I thought continuity provides an answer:
11:59:59.9999999999 is still AM.
12:00:00.0000000001 is clearly PM.
When should the AM switch to PM? My intuition says at the same time that the 11 switches to a 12 (and all the 9's switch to 0's). Thus, noon is pm.
Having said that, in reality the solution is banish the abominable 12 hour clock, and use the 24 hour clock.
That also removes the ambiguity whether "Midnight on January 1st 2017" means 2017-01-01 00:00 or 2017-01-01 24:00 == 2017-01-02 00:00.
I don't want to be offensive, but this is just another example where anglo-american standards for time and length measurements are ill-defined and lead to confusion. Instead, we have the SI system for the rest of the world and we have international standards for counting time -- with time going from 00:00:00 to 24:59:59 a day. I wonder why people refrain to adopt a working system in favour of culture. I never understood why culture and tradition is an argument for inexactness.
When the bells of Big Ben — or any chiming clock that rings out the hours of the day — chimes with one bell, we know that the first hour has just been completed. As one commenter observes, having it ring zero bells wouldn’t tell people what time it is. You can’t go from ringing eleven bells one hour to not ringing any bells at all an hour later to then ringing one bell the hour following the one in which you failed to ring any bells at all. People wouldn’t be able to tell what time it was because of something they didn’t hear!
Imagine this dialogue:
TOM: Oh good, it’s time for lunch! JERRY: Oh really, and how do you know that? TOM: Because it has to be noon, since I just now didn’t hear the clock!
You’ll probably never see a flight or a movie or something start right at 12:00; it’s just so much clearer at a glance to see that 11:55 AM/PM.
Fascinating. I've seen that at a lot of shops and places in Japan they go beyond the 24 hours – indicating continuity in a way.
For example of a shop is open in the pattern –
Monday, January 8th 21:00 till Tuesday, January 9th 02:00
The Japanese signboards will denote it as -
Open on Monday, 8th Jan 21:00-26:00
I think it's we quite convenient and let's the people know that the shop's time pattern sort of carries on from the previous day onto the next.
It's not confusing for us Europeans since we use 24 hour clocks. Midnight is 00. However I did not understand the reason the 24 hour clock caught on until now. TV schedules use 24 hour clocks to avoid this ambiguity.
The instant it becomes noon, it is no longer ante meridian (before noon). Thus we have to make an arbitrary allocation, and it makes a lot more sense to lump 12:00 with 12:01-12:59, rather than with 11:00-11:59.
This has always been a pet peeve of mine. Makes it really hard to answer simple questions like, how many hours pass between 11am and 12am?