At least we're not stuck with the Roman "inclusive counting" system that included one extra number in ranges* so that e.g. weeks have "8" days and Sunday is two days before Monday since Monday is itself included in the count.
French (and likely other Latin languages?) are not quite so lucky. "En 8" means in a week, "une quinzaine" (from 15) means two weeks...
If we're on a Tuesday, and I say we're meeting Wednesday in eight, that Wednesday is indeed 8 days away.
Now I'm fascinated by this explanation, which covers the use of 15 as well. I'd always thought of it as an approximation for a half month, which is roughly 15 days, but also two weeks.
To partially answer the other Latin languages, Portuguese also uses "quinze dias" (fifteen days) to mean two weeks. But I don't think there is an equivalent of the "en huit". We'd use "na quarta-feira seguinte" which is equivalent to "le mercredi suivant".
Most beginners still start out thinking in one scale at a time (except perhaps Guitar, which sorta has its own system that's more efficient for playing basic rock). So thinking about music as having 7 notes over a base "tonic" note, plus some allowed modifications to those notes, is still a very useful model.
The problem is that these names percolated down to the intervals. It is silly that a "second" is an interval of length 1. One octave is an 8th, but two octaves is a 15th. Very annoying. However, it still makes sense to number them based on the scale, rather than half-steps: every scale contains one of every interval over the tonic, and you have a few choices, like "minor thirds vs. major thirds" (or what should be "minor seconds vs. major seconds"). It's a lot less obvious that you should* only include either a "fourth" (minor 3rd) or a "fifth" (major 3rd), but not both. I think we got here because we started by referring to notes by where they appear in the scale ("the third note"), and only later started thinking more in terms of intervals, and we wanted "a third over the tonic" to be the same as the third note in the scale. In this case it would have been nice if both started at zero, but that would have been amazing foresight from early music theorists.
* Of course you can do whatever you want -- if it sounds good, do it. But most of the point of these terms (and music theory in general) is communicating with other musicians. Musicians think in scales because not doing so generally just does not sound good. If your song uses a scale that includes both the minor and major third, that's an unusual choice, and unusual choices requiring unusual syntax is a good thing, as it highlights it to other musicians.
Yes, we are. C gives pointers one past the end of an array meaningful semantics. That's in the standard. You can compare them and operate on them but not de-reference them.
Amusingly, you're not allowed to go one off the end at the beginning of a C or C++ array. (Although Numerical Recipes in C did it to mimic FORTRAN indices.) So reverse iterators in C++ are not like forward iterators. They're off by 1.
[1] https://devblogs.microsoft.com/oldnewthing/20211112-00/?p=10...
Nelson Elhage wrote about an alternate interpretation: https://blog.nelhage.com/2015/08/indices-point-between-eleme...
first, second, twoth, third, fourth, ...
or shortened:
0st, 1nd, 2th, 3th, 4th ...
Where is the first item? Slot 0. How much space does one item take up* (ignoring administrative overheads)? The first and only item takes up 1 space.