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I was wondering if the 1-based arrays (and option to change index base) would factor into this. > OffsetArrays in particular proved to be a strong source of co

I was wondering if the 1-based arrays (and option to change index base) would factor into this. > OffsetArrays in particular proved to be a strong source of correctness bugs. The package provides an array type that leverages Julia’s flexible custom indices feature to create arrays whose indices don’t have to start at zero or one. Array indexing is such a core thing and I don't understand why anything mathematical or scientific would start with 1.

sdfhdhjdw3 5y ago
> Array indexing is such a core thing and I don't understand why anything mathematical or scientific would start with 1. Because that's how maths work? Literally everywhere in maths you count from 1, except in software engineering. That's why. I hope that clarified your confusion.
- planede 5y ago
  My hot take is that 1-based indexing is often a mistake in math too. It's also not universal, even within math. And linear algebra doesn't need 1-based indexing either, and some operations are even more easily expressed with 0-based indexing.
- wnoise 5y ago
  Starting with 0 is quite common in series, e.g. Taylor, Fourier, Chebyshev expansions, etc.
  - sdfhdhjdw3 5y ago
    No... in those cases you're starting with 0 because that's the lowest exponent of a polynomial.
    - wnoise 5y ago
      You're saying no while explaining my reasoning. What index to start with only strongly matters when the indexes have semantics. Otherwise you should just treat it as an opaque index, i.e. eachindex(), keys(), etc. In math when there are semantics, the indices usually include 0. When not (vector components, matrix indices, etc), they usually (but not uniformly) don't. The one nice side-benefit of Julia's mistake in adopting 1-based indexing is that it provided an extra impetus to build machinery to handle arbitrary indexing, though too much code still doesn't work correctly, and code still gets written to only handle 1-based arrays.
      - CRConrad 4y ago
        > What index to start with only strongly matters when the indexes have semantics. Which in everyday computing (as opposed to mathematics) they often do, and those cases are (most?) often, in human terms, much more natural to start from 1: "I have an array of N elements. The first of a bunch of things is thing number one, and the last of N things is thing number N." Hence: N_things: Array[1-N] of Thing; for i := 1 to N do begin Whatever := Whatever + Whateverize(N_things[i]); end; // for i := 1 to N... Yeah, that's how old I am: That's Pascal. (With some declarations skipped, and I may have misremembered some syntax.) The canonical example is of course the original Wirth-style max-255-ASCII-characters fixed-length[1] String type: In a string of length N, the nth character is at position n in the string. Character number N is the last one. > The one nice side-benefit of Julia's mistake in adopting 1-based indexing is that it provided an extra impetus to build machinery to handle arbitrary indexing 1) Arguably, as per the above, not a mistake. 2) Muahaha, "build machinery"? No need to build anything new; that's already existed since the early 70s. (Yeah, that's how old I am: Not adding 19 in front. There was only one "the seventies".) It's not like starting at 1 was mandatory; you could well declare My_fifty_things: Array[19-68] of Thing; And then "for i := 19 to 68 do ..." whatever with it, if those specific numbers happened to be somehow essential to your code. (At least in Turbo, but AFAICR also in original Wirth Pascal. Though probably with the max-255-ASCII-elements limitation in Wirth, and possibly also in Turbo up to v. 2 or 3 or so.) __ [1]: Though from at least Turbo Pascal 3 (probably earlier; also think I saw it on some minicomputer implementation) with the backdoor of changing the length by directly manipulating -- surprise, surprise, it exists! String was a built-in type with its own implementation -- the length bit at index [0]. Better start out with your string declared as length 255, though, so you don't accidentally try to grow it beyond what's allocated.
        wnoise 4y ago
