Whereas 0 based indexing is based on convention from other languages where it arguably made more sense because it was just a convenience over pointer arithmetic. What reason other than convention is there for 0 based array indexing in any any language where an array isn't just a memory location and the index a calculation of type-size times index bytes?
Which is a valid argument for numbering starting at zero, but not just for programming languages, but in general and including human spoken languages. The common counter-argument is "People don't generally think that way unless trained to do so". Like many things in life, often convention and momentum often trump reasoned argument.
In general, much of what's chosen for language design is influenced to some degree by convention. This is a valid design choice, because you're maximizing use of existing domain knowledge of your audience.
In this specific case, I would argue that since in many languages where an array isn't a small shim over memory management (Ruby, Python, Perl, JS, etc) where easing user friendliness is at a premium over performance, 1 based array indexing would make better sense... if most people adopting those languages weren't already fairly well acquainted with 0 based indexing from CS programs or exposure to other languages (and it wasn't a simple concept to understand). Since many new users are familiar with it, and it is easy to understand, it's simple to just go with what some percentage of people already know, so convention wins out.
Maybe this is a stupid idea, but at this point the economy is tied to 0-based indexing so much, that I would rather get math moved to 0-based indexing, than computing to 1-based indexing.
Being able to easily port code between languages (and math articles) is important, when there's no clear winner, I like consistency.
Good luck with that. The 0-based indexing is non-existent outside of programming. No one who doesn't do pointer arithmetic would come up with it.
In mathematics 1...N is a perfectly good notation. Julia expresses the same idea with 1:N. This is consistent with spoken language (1 denotes the 1st element). Consistency, if anything, would not come down in favor of the software engineering choice here.
A lot of new very important papers in i.e. machine learning, quantitative finance come _after_ being implemented in computer code. I just looked at some, and they already seem to use 0 index for the initial states / base layer... here's just one example, where 0 and 1 based indexing is mixed, but I see it everywhere:
