Is 12 O'clock Noon AM or PM?
When specifying clock times it is impractical to try and interpret the meanings of AM and PM in their literal senses (i.e., "Ante Meridiem" and "Post Meridiem," respectively), because the meridian is defined in terms of a particular observer. Therefore local noon seldom (if ever) occurs exactly at "clock-time" noon (i.e., twelve o'clock). So if one were to interpret the meaninings of AM and PM literally, then the exact time at which "AM becomes PM" would not be at 12 o'clock, but would instead occur at different times for observers at different locations. Instead we should interpret AM as simply being a reference to the first half of the day, and PM as being a reference to the second half of the day.
Therefore, 12:00 noon is actually 12:00 AM, because 12:00 AM means that 12 hours of time have elapsed since the start of the first half of the day (i.e., since midnight). (To refer to noon as being 12:00 PM would be tantamount to making the clearly absurd claim that noon occurs 12 hours later than noon!)
(No, 12:01 in the afternoon is not PM either. It doesn't become PM until one o'clock.)
Still, there remains a nagging compulsion in the back of your mind. You're probably thinking: "If it's even as little as a fraction of a second into the afternoon, then it's just somehow got to be PM. After all, PM refers to the afternoon, doesn't it? So why can't we legitimately use PM?"
The answer is: We can! (But if we do, then we can no longer refer to the time as being 12 o'clock.) As we have already indicated, whenever we express a time in terms of PM hours, we are specifying (or counting) the number of hours (and minutes and seconds) that have elapsed since noon. So if we want to express noon itself as a PM time then all we have to do is count the number of hours between noon and itself. Therefore:
And of course, by identical reasoning:
What? You say that your clock doesn't have a zero on it? Well, that's easy enough to fix. Just scrape off the twelve (which never should have been put there in the first place) and paste on a zero instead! After all, who in their right mind would ever want to suggest that we should begin counting things (such as the hours of a new day) by starting with -- twelve!
(When I presented this information on one of my radio shows several years ago, a listener came down to the station the next day and presented me with just such a clock on which he had carefully replaced the twelve with a zero! That clock is still mounted on the wall in the lobby at KSCO.)