        > often, in human terms, much more natural to start from 1 This meaning of natural is highly cultural dependent. It took the Greeks a startlingly long time to accept that one was a number (because it's a singleton), much less zero. I do not e.g. want arrays that can't have length one, because they have to be containing a number of things. > No need to build anything new; Well, no, not "new". Arrays with arbitrary bounds is a well-trod path. But they still had to make it work in Julia: CartesianIndices, LinearIndices, and overloading of "begin", and "end" keywords, etc. And the radical dependence on multimethod dispatch meant they couldn't quite just reuse existing work from other languages.
davisoneee 5y ago
I'll start by saying that I greatly prefer 0-based, and have used but 0- and 1-based indexing, but the choice is largely arbitrary. 0 makes sense as the '0-th offset' when thinking from a pointer perspective, but I often find when teaching, that 1-based comes more naturally for many students (the 'first' item). You mention mathematical or scientific work...but I often/mainly see enumerations (such as weights x_1, x_2, ... x_n or SUM 1 to N) start with 1, so for these 1-based can be a more natural/direct translation of mathematical notation to code.
- jjgreen 5y ago
  Not for polynomial coefficient indices :-)
  - xscott 5y ago
    Or Fourier coefficients :-) Or pretty much anything where the index/subscript is related to the math itself. Math textbooks and papers tend to use 1-based subscripts when it doesn't matter. It's hard to come up with examples where starting at 1 facilitates the actual math.
  - MzxgckZtNqX5i 5y ago
    Just for consistency: a_n is the coefficient of x^n, so the constant term ends up being a_0. Based on my experience, numbering starts from one (like (x_1, x_2, x_3) as point of R^3) and off-sets from zero, e.g., when dealing with discrete time, t_0 is the first.
- rocqua 5y ago
  My experience is that 0-based offsets (and use of < or even != for upper bounds) mean that I should almost never have to write something like idx - 1 or idx + 1. I came to 0-based offsets later in my career, having started with Matlab. So I have some real experience with 1-based offsets. Experience that was 'untainted' by being used to a different option. I much prefer 0-based. Especially because I now sort-off have a linter rule in my head 'if I am writing i - 1 then I am making a mistake or doing something the wrong way'. Which has been quite successful.
temp8964 5y ago
> Array indexing is such a core thing and I don't understand why anything mathematical or scientific would start with 1. From data analytic point of view, indexing should start with 1. When we analyze a data table, we always call the first row as the 1st row, or row #1, not row #0. It will be very strange to label rows as 0, 1, 2, 3, .... It may be fine for people with Computer Science background. But it would create so much confusion for almost everyone else...
- throwawaymaths 5y ago
  It causes problems for people with a CS background too. I once numbered machines in racks with zero-indexing (so that they could match up with zero-indexed ip addresses). Even though literally everyone who touched those machines had CS background: DO NOT DO THIS.
  - dekhn 5y ago
    It just amuses me that one of the big differences between the US and EU is which floor is "first" and which one is "zero" or "minus one".
    - FabHK 5y ago
      Yes. A German friend of mine moved into her student dormitory in the US, and when she was told that her room was on the first floor, asked whether there was a lift, because she had a heavy suitcase... Having said that, given that there are basements (in Europe, at least), it makes sense to call the ground floor 0. We are dealing with integers here, not natural numbers.
      - CRConrad 4y ago
        But floors of multi-storey buildings are a pretty unique exception in the real world in having a characteristic where zero -- the number of stairs you need to climb from the ground floor -- has an actual tangible meaning (on the ground floor). How many other such examples can you (editorial you; anyone) come up with? Not many, I'd bet.
hprotagonist 5y ago
> Array indexing is such a core thing and I don't understand why anything mathematical or scientific would start with 1. So, no FORTRAN, huh?
