djikstra does: we're arging about, if I have a list L, and I write into my computer L[a, b], which elements of L are returned? My argument is kind of a physical metaphor, take the real number line as a physical axis (like you're doing physics), and take a load of toy trucks that each have length of 1 (I guess you choose your coordinate system to make the length 1) and put them down end to end. If I was a physicist, and I asked you to pick up 3 trucks starting at 0, and I was using real numbers and a vector I'd say it like this, pick up the trucks in the range [0, 3) on my axis. Now if you choose 0 indexing + (closed, open) for your slicing, then a (python) programmer would say to another programmer, take the slice [0:3] to get the 3 trucks. So the slice numbers correspond perfectly to the vector description of the space that the items occupy. That's why in this slicing system taking L[a, b] then b-a = the number of items you get. Because it's matched perfectly with a real-number vector description of the space the items occupy on a real number line. All the other advantages like (I can describe an empty interval: [0:0]), I can describe taking the last element and it feels right [-1: 0] follow from this physical-space homomorphism. That last one: in a circular (modular?) space, walk left 1 and then come back right 1 and pick up the element you pass over. In 1-based: [0: 1] = the last element? I don't know if any languages do this but either you can't and that's sad or you can and it is incredibly counterintuitive.

zimablue 8y ago

Hey, thanks for trying to reply substantively. You haven't understood what I was saying, which is fair enough because I didn't present it very clearly probably. The line where you start talking about something else is this: "So you’re saying I have a 1-dimensional, ordered set S, whose elements are real numbers". No, I'm not saying that. Firstly to define the question as Djikstra does: we're arging about, if I have a list L, and I write into my computer L[a, b], which elements of L are returned? My argument is kind of a physical metaphor, take the real number line as a physical axis (like you're doing physics), and take a load of toy trucks that each have length of 1 (I guess you choose your coordinate system to make the length 1) and put them down end to end. If I was a physicist, and I asked you to pick up 3 trucks starting at 0, and I was using real numbers and a vector I'd say it like this, pick up the trucks in the range [0, 3) on my axis. Now if you choose 0 indexing + (closed, open) for your slicing, then a (python) programmer would say to another programmer, take the slice [0:3] to get the 3 trucks. So the slice numbers correspond perfectly to the vector description of the space that the items occupy. That's why in this slicing system taking L[a, b] then b-a = the number of items you get. Because it's matched perfectly with a real-number vector description of the space the items occupy on a real number line. All the other advantages like (I can describe an empty interval: [0:0]), I can describe taking the last element and it feels right [-1: 0] follow from this physical-space homomorphism. That last one: in a circular (modular?) space, walk left 1 and then come back right 1 and pick up the element you pass over. In 1-based: [0: 1] = the last element? I don't know if any languages do this but either you can't and that's sad or you can and it is incredibly counterintuitive.