Vectors are zero based in Common Lisp; the 1960 Lisp 1 manual describes arrays; they are zero based.

Zero based is much more sane. If the array is regarded as being made up of larger groups of elements, say groups of 8, then ⌊index/8⌋ gives us the group and group x 8 gives us the base element of group. Not so if index is one-based.

Zero based multi-dimensional coordinates are easy to convert to a flat address. E.g. 3D case: just ABz + By + x.

Imagine distances were one based (so that either 1 m or 1 km means no displacement), and then trying to convert a given distance between m and km. Yikes!

Music intervals are one-based, to their great detriment. We end up with a "rule of nine" for interval inversion and that comes from the octave of the diatonic scale having seven notes!

One-based indexing is okay when the indices don't have a strong numeric meaning (beyond basic successor/predecessor relationships), or none at all (basically are symbolic and could be replaced by any set that can be enumerated by the natural numbers).

As soon as the index domain is involved in displacement calculations that feature multiplication and division, anything but zero based is disadvantaged.

I also have read Dijkstra, it doesn't mean I agree with everything he wrote.

In Algol based languages indexes are customizable, I don't remember ever writing array [0..9] of Integer instead of array [1..10] of Integer.

C, C++ and their descendants took over and I just had to adapt.

I haven’t, so far, encountered a single occasion in which I would need to manually flatten-deflatten indices: Julia has multidimensional arrays of any dimension N, and you can access their content in a linear fashion without any effort (simply provide one index instead of N)

Still, the implementation has to internally do ABC(z - 1) + AB(y - 1) + A(x - 1), compensating for the pointless bias at every dimension.

It's just a wanton complication, like insisting on Roman numerals instead of a radix enumeration.

Well, I’d say the analogy with Arabic vs Roman numerals is a bit of a stretch. Seriously, it is just a matter of shifting by one, humanity has much bigger problems to focus on!

The implementation already has to do lots of internal stuff to map high level language abstractions to actual real hardware capabilities, index calculations is just another one.