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The revulsion a lot folks express at one based indexing is always bizarre to me. I write code in c, python and matlab. Switching between these is really not tha

by bob457 7y ago

The revulsion a lot folks express at one based indexing is always bizarre to me. I write code in c, python and matlab. Switching between these is really not that hard. The two indexing models just seem to be convenient/painful for different things. And yes, perhaps one based indexing introduces a class of bugs when you need to call into c. But zero based indexing has the same problem if you need to call into fortran, and calling fortran is really common for numerical code.

derriz 7y ago
I agree and I would have been a shrill critic of any 1-based indexing. Most of the classic linear algebra algorithms seem to be described using 1-based indexing and the last time I needed to use one of these algorithms, I stubbornly tried to translate everything into zero-based indexing which was more difficult than you'd imagine and it was difficult to have confidence that I had correctly captured the algorithm. I switched to using a 1-based matrix implementation and everything became trivial. It's not that hard to switch between looping from 0 to n (exclusive) and looping from 1 to n (inclusive).
maxdamantus 7y ago
The issue is whether you want to cater to established conventions (both in mathematics where 1-based indexing is typical, but non-mathematicians will also similarly use 1-based counting), or you want to cater to what is most logical. I suspect the main reason 1-based seems convenient for some things is because of convention. Note that 0 wasn't even really used in mathematics until hundreds of years after our system of counting years was created. Since our year counting is 1-based, we end up with odd things like "2019" being the "19th year" of the "21st century" as opposed to "2018" being "year 18" of "century 20". I suspect it's also fairly unintuitive that the current century began in the year "2001" rather than "2000".
- oconnor663 7y ago
  > as opposed to "2018" being "year 18" of "century 20" Wow that's the best argument in favor of 0-based counting I've ever heard :)
- pjmlp 7y ago
  Had Pascal/Modula-2/Ada won over C and we wouldn't be even discussing this.
jhbadger 7y ago
Pretty much all languages designed for mathematics use 1-based indexing. Mathematica, R, Matlab, Fortran, etc. Either people have to think that the designers of these languages all made a mistake, or realize that it makes much more sense for mathematical computing to follow mathematical standards.
- maxdamantus 7y ago
  Is it possible that mathematics got it slightly wrong? The whole concept of 0 is relatively recent. Plenty of mathematics comes from before its inclusion, so presumably the idea of maintaining convention was there for successive mathematicians too.
  - ddragon 7y ago
    It's not about right or wrong, it's just that they work for different things but programming languages unlike math or human languages have to pick only one as default. 1-index is good for counting, if I want the first element up to the 6th element, then I pick 1:6 which is more natural than 0:5 (from the 0th to the 5th). 0-index is good for offset, for example I'm born on the first year of my life, but I wasn't born as a 1 year old, but as a "0 year old". And since pointer arithmetic is based on offset, it wouldn't make sense for C to use anything other than 0-index. But mathematical languages aren't focusing on mapping the hardware in any way, but to map the mathematics which already uses 1-index for vector/matrix indexing. You can see the relation of languages in [1]. If you want to write generic code for arrays in Julia, you shouldn't use direct indexing anyway, but iterators [2] which allows you to use arrays with any offset you want according to your problem, and for stuff that is tricky to do with 1-indexing like circular buffer the base library already provides solutions (such as mod1()). [1] https://en.wikipedia.org/wiki/Comparison_of_programming_languages_(array)#Array_system_cross-reference_list https://en.wikipedia.org/wiki/Comparison_of_programming_lang... [2] https://julialang.org/blog/2016/02/iteration https://julialang.org/blog/2016/02/iteration
    - maxdamantus 7y ago
      > 1:6 which is more natural than 0:5 (from the 0th to the 5th) This is again just begging the question. When you want to refer to the initial element as the "1st", it is due to the established convention of starting to count from 1. The point is that the reasonining for starting from 1 might only be that: conventional, not based on some inherent logic.
pjmlp 7y ago
A side effect of C winning over the alternatives, which either were 1 based, or had the option to specify it

by bob457 7y ago

derriz 7y ago

I agree and I would have been a shrill critic of any 1-based indexing. Most of the classic linear algebra algorithms seem to be described using 1-based indexing and the last time I needed to use one of these algorithms, I stubbornly tried to translate everything into zero-based indexing which was more difficult than you'd imagine and it was difficult to have confidence that I had correctly captured the algorithm. I switched to using a 1-based matrix implementation and everything became trivial. It's not that hard to switch between looping from 0 to n (exclusive) and looping from 1 to n (inclusive).

maxdamantus 7y ago

The issue is whether you want to cater to established conventions (both in mathematics where 1-based indexing is typical, but non-mathematicians will also similarly use 1-based counting), or you want to cater to what is most logical. I suspect the main reason 1-based seems convenient for some things is because of convention. Note that 0 wasn't even really used in mathematics until hundreds of years after our system of counting years was created. Since our year counting is 1-based, we end up with odd things like "2019" being the "19th year" of the "21st century" as opposed to "2018" being "year 18" of "century 20". I suspect it's also fairly unintuitive that the current century began in the year "2001" rather than "2000".

oconnor663 7y ago
> as opposed to "2018" being "year 18" of "century 20" Wow that's the best argument in favor of 0-based counting I've ever heard :)
pjmlp 7y ago
Had Pascal/Modula-2/Ada won over C and we wouldn't be even discussing this.

jhbadger 7y ago

Pretty much all languages designed for mathematics use 1-based indexing. Mathematica, R, Matlab, Fortran, etc. Either people have to think that the designers of these languages all made a mistake, or realize that it makes much more sense for mathematical computing to follow mathematical standards.

maxdamantus 7y ago
Is it possible that mathematics got it slightly wrong? The whole concept of 0 is relatively recent. Plenty of mathematics comes from before its inclusion, so presumably the idea of maintaining convention was there for successive mathematicians too.
- ddragon 7y ago
  It's not about right or wrong, it's just that they work for different things but programming languages unlike math or human languages have to pick only one as default. 1-index is good for counting, if I want the first element up to the 6th element, then I pick 1:6 which is more natural than 0:5 (from the 0th to the 5th). 0-index is good for offset, for example I'm born on the first year of my life, but I wasn't born as a 1 year old, but as a "0 year old". And since pointer arithmetic is based on offset, it wouldn't make sense for C to use anything other than 0-index. But mathematical languages aren't focusing on mapping the hardware in any way, but to map the mathematics which already uses 1-index for vector/matrix indexing. You can see the relation of languages in [1]. If you want to write generic code for arrays in Julia, you shouldn't use direct indexing anyway, but iterators [2] which allows you to use arrays with any offset you want according to your problem, and for stuff that is tricky to do with 1-indexing like circular buffer the base library already provides solutions (such as mod1()). [1] https://en.wikipedia.org/wiki/Comparison_of_programming_languages_(array)#Array_system_cross-reference_list https://en.wikipedia.org/wiki/Comparison_of_programming_lang... [2] https://julialang.org/blog/2016/02/iteration https://julialang.org/blog/2016/02/iteration
  - maxdamantus 7y ago
    > 1:6 which is more natural than 0:5 (from the 0th to the 5th) This is again just begging the question. When you want to refer to the initial element as the "1st", it is due to the established convention of starting to count from 1. The point is that the reasonining for starting from 1 might only be that: conventional, not based on some inherent logic.

pjmlp 7y ago

A side effect of C winning over the alternatives, which either were 1 based, or had the option to specify it