In time and angular measurement, the prime notation ′ is minutes, and the double prime ″ is the second
An hour is h
Indeed, in my pre-caffeinated state I had this post in mind...
Without question.
I very strongly suspect the person you were conversing with didn't spot that you said hours and minutes instead of minutes and seconds.
I very strongly suspect the person she is conversing with is a sock on her hand. You are correct in that the question is being asked of this purported expert in a way that seems to perpetuate ongoing ambiguity. The question is whether,
by any established convention, ″ can mean either minutes or seconds depending on context. It is not whether any person once used ″ to mean seconds.
But the...
...which explains why º always refers to the basic division of a physically-derived extent. A day—as an extent of time—is defined by a physical phenomenon (the time take by Earth to rotate once) just as the extent of temperature is defined as the liquid phase of water, and the extent of rotation is defined by the physical circle. This is why º
must mean degrees of arc or degrees of temperature and why º once
had to mean hours (allegedly in medical practice). The subsequent divisions notated with ′, ″, ‴, ⁗, etc. do not "shift" according to context in these systems. Vixen admits that this is true for lengths and angles, but simply invents her own head-canon for why we should allow this for time. It's pure, face-saving nonsense. You can read that whole 11-page thread to see just how desperate and nonsensical her arguments became.
h is the SI abbreviation for hours.
min is the SI abbreviation for minutes.
s is the abbreviation for seconds. But of these only seconds is strictly canonical. Inasmuch as SI abhors non-decimal multiples of basic units, the customary sub-day multiples are tolerated depending on the implied precision. But, for example, we still reckon rocket engine firing times strictly only in seconds (and their decimalizations) in official documents.
One hill I propose incidentally to die on is the use of spacing. NIST mandates a space between the numeral and its units. I am forever seeing lengths rendered as
10mm instead of
10 mm. Consequently, durations should be rendered such as,
4 min 33 s, or
15 h 21 min 44 s if you're listening to Wagner. But alas we too often will see
4h to indicate four hours.
The common colon notation for time (nn:nn) is used despite sometimes being ambiguous without context. 1:54 as the runtime of a movie is just under two hours, while 1:54 as the length of a song is just under two minutes.
I've hypothesized that Vixen is recalling the potential ambiguity of colon-delimited time being pointed out in a class, and misremembering it as being taught that there were multiple interpretations of prime and double-prime.
Without commenting on the hypothesis, I'll point out that this is why colon notation for time duration is almost completely disallowed in scientific writing for just this reason. However, there is an international standard for notating date and time (ISO-8601) that allows the time portion to be notated with a colon as in
hh:mm:ss. In appropriate cases the seconds portion may be omitted, in which it's understood that
dd:dd means hours and minutes, never minutes and seconds.
Those are for calendrical time
points. To complicate matters immensely, ISO-8601 specifies a notation for calendrical time
durations that is entirely incompatible with SI. These are more useful to commerce than to science.