Priority is tricky to nail down e.g. the EDSAC was operational a year before the Mark 1 (which actually was not operational until 1949). Because of the "B" Williams Tube which held the two index registers of the Mark 1, many other manufacturers -- e.g. Burroughs -- later called their index registers "B registers". (Also, I think the Univac I and II were successful commercially, and earlier than the 704.)

I started programming in earnest and for money in 1961 mostly in machine code on a variety of machines, and I'm pretty sure that the notions of single dimensional sequential locations of memory as structures (most often called arrays, but sometimes called lists), predated the idea of index registers. This is because I distinctly remember being first taught how to move through arrays sequentially just by direct address modification -- this was called indexing in the Air Force -- and later being introduced to the index register or registers -- depending on the machine.

My strong guess (from above) is that the array as sequential memory accessed by address modification of some kind was a primary idea in the very first useful computers in the late 40s, and that this idea pre-dated index registers.

It would be well worth your time to look at the instruction set of EDSAC, and try writing some programs.

The paper is about, among other things, the history of the array data structure. It's far too early to advertise, but you can see a very early version on my GitHub account. :)

I was surprised to discover recently that the word 'array' prior to 1950 was used exclusively to describe two dimensional tables of numbers that one might find in a matrix or determinant. But by the advent of FORTRAN I in 1957 and ALGOL 58, 'array' now referred exclusively to a one-dimensional entity, as compared with 'n-dimensional arrays'. I was interested in digging through John Backus's papers from this era to see if I could find any clues.

I was able to narrow down the near window to 1952-1954, since the FORTRAN preliminary report of 1954 uses the word 'array' casually in the modern one-dimensional sense as interchangeable with 'subscripted variables', the latter being the more common terminology at the time. By comparison, a virtually unknown paper by Rutishauser in 1952 describing the "for" loop did not use the word 'array' at all, only 'subscripted variables'. (Rutishauser was an accomplished mathematician and quite possibly the world's first computational scientist.) A paper by Laning and Zierler at MIT in 1954 describing a formula compiler also used only the term 'subscripted variables'.

Backus's papers also have evidence showing that FORTRAN I was clearly written specifically to take advantage of the IBM 704's machine capabilities. Not only was the IBM 704 the world's first commercially successful computer, it was also an improvement over the preceding IBM 701 in providing index registers (3 of them) and floating point instructions which were fast for its era. Backus's papers describe how providing hardware support for indexing and floating point was revolutionary, as all programs up to that time had to write in all these instructions by hand (and for many programs was pretty much all they did).

So it is clear to me now that the changeover in the implied dimensionality of the word 'array' must be related to how the array developed as a data structure abstracting away indexing operations. By the time IAL (pre-ALGOL) came on the scene in 1958, the idea of indexable homogeneous containers was already well established. But I still haven't found any strong smoking gun evidence introducing the one-dimensional sense of the word. I suspect further digging into the description of the IBM 704 may be necessary. The 704 was not the first to provide index registers, but it may have been the first to call them as such. (The Manchester Mark I computer of 1948 appears to be the first computer with an index register, but it was called a B line. The [patent](https://www.google.com/patents/US3012724) claiming to cover index registers uses the term "control instruction" - no arrays mentioned - but it very cutely describes numbers as residing in known locations or "addresses" in quotes.)

Speed has a moral dimension: to be fast is to be in tune with the facts of the world as it truly is, as the Atman has provided, without illusion.

Speed has a social dimension: to make the user wait unnecessarily is to express disrespect, even contempt.

Speed has an architectural dimension: to be fast, the operations have to match the parts of the system and their relationships.

Speed has a spiritual dimension: to achieve speed demands that you humble yourself before the structures of the machine as it truly is, not some comfortable abstraction.