coldtea 5y ago
>Array indexing is such a core thing and I don't understand why anything mathematical or scientific would start with 1. Because starting with 0 is neither math nor array indexing in general. It's just how the base addresss of an array pointer memory block was referenced in C (and it spread from there). Which is why all math focused languages use 1-based (fortran, apl, matlab, r, mathematica, etc.)
- _vdpp 5y ago
  It makes iteration less error-prone too when the index of the last element is equal to the length of the array. In C it’s pretty easy to iterate past the end of an array if you use <= by mistake in a for loop, or forget a “length - 1” somewhere.
- SeanLuke 5y ago
  > C (and it spread from there). BCPL.
- Rayhem 5y ago
  > Because starting with 0 is neither math nor array indexing in general. It very, very much is. Polynomials all start at a zero "index", as does just about every expansion I can think of (Fourier, Bessel, Legendre, Chebyshev, Spherical Harmonic, etc.) Combinatorics, too, make lots of use of zero indices and zero-sized sets. As for arrays, I'll leave it to Dijkstra[1] to explain why zero indexing is most natural. Zero indexing overwhelmingly makes the most sense in both math and computers because indexing is a different operation than counting. [1]: https://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html https://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/E...
  - coldtea 5y ago
    >It very, very much is. Polynomials all start at a zero "index" Notice how you had to put index in quotes. Because it's not an index, it's the degree of each polynomial term, which is a power.
    - 5y ago
lahvak 5y ago
As other posters noted, in mathematics both 0 based and 1 based indexing is used. When dealing with matrices and vectors (including data tables and data columns), there is a strong preference for 1 based indexing: first row, first column, first entry, etc. Most matrix and vector based algorithms in literature use 1 based indexing. Programming these in a language with 0 based indexing is a mess, and a common source or errors. When dealing with sequences, especially recursively defined ones, there is usually an initial value (indexed with 0) and then the n-th value is obtained by n applications of the recursive step, so 0 based indexing makes more sense, but in literature there is no fixed convention, and you can find examples with 0 based and with 1-based indexing. Another example of 0 based indexing in math are polynomials (and in extension, power series) where the index is the degree of the term, or in general any functional series where the 0-th term is the constant term. There are also negative indices.
CRConrad 4y ago
> Array indexing is such a core thing and I don't understand why anything mathematical or scientific would start with 1. Counting things is such a core thing to humans that when we have a bunch of N things we think of them as thing #1 to thing #N. We start counting from 1, not 0. Indexing from 0 in computing is adapting the human mind to the computer, purely for performance reasons that may have been relevant in the 50s or 60s but were beginning to be obsolete by the 70s. It was done so you could access elements of an array by the simplest possible calculation of your offset into heap memory. When your first element is stored at Starting_address, you need i for that first element to be = 0, just so you don't need to have the compiler add another constant term for each element to "Element is at Starting_address + i * sizeof(element)". Would have been trivial, even then (as Wirth showed) to add that constant term calculation to compilers, but it was done without in C because that eliminated one whole integer operation from each (set of?) array access(es). In stead, we got the mental gymnastics of for(i=0, i++, i<=N-1) {...} and its many variations (in stead of just for i := 1 to N...), which surely have caused orders of magnitude more headaches in off-by-one bugs over the years than it saved on performance.
DNF2 4y ago
There are good arguments for using either 0- or 1-based indices. As you should be aware, there are many languages on each side. While preferring one over the other is perfectly fine, I question the intellectual honesty of anyone claiming incredulity about opposite choice.

