WHY 1-BASED INDEXING IS *OK*.

Some programmers markedly object to the presence of 1-based array indexing in programming languages. This happens every time a new language appears which uses it, the latest being Julia. But why? One of the arguments is because 0-based indexing is more natural. Really? Ever start counting anything at 0? How many eggs are in an egg carton – ahhh 12? But when I take out the first, is it egg number 0?

Starting array indexing at 1 is natural for counting. So an array with 100 elements will be indexed from 1 to 100, not 0 to 99. Zero-based indexing is more of an artifact of C than anything else. Languages like C and C++ use pointers to store data, so it makes more sense to have their indices start at zero. Finding an array element in contiguous memory is then easy.

Element address = address of array + index × (size of type)

Arrays basically simulate matrices and vectors in mathematics, which used 1-based indices before the computer era, and still do in many cases. Both Fortran and Matlab use 1-based indexing, as do most matrices and vectors. Pascal and Ada allow for indexing to be generic. You want array indexing from -7 to 7… no problem – maybe generic indexing is the best approach? Some types of array manipulation are easier using zero-based indexing, and in certain circumstances zero-based indexing produces cleaner code. Some of the reason why many people like 0-based indexing is the same reason they get nauseous looking at a Cobol program – they are use to programming predominantly in C-like languages, where 0-based indexing is the norm.

Dijkstra in his article “Why numbering should start at zero“, argues 0 ≤ i < N is a “nicer” range than 1 ≤ i < N+1 and doesn’t really care for 1 ≤ i ≤ N. This really doesn’t make much sense – there are no aesthetic qualities associated with conditional statements. Guido van Rossum gives a rationale for why Python uses 0-based indexing, which boils down to being “swayed by the elegance of half-open intervals“. He does make a good point that splitting a string into three components using a[:i], a[i:j], and a[j:] is nice. But one also has to like the fact that i:j implies from i to <j.

Sure, for veteran programmers, 0-based indexing is no big issue, but for novice programmers, 0-based indexing is a huge usability issue. An array has 10 elements, but the 1st is actually the 0th, and the 10th is actually the 9th. Mathematically-focused languages like Matlab, Fortran, and Julia are okay having 1-based indexing. To each their own. Look some people like 0-based indexing and others like 1-based. There may be no right answer… and maybe that little bit of extra brain work in 1-based languages isn’t such a bad thing.

Comment I selected:
This must figure inside of any computer science class as “first paradigm” to understand as tool for programming tasks.

Personally I started to program in Basic, Fortran, Pascal, and after 10 years later in Gauss, Matlab, Maple, Mathematica, Python and now Cuda. For ending today (after a natural fixed point in Matlab because its readability and easy of coding mathematics) with Julia and Cuda Fortran as the most elegant ways foe expressing the scientific programming (i.e. 1-based indexing for CPU and GPU coding).

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