Noon, midnight, AM, PM, what's the deal?

Hey, Matt:

Why are people still messing up AM and PM in terms of noon and midnight?

-- Anup, the net

So what are you saying--noon is AM? Noon is PM? Noon is neither. Noon is noon, midnight is midnight. There's no 12:00 PM or 12:00 AM. For a fraction of a second each day, there's only noon and midnight.

AM/PM's Just a Minimart to Me

An anonymous contributor submitted the following, re 12 a.m., 12 p.m., noon, and midnight:

You say noon is noon, and midnight is midnight. There's no 12:00 p.m. or 12:00 a.m. Well, noon is 12 a.m., "m" being meridian, but there certainly is a 12:00 a.m. and a 12:00 p.m., and they're both midnight. Twelve a.m. is 12 hours ante meridian, 12 hours before noon of the coming day. And midnight is also 12:00 p.m., 12 hours after noon of the day that is just coming to an end.

And as if that's not enough, consider this from "Timeless of San Diego":

As I understand it, what you're saying is that neither noon nor midnight exist in time at all. That if we use our Popiel Time-O-Matic to divide the seconds into ever smaller pieces trying to find that elusive point in time during which noon occurs, what we find in fact is that time is pointless, and noon never "occurs." We can only determine that it is 11:59 a.m. and some billionths or trillionths of a second before noon, or 12:00 p.m. and some billionths or trillionths of a second after noon. That time has length, but no breadth. In which case, the irritation of [the person who asked the question] with those who err in the AM/PM way, may have been pacified by you letting your readers know that 12:00 p.m. indicates any point in time after that timeless moment we call noon, the earliest moments of the beginning of the second half of your day.

Hmmm. Huh? Um, yeah. I'm not gonna argue.