sdfhdhjdw3 5y ago

> Array indexing is such a core thing and I don't understand why anything mathematical or scientific would start with 1. Because that's how maths work? Literally everywhere in maths you count from 1, except in software engineering. That's why. I hope that clarified your confusion.

planede 5y ago
My hot take is that 1-based indexing is often a mistake in math too. It's also not universal, even within math. And linear algebra doesn't need 1-based indexing either, and some operations are even more easily expressed with 0-based indexing.
wnoise 5y ago
Starting with 0 is quite common in series, e.g. Taylor, Fourier, Chebyshev expansions, etc.
- sdfhdhjdw3 5y ago
  No... in those cases you're starting with 0 because that's the lowest exponent of a polynomial.
  - wnoise 5y ago
    You're saying no while explaining my reasoning. What index to start with only strongly matters when the indexes have semantics. Otherwise you should just treat it as an opaque index, i.e. eachindex(), keys(), etc. In math when there are semantics, the indices usually include 0. When not (vector components, matrix indices, etc), they usually (but not uniformly) don't. The one nice side-benefit of Julia's mistake in adopting 1-based indexing is that it provided an extra impetus to build machinery to handle arbitrary indexing, though too much code still doesn't work correctly, and code still gets written to only handle 1-based arrays.
    - CRConrad 4y ago
      > What index to start with only strongly matters when the indexes have semantics. Which in everyday computing (as opposed to mathematics) they often do, and those cases are (most?) often, in human terms, much more natural to start from 1: "I have an array of N elements. The first of a bunch of things is thing number one, and the last of N things is thing number N." Hence: N_things: Array[1-N] of Thing; for i := 1 to N do begin Whatever := Whatever + Whateverize(N_things[i]); end; // for i := 1 to N... Yeah, that's how old I am: That's Pascal. (With some declarations skipped, and I may have misremembered some syntax.) The canonical example is of course the original Wirth-style max-255-ASCII-characters fixed-length[1] String type: In a string of length N, the nth character is at position n in the string. Character number N is the last one. > The one nice side-benefit of Julia's mistake in adopting 1-based indexing is that it provided an extra impetus to build machinery to handle arbitrary indexing 1) Arguably, as per the above, not a mistake. 2) Muahaha, "build machinery"? No need to build anything new; that's already existed since the early 70s. (Yeah, that's how old I am: Not adding 19 in front. There was only one "the seventies".) It's not like starting at 1 was mandatory; you could well declare My_fifty_things: Array[19-68] of Thing; And then "for i := 19 to 68 do ..." whatever with it, if those specific numbers happened to be somehow essential to your code. (At least in Turbo, but AFAICR also in original Wirth Pascal. Though probably with the max-255-ASCII-elements limitation in Wirth, and possibly also in Turbo up to v. 2 or 3 or so.) __ [1]: Though from at least Turbo Pascal 3 (probably earlier; also think I saw it on some minicomputer implementation) with the backdoor of changing the length by directly manipulating -- surprise, surprise, it exists! String was a built-in type with its own implementation -- the length bit at index [0]. Better start out with your string declared as length 255, though, so you don't accidentally try to grow it beyond what's allocated.
      - wnoise 4y ago
        > often, in human terms, much more natural to start from 1 This meaning of natural is highly cultural dependent. It took the Greeks a startlingly long time to accept that one was a number (because it's a singleton), much less zero. I do not e.g. want arrays that can't have length one, because they have to be containing a number of things. > No need to build anything new; Well, no, not "new". Arrays with arbitrary bounds is a well-trod path. But they still had to make it work in Julia: CartesianIndices, LinearIndices, and overloading of "begin", and "end" keywords, etc. And the radical dependence on multimethod dispatch meant they couldn't quite just reuse existing work from other languages.

davisoneee 5y ago

I'll start by saying that I greatly prefer 0-based, and have used but 0- and 1-based indexing, but the choice is largely arbitrary. 0 makes sense as the '0-th offset' when thinking from a pointer perspective, but I often find when teaching, that 1-based comes more naturally for many students (the 'first' item). You mention mathematical or scientific work...but I often/mainly see enumerations (such as weights x_1, x_2, ... x_n or SUM 1 to N) start with 1, so for these 1-based can be a more natural/direct translation of mathematical notation to code.

jjgreen 5y ago
Not for polynomial coefficient indices :-)
- xscott 5y ago
  Or Fourier coefficients :-) Or pretty much anything where the index/subscript is related to the math itself. Math textbooks and papers tend to use 1-based subscripts when it doesn't matter. It's hard to come up with examples where starting at 1 facilitates the actual math.
- MzxgckZtNqX5i 5y ago
  Just for consistency: a_n is the coefficient of x^n, so the constant term ends up being a_0. Based on my experience, numbering starts from one (like (x_1, x_2, x_3) as point of R^3) and off-sets from zero, e.g., when dealing with discrete time, t_0 is the first.
rocqua 5y ago
My experience is that 0-based offsets (and use of < or even != for upper bounds) mean that I should almost never have to write something like idx - 1 or idx + 1. I came to 0-based offsets later in my career, having started with Matlab. So I have some real experience with 1-based offsets. Experience that was 'untainted' by being used to a different option. I much prefer 0-based. Especially because I now sort-off have a linter rule in my head 'if I am writing i - 1 then I am making a mistake or doing something the wrong way'. Which has been quite successful.

temp8964 5y ago

> Array indexing is such a core thing and I don't understand why anything mathematical or scientific would start with 1. From data analytic point of view, indexing should start with 1. When we analyze a data table, we always call the first row as the 1st row, or row #1, not row #0. It will be very strange to label rows as 0, 1, 2, 3, .... It may be fine for people with Computer Science background. But it would create so much confusion for almost everyone else...

throwawaymaths 5y ago
It causes problems for people with a CS background too. I once numbered machines in racks with zero-indexing (so that they could match up with zero-indexed ip addresses). Even though literally everyone who touched those machines had CS background: DO NOT DO THIS.
- dekhn 5y ago
  It just amuses me that one of the big differences between the US and EU is which floor is "first" and which one is "zero" or "minus one".
  - FabHK 5y ago
    Yes. A German friend of mine moved into her student dormitory in the US, and when she was told that her room was on the first floor, asked whether there was a lift, because she had a heavy suitcase... Having said that, given that there are basements (in Europe, at least), it makes sense to call the ground floor 0. We are dealing with integers here, not natural numbers.
    - CRConrad 4y ago
      But floors of multi-storey buildings are a pretty unique exception in the real world in having a characteristic where zero -- the number of stairs you need to climb from the ground floor -- has an actual tangible meaning (on the ground floor). How many other such examples can you (editorial you; anyone) come up with? Not many, I'd bet.

hprotagonist 5y ago

> Array indexing is such a core thing and I don't understand why anything mathematical or scientific would start with 1. So, no FORTRAN, huh?

coldtea 5y ago

>Array indexing is such a core thing and I don't understand why anything mathematical or scientific would start with 1. Because starting with 0 is neither math nor array indexing in general. It's just how the base addresss of an array pointer memory block was referenced in C (and it spread from there). Which is why all math focused languages use 1-based (fortran, apl, matlab, r, mathematica, etc.)

_vdpp 5y ago
It makes iteration less error-prone too when the index of the last element is equal to the length of the array. In C it’s pretty easy to iterate past the end of an array if you use <= by mistake in a for loop, or forget a “length - 1” somewhere.
SeanLuke 5y ago
> C (and it spread from there). BCPL.
Rayhem 5y ago
> Because starting with 0 is neither math nor array indexing in general. It very, very much is. Polynomials all start at a zero "index", as does just about every expansion I can think of (Fourier, Bessel, Legendre, Chebyshev, Spherical Harmonic, etc.) Combinatorics, too, make lots of use of zero indices and zero-sized sets. As for arrays, I'll leave it to Dijkstra[1] to explain why zero indexing is most natural. Zero indexing overwhelmingly makes the most sense in both math and computers because indexing is a different operation than counting. [1]: https://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html https://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/E...
- coldtea 5y ago
  >It very, very much is. Polynomials all start at a zero "index" Notice how you had to put index in quotes. Because it's not an index, it's the degree of each polynomial term, which is a power.
  - 5y ago

lahvak 5y ago

As other posters noted, in mathematics both 0 based and 1 based indexing is used. When dealing with matrices and vectors (including data tables and data columns), there is a strong preference for 1 based indexing: first row, first column, first entry, etc. Most matrix and vector based algorithms in literature use 1 based indexing. Programming these in a language with 0 based indexing is a mess, and a common source or errors. When dealing with sequences, especially recursively defined ones, there is usually an initial value (indexed with 0) and then the n-th value is obtained by n applications of the recursive step, so 0 based indexing makes more sense, but in literature there is no fixed convention, and you can find examples with 0 based and with 1-based indexing. Another example of 0 based indexing in math are polynomials (and in extension, power series) where the index is the degree of the term, or in general any functional series where the 0-th term is the constant term. There are also negative indices.

CRConrad 4y ago

> Array indexing is such a core thing and I don't understand why anything mathematical or scientific would start with 1. Counting things is such a core thing to humans that when we have a bunch of N things we think of them as thing #1 to thing #N. We start counting from 1, not 0. Indexing from 0 in computing is adapting the human mind to the computer, purely for performance reasons that may have been relevant in the 50s or 60s but were beginning to be obsolete by the 70s. It was done so you could access elements of an array by the simplest possible calculation of your offset into heap memory. When your first element is stored at Starting_address, you need i for that first element to be = 0, just so you don't need to have the compiler add another constant term for each element to "Element is at Starting_address + i * sizeof(element)". Would have been trivial, even then (as Wirth showed) to add that constant term calculation to compilers, but it was done without in C because that eliminated one whole integer operation from each (set of?) array access(es). In stead, we got the mental gymnastics of for(i=0, i++, i<=N-1) {...} and its many variations (in stead of just for i := 1 to N...), which surely have caused orders of magnitude more headaches in off-by-one bugs over the years than it saved on performance.

DNF2 4y ago

There are good arguments for using either 0- or 1-based indices. As you should be aware, there are many languages on each side. While preferring one over the other is perfectly fine, I question the intellectual honesty of anyone claiming incredulity about opposite choice.